cosmology history research paper

• Search Menu
• Browse content in Arts and Humanities
• Browse content in Archaeology
• Anglo-Saxon and Medieval Archaeology
• Archaeological Methodology and Techniques
• Archaeology by Region
• Archaeology of Religion
• Archaeology of Trade and Exchange
• Biblical Archaeology
• Contemporary and Public Archaeology
• Environmental Archaeology
• Historical Archaeology
• History and Theory of Archaeology
• Industrial Archaeology
• Landscape Archaeology
• Mortuary Archaeology
• Prehistoric Archaeology
• Underwater Archaeology
• Urban Archaeology
• Zooarchaeology
• Browse content in Architecture
• Architectural Structure and Design
• History of Architecture
• Residential and Domestic Buildings
• Theory of Architecture
• Browse content in Art
• Art Subjects and Themes
• History of Art
• Industrial and Commercial Art
• Theory of Art
• Biographical Studies
• Byzantine Studies
• Browse content in Classical Studies
• Classical History
• Classical Philosophy
• Classical Mythology
• Classical Literature
• Classical Reception
• Classical Art and Architecture
• Classical Oratory and Rhetoric
• Greek and Roman Epigraphy
• Greek and Roman Law
• Greek and Roman Archaeology
• Greek and Roman Papyrology
• Late Antiquity
• Religion in the Ancient World
• Digital Humanities
• Browse content in History
• Colonialism and Imperialism
• Diplomatic History
• Environmental History
• Genealogy, Heraldry, Names, and Honours
• Genocide and Ethnic Cleansing
• Historical Geography
• History by Period
• History of Agriculture
• History of Education
• History of Emotions
• History of Gender and Sexuality
• Industrial History
• Intellectual History
• International History
• Labour History
• Legal and Constitutional History
• Local and Family History
• Maritime History
• Military History
• National Liberation and Post-Colonialism
• Oral History
• Political History
• Public History
• Regional and National History
• Revolutions and Rebellions
• Slavery and Abolition of Slavery
• Social and Cultural History
• Theory, Methods, and Historiography
• Urban History
• World History
• Browse content in Language Teaching and Learning
• Language Learning (Specific Skills)
• Language Teaching Theory and Methods
• Browse content in Linguistics
• Applied Linguistics
• Cognitive Linguistics
• Computational Linguistics
• Forensic Linguistics
• Grammar, Syntax and Morphology
• Historical and Diachronic Linguistics
• History of English
• Language Acquisition
• Language Variation
• Language Families
• Language Evolution
• Language Reference
• Lexicography
• Linguistic Theories
• Linguistic Typology
• Linguistic Anthropology
• Phonetics and Phonology
• Psycholinguistics
• Sociolinguistics
• Translation and Interpretation
• Writing Systems
• Browse content in Literature
• Bibliography
• Children's Literature Studies
• Literary Studies (Asian)
• Literary Studies (European)
• Literary Studies (Eco-criticism)
• Literary Studies (Modernism)
• Literary Studies (Romanticism)
• Literary Studies (American)
• Literary Studies - World
• Literary Studies (1500 to 1800)
• Literary Studies (19th Century)
• Literary Studies (20th Century onwards)
• Literary Studies (African American Literature)
• Literary Studies (British and Irish)
• Literary Studies (Early and Medieval)
• Literary Studies (Fiction, Novelists, and Prose Writers)
• Literary Studies (Gender Studies)
• Literary Studies (Graphic Novels)
• Literary Studies (History of the Book)
• Literary Studies (Plays and Playwrights)
• Literary Studies (Poetry and Poets)
• Literary Studies (Postcolonial Literature)
• Literary Studies (Queer Studies)
• Literary Studies (Science Fiction)
• Literary Studies (Travel Literature)
• Literary Studies (War Literature)
• Literary Studies (Women's Writing)
• Literary Theory and Cultural Studies
• Mythology and Folklore
• Shakespeare Studies and Criticism
• Browse content in Media Studies
• Browse content in Music
• Applied Music
• Dance and Music
• Ethics in Music
• Ethnomusicology
• Gender and Sexuality in Music
• Medicine and Music
• Music Cultures
• Music and Religion
• Music and Culture
• Music and Media
• Music Education and Pedagogy
• Music Theory and Analysis
• Musical Scores, Lyrics, and Libretti
• Musical Structures, Styles, and Techniques
• Musicology and Music History
• Performance Practice and Studies
• Race and Ethnicity in Music
• Sound Studies
• Browse content in Performing Arts
• Browse content in Philosophy
• Aesthetics and Philosophy of Art
• Epistemology
• Feminist Philosophy
• History of Western Philosophy
• Metaphysics
• Moral Philosophy
• Non-Western Philosophy
• Philosophy of Science
• Philosophy of Action
• Philosophy of Law
• Philosophy of Religion
• Philosophy of Language
• Philosophy of Mind
• Philosophy of Perception
• Philosophy of Mathematics and Logic
• Practical Ethics
• Social and Political Philosophy
• Browse content in Religion
• Biblical Studies
• Christianity
• East Asian Religions
• History of Religion
• Judaism and Jewish Studies
• Qumran Studies
• Religion and Education
• Religion and Health
• Religion and Politics
• Religion and Science
• Religion and Law
• Religion and Art, Literature, and Music
• Religious Studies
• Browse content in Society and Culture
• Cookery, Food, and Drink
• Cultural Studies
• Customs and Traditions
• Ethical Issues and Debates
• Hobbies, Games, Arts and Crafts
• Lifestyle, Home, and Garden
• Natural world, Country Life, and Pets
• Popular Beliefs and Controversial Knowledge
• Sports and Outdoor Recreation
• Technology and Society
• Travel and Holiday
• Visual Culture
• Browse content in Law
• Arbitration
• Browse content in Company and Commercial Law
• Commercial Law
• Company Law
• Browse content in Comparative Law
• Systems of Law
• Competition Law
• Browse content in Constitutional and Administrative Law
• Government Powers
• Judicial Review
• Local Government Law
• Military and Defence Law
• Parliamentary and Legislative Practice
• Construction Law
• Contract Law
• Browse content in Criminal Law
• Criminal Procedure
• Criminal Evidence Law
• Sentencing and Punishment
• Employment and Labour Law
• Environment and Energy Law
• Browse content in Financial Law
• Banking Law
• Insolvency Law
• History of Law
• Human Rights and Immigration
• Intellectual Property Law
• Browse content in International Law
• Private International Law and Conflict of Laws
• Public International Law
• IT and Communications Law
• Jurisprudence and Philosophy of Law
• Law and Politics
• Law and Society
• Browse content in Legal System and Practice
• Courts and Procedure
• Legal Skills and Practice
• Primary Sources of Law
• Regulation of Legal Profession
• Medical and Healthcare Law
• Browse content in Policing
• Criminal Investigation and Detection
• Police and Security Services
• Police Procedure and Law
• Police Regional Planning
• Browse content in Property Law
• Personal Property Law
• Study and Revision
• Terrorism and National Security Law
• Browse content in Trusts Law
• Wills and Probate or Succession
• Browse content in Medicine and Health
• Browse content in Allied Health Professions
• Arts Therapies
• Clinical Science
• Dietetics and Nutrition
• Occupational Therapy
• Operating Department Practice
• Physiotherapy
• Radiography
• Speech and Language Therapy
• Browse content in Anaesthetics
• General Anaesthesia
• Neuroanaesthesia
• Browse content in Clinical Medicine
• Acute Medicine
• Cardiovascular Medicine
• Clinical Genetics
• Clinical Pharmacology and Therapeutics
• Dermatology
• Endocrinology and Diabetes
• Gastroenterology
• Genito-urinary Medicine
• Geriatric Medicine
• Infectious Diseases
• Medical Oncology
• Medical Toxicology
• Pain Medicine
• Palliative Medicine
• Rehabilitation Medicine
• Respiratory Medicine and Pulmonology
• Rheumatology
• Sleep Medicine
• Sports and Exercise Medicine
• Clinical Neuroscience
• Community Medical Services
• Critical Care
• Emergency Medicine
• Forensic Medicine
• Haematology
• History of Medicine
• Browse content in Medical Dentistry
• Oral and Maxillofacial Surgery
• Paediatric Dentistry
• Restorative Dentistry and Orthodontics
• Surgical Dentistry
• Medical Ethics
• Browse content in Medical Skills
• Clinical Skills
• Communication Skills
• Nursing Skills
• Surgical Skills
• Medical Statistics and Methodology
• Browse content in Neurology
• Clinical Neurophysiology
• Neuropathology
• Nursing Studies
• Browse content in Obstetrics and Gynaecology
• Gynaecology
• Occupational Medicine
• Ophthalmology
• Otolaryngology (ENT)
• Browse content in Paediatrics
• Neonatology
• Browse content in Pathology
• Chemical Pathology
• Clinical Cytogenetics and Molecular Genetics
• Histopathology
• Medical Microbiology and Virology
• Patient Education and Information
• Browse content in Pharmacology
• Psychopharmacology
• Browse content in Popular Health
• Caring for Others
• Complementary and Alternative Medicine
• Self-help and Personal Development
• Browse content in Preclinical Medicine
• Cell Biology
• Molecular Biology and Genetics
• Reproduction, Growth and Development
• Primary Care
• Professional Development in Medicine
• Browse content in Psychiatry
• Addiction Medicine
• Child and Adolescent Psychiatry
• Forensic Psychiatry
• Learning Disabilities
• Old Age Psychiatry
• Psychotherapy
• Browse content in Public Health and Epidemiology
• Epidemiology
• Public Health
• Browse content in Radiology
• Clinical Radiology
• Interventional Radiology
• Nuclear Medicine
• Radiation Oncology
• Reproductive Medicine
• Browse content in Surgery
• Cardiothoracic Surgery
• Gastro-intestinal and Colorectal Surgery
• General Surgery
• Neurosurgery
• Paediatric Surgery
• Peri-operative Care
• Plastic and Reconstructive Surgery
• Surgical Oncology
• Transplant Surgery
• Trauma and Orthopaedic Surgery
• Vascular Surgery
• Browse content in Science and Mathematics
• Browse content in Biological Sciences
• Aquatic Biology
• Biochemistry
• Bioinformatics and Computational Biology
• Developmental Biology
• Ecology and Conservation
• Evolutionary Biology
• Genetics and Genomics
• Microbiology
• Molecular and Cell Biology
• Natural History
• Plant Sciences and Forestry
• Research Methods in Life Sciences
• Structural Biology
• Systems Biology
• Zoology and Animal Sciences
• Browse content in Chemistry
• Analytical Chemistry
• Computational Chemistry
• Crystallography
• Environmental Chemistry
• Industrial Chemistry
• Inorganic Chemistry
• Materials Chemistry
• Medicinal Chemistry
• Mineralogy and Gems
• Organic Chemistry
• Physical Chemistry
• Polymer Chemistry
• Study and Communication Skills in Chemistry
• Theoretical Chemistry
• Browse content in Computer Science
• Artificial Intelligence
• Computer Architecture and Logic Design
• Game Studies
• Human-Computer Interaction
• Mathematical Theory of Computation
• Programming Languages
• Software Engineering
• Systems Analysis and Design
• Virtual Reality
• Browse content in Computing
• Business Applications
• Computer Security
• Computer Games
• Computer Networking and Communications
• Digital Lifestyle
• Graphical and Digital Media Applications
• Operating Systems
• Browse content in Earth Sciences and Geography
• Atmospheric Sciences
• Environmental Geography
• Geology and the Lithosphere
• Maps and Map-making
• Meteorology and Climatology
• Oceanography and Hydrology
• Palaeontology
• Physical Geography and Topography
• Regional Geography
• Soil Science
• Urban Geography
• Browse content in Engineering and Technology
• Agriculture and Farming
• Biological Engineering
• Civil Engineering, Surveying, and Building
• Electronics and Communications Engineering
• Energy Technology
• Engineering (General)
• Environmental Science, Engineering, and Technology
• History of Engineering and Technology
• Mechanical Engineering and Materials
• Technology of Industrial Chemistry
• Transport Technology and Trades
• Browse content in Environmental Science
• Applied Ecology (Environmental Science)
• Conservation of the Environment (Environmental Science)
• Environmental Sustainability
• Environmentalist Thought and Ideology (Environmental Science)
• Management of Land and Natural Resources (Environmental Science)
• Natural Disasters (Environmental Science)
• Nuclear Issues (Environmental Science)
• Pollution and Threats to the Environment (Environmental Science)
• Social Impact of Environmental Issues (Environmental Science)
• History of Science and Technology
• Browse content in Materials Science
• Ceramics and Glasses
• Composite Materials
• Metals, Alloying, and Corrosion
• Nanotechnology
• Browse content in Mathematics
• Applied Mathematics
• Biomathematics and Statistics
• History of Mathematics
• Mathematical Education
• Mathematical Finance
• Mathematical Analysis
• Numerical and Computational Mathematics
• Probability and Statistics
• Pure Mathematics
• Browse content in Neuroscience
• Cognition and Behavioural Neuroscience
• Development of the Nervous System
• Disorders of the Nervous System
• History of Neuroscience
• Invertebrate Neurobiology
• Molecular and Cellular Systems
• Neuroendocrinology and Autonomic Nervous System
• Neuroscientific Techniques
• Sensory and Motor Systems
• Browse content in Physics
• Astronomy and Astrophysics
• Atomic, Molecular, and Optical Physics
• Biological and Medical Physics
• Classical Mechanics
• Computational Physics
• Condensed Matter Physics
• Electromagnetism, Optics, and Acoustics
• History of Physics
• Mathematical and Statistical Physics
• Measurement Science
• Nuclear Physics
• Particles and Fields
• Plasma Physics
• Quantum Physics
• Relativity and Gravitation
• Semiconductor and Mesoscopic Physics
• Browse content in Psychology
• Affective Sciences
• Clinical Psychology
• Cognitive Neuroscience
• Cognitive Psychology
• Criminal and Forensic Psychology
• Developmental Psychology
• Educational Psychology
• Evolutionary Psychology
• Health Psychology
• History and Systems in Psychology
• Music Psychology
• Neuropsychology
• Organizational Psychology
• Psychological Assessment and Testing
• Psychology of Human-Technology Interaction
• Psychology Professional Development and Training
• Research Methods in Psychology
• Social Psychology
• Browse content in Social Sciences
• Browse content in Anthropology
• Anthropology of Religion
• Human Evolution
• Medical Anthropology
• Physical Anthropology
• Regional Anthropology
• Social and Cultural Anthropology
• Theory and Practice of Anthropology
• Browse content in Business and Management
• Business Strategy
• Business History
• Business Ethics
• Business and Government
• Business and Technology
• Business and the Environment
• Comparative Management
• Corporate Governance
• Corporate Social Responsibility
• Entrepreneurship
• Health Management
• Human Resource Management
• Industrial and Employment Relations
• Industry Studies
• Information and Communication Technologies
• International Business
• Knowledge Management
• Management and Management Techniques
• Operations Management
• Organizational Theory and Behaviour
• Pensions and Pension Management
• Public and Nonprofit Management
• Strategic Management
• Supply Chain Management
• Browse content in Criminology and Criminal Justice
• Criminal Justice
• Criminology
• Forms of Crime
• International and Comparative Criminology
• Youth Violence and Juvenile Justice
• Development Studies
• Browse content in Economics
• Agricultural, Environmental, and Natural Resource Economics
• Asian Economics
• Behavioural Finance
• Behavioural Economics and Neuroeconomics
• Econometrics and Mathematical Economics
• Economic Systems
• Economic Methodology
• Economic History
• Economic Development and Growth
• Financial Markets
• Financial Institutions and Services
• General Economics and Teaching
• Health, Education, and Welfare
• History of Economic Thought
• International Economics
• Labour and Demographic Economics
• Law and Economics
• Macroeconomics and Monetary Economics
• Microeconomics
• Public Economics
• Urban, Rural, and Regional Economics
• Welfare Economics
• Browse content in Education
• Adult Education and Continuous Learning
• Care and Counselling of Students
• Early Childhood and Elementary Education
• Educational Equipment and Technology
• Educational Strategies and Policy
• Higher and Further Education
• Organization and Management of Education
• Philosophy and Theory of Education
• Schools Studies
• Secondary Education
• Teaching of a Specific Subject
• Teaching of Specific Groups and Special Educational Needs
• Teaching Skills and Techniques
• Browse content in Environment
• Applied Ecology (Social Science)
• Climate Change
• Conservation of the Environment (Social Science)
• Environmentalist Thought and Ideology (Social Science)
• Natural Disasters (Environment)
• Social Impact of Environmental Issues (Social Science)
• Browse content in Human Geography
• Cultural Geography
• Economic Geography
• Political Geography
• Browse content in Interdisciplinary Studies
• Communication Studies
• Museums, Libraries, and Information Sciences
• Browse content in Politics
• African Politics
• Asian Politics
• Chinese Politics
• Comparative Politics
• Conflict Politics
• Elections and Electoral Studies
• Environmental Politics
• European Union
• Foreign Policy
• Gender and Politics
• Human Rights and Politics
• Indian Politics
• International Relations
• International Organization (Politics)
• International Political Economy
• Irish Politics
• Latin American Politics
• Middle Eastern Politics
• Political Methodology
• Political Communication
• Political Philosophy
• Political Sociology
• Political Theory
• Political Behaviour
• Political Economy
• Political Institutions
• Politics and Law
• Public Administration
• Public Policy
• Quantitative Political Methodology
• Regional Political Studies
• Russian Politics
• Security Studies
• State and Local Government
• UK Politics
• US Politics
• Browse content in Regional and Area Studies
• African Studies
• Asian Studies
• East Asian Studies
• Japanese Studies
• Latin American Studies
• Middle Eastern Studies
• Native American Studies
• Scottish Studies
• Browse content in Research and Information
• Research Methods
• Browse content in Social Work
• Addictions and Substance Misuse
• Adoption and Fostering
• Care of the Elderly
• Child and Adolescent Social Work
• Couple and Family Social Work
• Developmental and Physical Disabilities Social Work
• Direct Practice and Clinical Social Work
• Emergency Services
• Human Behaviour and the Social Environment
• International and Global Issues in Social Work
• Mental and Behavioural Health
• Social Justice and Human Rights
• Social Policy and Advocacy
• Social Work and Crime and Justice
• Social Work Macro Practice
• Social Work Practice Settings
• Social Work Research and Evidence-based Practice
• Welfare and Benefit Systems
• Browse content in Sociology
• Childhood Studies
• Community Development
• Comparative and Historical Sociology
• Economic Sociology
• Gender and Sexuality
• Gerontology and Ageing
• Health, Illness, and Medicine
• Marriage and the Family
• Migration Studies
• Occupations, Professions, and Work
• Organizations
• Population and Demography
• Race and Ethnicity
• Social Theory
• Social Movements and Social Change
• Social Research and Statistics
• Social Stratification, Inequality, and Mobility
• Sociology of Religion
• Sociology of Education
• Sport and Leisure
• Urban and Rural Studies
• Browse content in Warfare and Defence
• Defence Strategy, Planning, and Research
• Land Forces and Warfare
• Military Administration
• Military Life and Institutions
• Naval Forces and Warfare
• Other Warfare and Defence Issues
• Peace Studies and Conflict Resolution
• Weapons and Equipment

• < Previous
• Next chapter >

1 (page 1) p. 1 A brief history

• Published: August 2001
• Cite Icon Cite
• Permissions Icon Permissions

Cosmology may be a relatively new science, but it asks some of the most ancient questions: is the universe infinite? How long has it been around? Will it ever end? ‘A brief history’ charts the historical development of cosmology as a subject of study and explains how some of the key ideas evolved. What do the various creation myths believe about the origins of the universe? What did the Greeks think and how did views change during the Renaissance? The modern era of scientific cosmology began with Einstein's general theory of relativity, published in 1915, which allowed for a consistent mathematical explanation for the Universe.

Signed in as

Institutional accounts.

• Google Scholar Indexing
• GoogleCrawler [DO NOT DELETE]

Personal account

• Sign in with email/username & password
• Get email alerts
• Save searches
• Purchase content
• Activate your purchase/trial code

Institutional access

• Sign in with a library card Sign in with username/password Recommend to your librarian
• Institutional account management
• Get help with access

Access to content on Oxford Academic is often provided through institutional subscriptions and purchases. If you are a member of an institution with an active account, you may be able to access content in one of the following ways:

IP based access

Typically, access is provided across an institutional network to a range of IP addresses. This authentication occurs automatically, and it is not possible to sign out of an IP authenticated account.

Sign in through your institution

Choose this option to get remote access when outside your institution. Shibboleth/Open Athens technology is used to provide single sign-on between your institution’s website and Oxford Academic.

• Click Sign in through your institution.
• Select your institution from the list provided, which will take you to your institution's website to sign in.
• When on the institution site, please use the credentials provided by your institution. Do not use an Oxford Academic personal account.
• Following successful sign in, you will be returned to Oxford Academic.

If your institution is not listed or you cannot sign in to your institution’s website, please contact your librarian or administrator.

Sign in with a library card

Enter your library card number to sign in. If you cannot sign in, please contact your librarian.

Society Members

Society member access to a journal is achieved in one of the following ways:

Sign in through society site

Many societies offer single sign-on between the society website and Oxford Academic. If you see ‘Sign in through society site’ in the sign in pane within a journal:

• Click Sign in through society site.
• When on the society site, please use the credentials provided by that society. Do not use an Oxford Academic personal account.

If you do not have a society account or have forgotten your username or password, please contact your society.

Sign in using a personal account

Some societies use Oxford Academic personal accounts to provide access to their members. See below.

A personal account can be used to get email alerts, save searches, purchase content, and activate subscriptions.

Some societies use Oxford Academic personal accounts to provide access to their members.

Viewing your signed in accounts

Click the account icon in the top right to:

• View your signed in personal account and access account management features.
• View the institutional accounts that are providing access.

Signed in but can't access content

Oxford Academic is home to a wide variety of products. The institutional subscription may not cover the content that you are trying to access. If you believe you should have access to that content, please contact your librarian.

For librarians and administrators, your personal account also provides access to institutional account management. Here you will find options to view and activate subscriptions, manage institutional settings and access options, access usage statistics, and more.

Our books are available by subscription or purchase to libraries and institutions.

• About Oxford Academic
• Publish journals with us
• University press partners
• What we publish
• New features  
• Open access
• Rights and permissions
• Accessibility
• Advertising
• Media enquiries
• Oxford University Press
• Oxford Languages
• University of Oxford

Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide

• Copyright © 2024 Oxford University Press
• Cookie settings
• Cookie policy
• Privacy policy
• Legal notice

This Feature Is Available To Subscribers Only

Sign In or Create an Account

This PDF is available to Subscribers Only

For full access to this pdf, sign in to an existing account, or purchase an annual subscription.

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals

Cosmology articles from across Nature Portfolio

Cosmology is the study of the universe; its birth, evolution, and ultimate fate. This includes further developing and refining the prevailing model, the Big Bang theory, investigating the universe’s rate of expansion, and measuring radiation left over from the Big Bang, the so-called cosmic microwave background.

Latest Research and Reviews

Partial Ly \(\alpha\) thermalization in an analytic nonlinear diffusion model

• Georg Wolschin

The accretion of a solar mass per day by a 17-billion solar mass black hole

A black hole at the centre of a quasar at a redshift of z  = 4 is accreting the mass of the Sun every day. The quasar’s extreme luminosity is equivalent to 50,000 times that of the Milky Way. Its broad-line region should be resolvable observationally and will provide an important test for broad-line region size–luminosity relationships.

• Christian Wolf
• Rachel L. Webster

A massive galaxy that formed its stars at z ≈ 11

A massive galaxy observed with the JWST indicates that the bulk of its stars formed within the first 500 million years of the Universe.

• Karl Glazebrook
• Themiya Nanayakkara
• Angel Chandro-Gomez

A younger Universe implied by satellite pair correlations from SDSS observations of massive galaxy groups

A comparison of observations and simulations of satellite galaxies around massive galaxy groups reveals significant differences, including correlated motions of pairs of satellite galaxies, which challenge the standard model of cosmology.

Weak-lensing detection of intracluster filaments in the Coma cluster

Researchers have detected the elusive dark matter component of cosmic filaments near the Coma galaxy cluster using gravitational lensing. This supports the idea that galaxy clusters grow at the intersection of cosmic filaments, shedding light on the structure of our universe.

• Kim HyeongHan
• M. James Jee
• Hyejeon Cho

Proposed physical mechanism that gives rise to cosmic inflation

• Bruce M. Law

News and Comment

‘Best view ever’: observatory will map Big Bang’s afterglow in new detail

The Simons Observatory will search for signs of gravitational waves that originated from the Big Bang.

• Davide Castelvecchi

Do black holes explode? The 50-year-old puzzle that challenges quantum physics

Stephen Hawking’s paradoxical finding that black holes don’t live forever has profound, unresolved implications for the quest for unifying theories of reality.

How dwarf galaxies lit up the Universe after the Big Bang

Some of the faintest objects ever observed suggest that small galaxies get the credit for clearing the ‘fog’ pervading the early cosmos.

• Sumeet Kulkarni

Giant ‘bubble’ in space could be source of powerful cosmic rays

Scientists have identified a region in the Milky Way capable of accelerating particles to super-high energy levels.

• Gemma Conroy

Volker Springel created the original GADGET code more than 25 years ago. Now it supports some of the largest simulations in astrophysics, and is being developed to do vastly more.

This new map of the Universe suggests dark matter shaped the cosmos

The eROSITA telescope’s detailed pictures are among the most precise cosmological measurements ever made.

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

What is the universe made of? How did it begin? How has it evolved over the 13.8 billion years since its origin?  And how will it end? These are the questions addressed by cosmology, the study of the universe as a whole. Research in cosmology involves astronomy, but also gravitational physics, particle physics, and challenging questions about the interpretation of phenomena we can’t see directly — such as the possible existence of something before the Big Bang.

Center for Astrophysics | Harvard & Smithsonian cosmologists study the universe in many ways:

Connecting theoretical models for the very early universe — cosmic inflation or an alternative scenario — with observable effects. Whatever happened in the first split-second after the Big Bang, it occurred while the universe was opaque to light, so we have to infer its properties indirectly. Some effects might show up in the CMB, while others might be visible in the large-scale structure of the universe. In both these cases, it’s because inflation leaves an imprint on the fluctuations of mass and energy in the universe, which grow as spacetime expands. Scientists Are Using the Universe as a ‘Cosmological Collider ’

Looking for signs of the first stars in the universe. These were likely much more massive than the average star around today, which made them unstable. The supernova explosions of these stars might be observable even that far away, either directly or indirectly through its effects on early galaxies. Explosion Illuminates Invisible Galaxy in the Dark Ages

Mapping the positions of galaxies to reconstruct the effects of dark energy. The Baryon Oscillation Spectroscopic Survey (BOSS) is an ongoing project to map baryon acoustic oscillations using tens of thousands of galaxies halfway across the universe. A One-Percent Measure of Galaxies Half the Universe Away

Tracing the structure of galaxies as produced by dark matter. According to dark matter theory, galaxies should come in a wide range of sizes, but many of those are too small to see easily. The next-generation Giant Magellan Telescope (GMT) will detect dwarf galaxies that are currently too faint to observe, providing a new realm for observing the effects of dark matter. Mapping Dark Matter

  Starting at the Beginning

The universe began 13.8 billion years ago in the event we call the Big Bang. We know this is true by a number of different lines of evidence. The current expansion of the universe demonstrates that it was much smaller in the past, as measured by how galaxies are moving away from each other at increasingly faster rates. The cosmic microwave background is evidence that the cosmos was much hotter and denser. The relative amounts of hydrogen and helium compared to other elements tells us the cosmos wasn’t hot and dense long enough to fuse heavier elements . And so on.

Cosmologists at the Center for Astrophysics | Harvard & Smithsonian work to fill in the details of that big picture.

The earliest moments after the Big Bang are still mysterious. According to the cosmic inflation hypothesis, quantum interactions drove the universe to expand by a factor of 1026 — more than a trillion trillion times — in a tiny split-second after the Big Bang. Among other things, inflation explains why the universe has the same contents and temperature in every direction, and how matter on the largest scales became organized. However, a lot about inflation is still mysterious, so theorists and observers work to describe it, search for any observable traces, as well as test for alternative possibilities.

For the first 380,000 years or so after the Big Bang, the cosmos was filled with a hot opaque plasma. The expansion of the universe spread that plasma out until it cooled enough to form the first stable atoms, and the cosmos became transparent. Light leftover from that transition formed the cosmic microwave background (CMB) , a low-energy bath of light filling the universe. Tiny variations in the CMB temperature reveal the relative amounts of the various contents of the universe, as well as revealing the density fluctuations that produced galaxies later on.

The first stars in the universe were probably born around 700 million years after the Big Bang. However, we don’t know for sure, since the earliest stars are too faint to see from such a great distance. Astronomers look for the earliest galaxies to find signs of those primordial stars, and study indirect clues about their nature.

The observable universe contains about 100 billion galaxies. These aren’t scattered randomly across the sky: gravity gathered them into a huge cosmic web , known as the large-scale structure of the universe. On an even grander scale, galaxies show traces of the sound waves known as baryon acoustic oscillations (BAO) that swept across the universe before the CMB formed. Cosmologists study the large-scale structure and BAO to measure the rate of cosmic expansion and understand how galaxies are organized on the largest scales.

All the atoms in the universe only make up about 5% of its total contents. The rest is dark matter and dark energy. Dark matter, which is about 27% of the contents of the universe, provides the gravitational foundation for building galaxies and galaxy clusters. The large-scale structure of the universe is produced by dark matter, but we still don’t know what it’s made of. Dark energy, making up the remaining 68% of the universe’s contents, causes the expansion of the universe to accelerate. The push-pull of dark matter and energy are what makes the universe look the way it does, so understanding exactly what these mysterious substances are and how they work is a major challenge of modern cosmology.

Artist’s impression of the history of the Universe, from the Big Bang on the left to the present day at the right. The scale is exaggerated to emphasize earlier eras of cosmic history.

• What conditions are necessary for life?
• Why do we need an extremely large telescope like the Giant Magellan Telescope?
• What happened in the early universe?
• Why do galaxies differ so much in size, shape, composition and activity?
• What is the universe made of?
• Quasars & Other Active Black Holes
• Astrochemistry
• Extragalactic Distance Scale
• Cosmic Microwave Background
• Dark Energy and Dark Matter
• Detector Technology
• Early Universe
• Galaxies - Merging and Interacting
• Galaxy Clusters
• Galaxy Formation and Evolution
• Gravitational Lensing
• Intergalactic Medium
• Large Scale Structure
• Optical and Infrared Astronomy
• Radio and Geoastronomy
• Theoretical Astrophysics

Related News

The giant magellan telescope’s final mirror fabrication begins, a massive galaxy supercluster in the early universe, cfa celebrates class of 2022 graduates, astrophysics student wins international 'dance your phd' competition, meet an astrophysicist: tanveer karim, active galactic nuclei and galaxy cluster cooling, astrophysicists reveal largest-ever suite of universe simulations, latest results from cosmic microwave background measurements, center for astrophysics celebrates class of 2021 graduates, to map the universe, astrophysicists launch largest sky survey yet, abacussummit, dark energy spectroscopic instrument (desi), james webb space telescope advanced deep extragalactic survey (jades), physics of the primordial universe, castles survey, cfa redshift catalog, telescopes and instruments, 1.2 meter (48-inch) telescope, 1.5-meter tillinghast (60-inch) telescope, einstein observatory, giant magellan telescope, lynx x-ray observatory, magellan telescopes, mmt observatory, pan-starrs-1 science consortium, south pole telescope, antarctica, spitzer space telescope, the submillimeter array - maunakea, hi.

MIT Kavli Institute

• For Students
• Job Opportunities
• Fellowships
• All Research Areas
• Science Themes
• Research Groups
• All Projects
• Ground Based Observatories
• Laboratory Experiments
• Space Based Observatories
• Outreach Efforts
• Outreach Efforts Archive
• Upcoming Events
• Events Calendar
• Past Events
• Other Events
• Learn More About Giving
• MKI Resources
• Research & Outreach
• Human Resources
• Student Resources
• IT Services
• Facilities Management
• Task Forces
• International Engagements
• For Emergencies
• Accessibilty

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• Philos Trans A Math Phys Eng Sci

100 years of mathematical cosmology: Models, theories and problems, Part B

Spiros cotsakis.

1 Institute of Gravitation and Cosmology, RUDN University, ul. Miklukho-Maklaya 6, Moscow 117198, Russia

2 Research Laboratory of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos, Greece

Alexander P. Yefremov

Associated data.

This article has no additional data.

We continue our overview of mathematical cosmology with a survey of the third and fourth periods of the development of the subject. The first Part includes the first two periods and is published separately. The third period (1980–2000) continues here with brief descriptions of the main ideas of inflation, the multiverse, quantum, Kaluza–Klein, and string cosmologies, wormholes and baby universes, cosmological stability and modified gravity. The last period, which ends today, includes various more advanced topics such as M-theoretic cosmology, braneworlds, the landscape, topological issues, the measure problem, genericity, dynamical singularities and dark energy. We emphasize certain threads that run throughout the whole period of development of theoretical cosmology and underline their importance in the overall structure of the field. We end this outline with an inclusion of the abstracts of all papers contributed to the second part of the Philosophical Transactions of the Royal Society A , theme issue ‘The future of mathematical cosmology’.

This article is part of the theme issue ‘The future of mathematical cosmology, Volume 2’.

1.  Introduction

This is the second part of our introductory survey of mathematical cosmology. The first part is contained in volume 1 of the Theme Issue ‘100 Years of mathematical cosmology’ and is separately published covering the period of development of mathematical cosmology starting from 1917 until 1980. In this second part, we cover the period since 1980, and provide brief descriptions of the emergence, development, importance and interconnections of most major subfields of theoretical mathematical cosmology, such as modified gravity and dark energy, inflationary, quantum, string, M-theoretic and brane cosmologies, wormholes, measures, stability, genericity and topology. Here, as in Part A, we focus on key theoretical discoveries as well as fundamental ideas that were to become (or, in fact, may become) instrumental in the development of the whole field. At the end of this paper, we include the contents of the individual invited contributions to volume 2 of the Theme Issue ‘The future of mathematical cosmology’.

2.  Third period, 1980–2000

In this section, we discuss the following novel ideas that emerged in this period:

• — Inflationary cosmology
• — The multiverse
• — Wave function of the universe
• — The cosmological measure problem
• — Baby universes and wormholes
• — Kaluza–Klein universes
• — String cosmology
• — f ( R ) gravity and cosmology
• — The issue of cosmological stability

(a) Inflation

In the late 1970s, dramatic discoveries in particle physics like asymptotic freedom and the various issues and approaches of how vacuum fluctuations may lead to models of grand unified theories of electromagnetic, weak and strong interactions, completely changed that field, and it was not long before the consequences of these developments for ‘early universe’ cosmology were followed. Particle physicists found in cosmology a testing ground for their theories, while cosmologists realized the power of high-energy arguments for the complex problems that they were facing at the time. Particle cosmology was thus born because of the need to better understand the behaviour of matter and fields in the extreme conditions of the big bang.

Inflationary cosmology [ 1 ,– 3 ], a paradigmatic application of particle physics ideas to cosmology. Unlike more ground-to-earth applications of nuclear physics and elementary particle theory to cosmology, like big-bang nucleosynthesis and baryogenesis, the appearance of inflation was a truly exotic idea, but at the same time had some attractiveness to many cosmologists who had a good background of general relativity. It was based on the transient effects of a scalar field for an accelerated expansion of the universe (in de Sitter’s and in Lemaître’s models discussed earlier, acceleration appears as a permanent property, not a transient one).

At a proper time hypersurface t ∼ 10 − 35   s , we imagine that the particles comprising the material content and occupying different vacua of different energies were displaced from their equilibrium states and were able to move to other vacua of lower energies. During this motion between initial and final vacuum states occupied by matter, the vacuum energy liberated creates a gravitational repulsive force similar to the original Einstein’s cosmological constant and so the universe accelerates for the brief period between the two, the old and the new, vacuum states.

This is very important. For each such pair of vacua, particles arriving at new vacua are able to form ‘bubbles of new vacua’ nucleating at different spatial regions in different times. According to Guth, this phase transition supercools the universe by 28 or more orders of magnitude below a critical temperature, and then leads to a huge expansion of exponential growth accompanied by a disastrous process of all sorts of irregularities in the curvatures and the matter density arising in this phase of evolution of the universe. (This was ameliorated, however, in subsequent models by other authors making the motion between vacua slower -leading to a unique bubble comprising the visible universe.) In fact, a slight change in the original scenario of Guth’s showed that in the ‘new inflation’ scenario (as in various others - see below), inflation is in fact eternal [ 4 ].

But the inflationary idea, common to all inflationary models that followed Guth’s, also leads to a much larger, homogeneous and isotropic universe, with many of the puzzling issues of the previous models practically solved. That includes the horizon, flatness, monopole, as well as other perplexing issues, unexplained in the standard model of cosmology. For instance, the visible universe today—our own bubble—comprised a huge number of causally disconnected regions at Planck time (and also at the time of inflation). But during inflation one of these regions was inflated to encompass all others, allowing thus a restored type of causal communication between them and leading to today’s observed uniformity.

In fact, it is a most important property of the resulting inflationary picture of the early universe, also improved and generalized by various later modifications or extensions, that by the same mechanism it also explains other additional properties: the temperature and energy-density fluctuations of the cosmic microwave background radiation as a result of the quantum phase during the inflationary stage, namely, the quantum fluctuations of the scalar field driving inflation (see [ 5 ] for background in the theory of cosmological fluctuations, [ 6 ] for an early review of the inflationary approach to this problem, [ 7 ] for the situation in the early 1990s and [ 8 ] for a modern review of this idea).

Today the development of the inflationary picture of the early universe continues. There are practically hundreds of model-dependent implementations of inflation in different theories, for instance in relativity, modified gravity, supergravity, superstring cosmology, M-theoretic cosmology, etc., but there are two issues of importance related to the inflationary scenario that require attention, and which show that inflation is certainly not the last word about the structure of the early universe.

The first is to test how successful inflation models fit cosmological data coming from observations made by various satellites and instruments, COBE, PLANCK, WMAP BICEP/KECK, etc. Indeed, many of the most popular inflationary models are now definitely falsified by these data. This is made possible by the consideration of the slow-roll parameters ϵ and η defined by the scalar field potential and its first and second derivatives. Eventually, the predictions of inflationary models are measured by certain combinations of the slow-roll parameters calculated in the models, the primordial tilt n s and the tensor-to-scalar ratio r . These are functions of the number N of the inflationary e -folds, which occur between the time when a given perturbation leaves the horizon and the end of the inflationary period, and describe quantum fluctuations induced by inflation such as the gravitational wave energy spectrum. Interestingly, current observations give a value of r < 0.036 at 95 % confidence [ 9 ], too low for most inflationary models to predict.

The second issue is what would be a believable prequel to the inflationary stage that would make the inflationary idea more natural. We shall come back to this issue in subsequent sections of this paper.

(b) Multiverse

Even though according to inflation the bubble leading to our visible domain adequately expanded and inflated solving in this way many of the cosmological conundrums of standard cosmology, the complex process of creation and evolution of the whole network of such distinct inflating bubbles may lead to a very awkward situation, now elaborated to what is called the multiverse .

The fact that inflation can be eternal was realized soon after Guth’s original idea, by Paul Steinhardt [ 4 ] and by Alexander Vilenkin [ 10 ] for new inflation, and later by Andrei Linde [ 11 ] in the context of the chaotic inflation scenario, where the potential of the scalar field driving inflation has no flat plateaux. Linde used heuristic arguments to imply that the process of large-scale fluctuations of the scalar field leads to an eternal , self-reproducing , inflationary multiverse . In this, each inflating bubble consists of further inflating subregions with each one of these in turn having further similar ones, at infinitum, a process seemingly progressing endlessly to the future as well to the past. In this multiverse, the density parameter Ω varies continuously between 0 and 1, so our bubble together with infinitely others with Ω ∈ ( 0.2 , 0.3 ) lies somewhere in the structure with non-zero probability.

It is a difficult problem how to calculate probabilities in the multiverse [ 12 ], and in a situation like this one may produce arguments leading to an overall controversial picture (cf. e.g. [ 13 ] and references therein) for the probability of the occurrence of a stage of inflation. For instance, in [ 14 , 15 ] one finds opposite views and probabilities ranging from almost one to almost zero. Despite being hard to believe, this picture appears nevertheless as a natural extension within the wider context and philosophy of inflationary cosmology, and some recent progress has indeed been made (see §3c). In fact, most authors agree that inflation is future-eternal [ 16 ], but probably not being so in the past [ 17 ] without violating the null energy condition [ 18 ].

(c) Quantum cosmology

For the consideration of the initial state of the universe as a quantum problem, the so-called programme of quantum cosmology , one such approach is through the Wheeler–DeWitt equation advocated by DeWitt [ 19 ] and Wheeler [ 20 ], describing the evolution of the quantum wave function of the universe considered as a quantum object. Solutions of the Wheeler–DeWitt equation then give probabilities for the universe to evolve from one state to another, provided one gives prescribes how to specify ‘initially’ both the probability amplitude and its first derivative normal to the initial hypersurface in superspace (this is a set describing the space of all 3-geometries). One approach to the study of this equation was to consider the limiting case of ‘minisuperspace’, a subset of the full problem where most of the gravitational degrees of freedom are frozen out. This turns the whole quantum cosmology problem, considered in ‘canonical quantum gravity’, into a more manageable quantum mechanics problem, and many different models have been considered in this framework.

A prequel theory to inflation remains a very mysterious problem and its solution is largely unknown even today. This is perhaps one of the most important ingredients necessary to make our current (and future) cosmological standard models more complete. In a sense, initial or boundary conditions are necessary for any cosmological model to be more predictive. All these issues became more substantial and received a blow of original ideas in the 1980s (the decade 1980–1990 may be called indeed a ‘golden decade’ in theoretical cosmology research).

In 1983, Hartle & Hawking introduced a radical approach using path integral methods to describe the problem of initial conditions in quantum cosmology introduced in the 1960s [ 21 ]. That approach, called the no-boundary proposal for the wave function of the universe, suggested a beginning of the universe not as dramatic as that appearing in the standard model of the universe. In fact, there is a beginning but the initial singularity is now replaced by a situation where time is imaginary, there is a smooth passage to a quantum regime, a creation ‘from nothing’. The Hartle–Hawking wave function also peaks as most probably states those that describe infinitely large and empty universes.

However, it soon became clear that other, equally probable and similarly constructed, ‘creation-from-nothing’ proposals are possible, but with completely different predictions. For instance, a small, hot early universe, pretty much like the standard big bang model of the classical universe, is the prediction of A. Vilenkin’s tunnelling model creation-from-nothing 1985 model [ 22 ], which also predicts a period of exponential expansion [ 23 ].

Soon however, the problem arose of what it means for the universe to be in a typical quantum state , and what is the meaning probability in quantum cosmology as well as the possible set of all these different wave functions (see [ 24 ] for a clear discussion of the difficulties in defining a probability of inflation in a simple minisuperspace model). This is a very deep problem and is related to the measure problem in cosmology and the issue of how to define probabilities in a cosmological setting (see the next section).

The first works resulted in a huge proliferation of very interesting subsequent papers on quantum cosmology during the 1980s (see [ 25 ] for a bibliography of papers for that period), addressing an impressive variety of very deep questions and meaning in cosmology (prediction, time, creation, etc.).

Finally, we mention a very different approach to quantum cosmology, loop quantum cosmology (LQC). This is based on an approach to the quantization of gravity using new Hamiltonian variables (the Ashtekar variables), and taking seriously the Dirac quantization method of field theory. LQC also uses a different set of connections than the Levi–Civita one, the spin connection, and this results in an improved behaviour of the original Wheeler–De Witt equation. This also gives a bounce instead of the initial singularity in FRWL models considered in LQC, whereas many other cosmological properties acquire a new light in this framework. For reviews, see [ 26 , 27 ].

(d) Measure-theoretic cosmology

There are many situations in theoretical and mathematical cosmology where one is interested in ‘typical behaviour’, the ‘most probable state’ a cosmological system may assume, in short, one is interested in a measure of the ‘degree of genericity of a given property’. For example, in inflationary cosmology, there is the question of how typical is an inflationary stage within a given set of solutions. For instance, consider a flat FRWL model with a perfect fluid with equation of state p = w ρ , where p , ρ are the pressure and the density of the fluid, respectively. Then, for different values of the parameter w , one obtains different dynamical regimes described by exact solutions for given w values, and the question arises as to what is the long-time behaviour of the solutions of the system. For a scalar field potential quadratic in the field, it may be shown [ 28 ] that inflationary stages are an unavoidable property of most solutions of the associated dynamical system, and in addition for exponential potentials, power-law inflationary stages are likewise a stable attractor of the system [ 29 ].

To study probabilities in a classical or quantum context in cosmology more generally, it is necessary to have a suitable measure in the space of all classical solutions of the theory, much like the Liouville measure (i.e. the volume element) in statistical physics.

Such a measure was first proposed by Henneaux [ 30 ] and by Gibbons et al . [ 31 ], and we shall refer to it as the HGHS canonical measure on the set of all universes. This measure plays the role of a Liouville-type measure in a minisuperspace approximation of the cosmological phase space, and its construction assumes a Hamiltonian flow and associated symplectic structure and constitutes an adaptation of the symplectic quotient construction in cosmological problems.

The application of the HGHS measure to cosmology, most importantly perhaps to the structure of the multiverse, is, however, plagued with various infinities. In addition, there are various conflicting claims in the literature for inflationary versus non-inflationary solutions; in many cases of interest such as a massive scalar field [ 32 ], R 2 inflation [ 33 ] and Bianchi-I inflation [ 34 ], the HGHS measure gives infinite answers on both types of solution. In [ 35 ] (see also [ 36 ]), however, a cut-off in the dynamics is introduced, for which the resulting measure becomes finite because the probability of N e -folds of inflation is then exponentially suppressed, thus making inflation improbable.

Other studies of the measure such as [ 37 ] point out related difficulties associated with the HGHS measure, such as the use of minisuperspace approximations, the lack of inhomogeneity considerations, as well as the lack of any interaction between different pocket universes in the ensemble to which the measure is applied (so as to allow for ‘equilibration’ on the relevant scales), while a comparison between different measures can be found in [ 38 ]. A broader perspective on measures in the multiverse is found in [ 39 ].

Despite all these extremely valuable works, it is indeed true that the measure problem is currently unresolved and more research is clearly needed in this most interesting problem of mathematical cosmology.

(e) Wormholes and baby universes

Wormholes connect parts of an asymptotically flat (Euclidean) region in space–time, or perhaps two different asymptotically flat regions, and are important because according to Hawking describe possible quantum states of closed universes that branch off from our own [ 40 ]. One may imagine wormholes as small tubes connecting various types of two closed 3-boundaries, or ‘baby universes’, the latter being closed carry zero energy and momenta. (The word ‘semi-wormhole’ is sometimes used to designate a tube that connects a state with no baby universe to another with one.)

The importance of wormhole-like objects in quantum cosmology took off in the late 1980s when Coleman showed how they can be used to make the cosmological constant vanish [ 41 ]. For this purpose, he used the Hartle–Hawking wave function to show that it had a peak at configurations for which the cosmological constant vanished. In this situation, λ is contained in the leading term in an expansion of the classical action, while all other higher-order terms (i.e. − R + a R 2 + b Ric 2 + c Riem 2 + ⋯ , with the coefficients depending on the wormhole being summed) vanish, being the saddle points of the action, i.e. Einstein spaces. Then the effective action Γ is found to be simply inversely proportional to λ , hence peaked at λ = 0 .

This spectacular result was criticized because it was thought that it led to a situation having a network of large wormholes on very large scales with very high density (of the wormhole ends in the dominant Euclidean field configurations)—a catastrophic prediction of strong, non-local interactions [ 42 ]. Nevertheless, it led to a very large number of works on the varied physical effects of wormholes (see, for instance, the interesting proceedings at that time [ 43 ]).

Another cosmological application of wormholes is in the construction of bouncing models which avoid an initial singularity. It was first shown by Morris and Thorne that wormholes can be solutions to the Einstein equations that violate the null energy condition but allow for time travel [ 44 , 45 ]. Various such wormhole solutions exist with matter models, or various scalar fields, in modified gravity, scalar-tensor theories, or in brane universes, see [ 46 , 47 ]. A particularly interesting wormhole solution that requires no violation of the energy conditions, is a cylindrical wormhole with spherical topology near the throat [ 48 ]. Another example of such a configuration is a generalization of the Tolman universe (see the section on the Tolman universe in Part A of this survey). That was a bouncing universe but the nature of the bounce is somewhat ambiguous as it is not precisely specified. Wormhole solutions connecting a previous phase in the evolution of the universe to the current one can provide the missing link, and many such models have been built (see [ 49 ] for a textbook presentation). A Tolman wormhole is an example of such a bouncing model with the strong energy condition being violated [ 50 ].

(f) Kaluza–Klein cosmology

An additional, important input to ‘alternative’ cosmology was provided by the multitude of possibilities in the development of Kaluza–Klein cosmologies (see [ 7 , 51 , 53 ] for a concise, almost textbook treatment, while [ 54 ] is more suitable for relativists (this paper contains almost 400 references)).

In such a higher-dimensional setting, there are two kinds of spatial dimensions, the usual ‘external’ (large) ones and the internal (small, that is ‘compact’ ones, see below) dimensions, which play a key role in determining the structure of the physical laws in the overall higher-dimensional set-up (extra time-like dimensions are associated with ghost instabilities and are thus less favourable). There is a fundamental ‘cylinder condition’ that defines circle-compactification, meaning that nothing depends on the extra Y coordinate, or equivalently, the space that is defined by the extra coordinate(s) is compact in the subspace topology.

This leads to a very small scale (volume) of the compact dimensions compared with the remaining ones, and so their associated energy must be very high. Since in these models, the Newton constant, which gives the range of the gravitational interaction, appears as inversely proportional to the very small volume of the compact internal dimensions, this led some to propose a higher-dimensional mechanism for explaining why the gravity scale is so much larger than those of all the other interactions, the so-called hierarchy problem (see §3b).

Also the fundamental physical constants that appear in the low-energy theory that we observe have values that crucially depend on integrating over the extra dimensions. The internal dimensions are also static, in distinction to the external ones that are dynamic, usually expanding or contracting, and this situation has led to a great number of works that approach the standard problems of cosmology (nature of singularities, bouncing models, horizon problem, etc.) from such a higher-dimensional perspective (cf. the quoted references for various examples of such models).

One particularly interesting development in this context has been the issue of whether or not chaotic Mixmaster behaviour is possible with more spatial dimensions. After initial results [ 55 , 56 ] about the disappearance of chaotic behaviour in vacuum five- and seven-dimensional Kaluza–Klein universes, respectively, with static internal dimensions, in a series of very interesting papers in the middle 1980s, J. Demaret et al. argued that in homogeneous [ 57 ] as well as inhomogeneous [ 58 ] vacuum Kaluza–Klein cosmologies more dimensions lead to less chaos, in particular, chaos disappears in 11 or more space–time dimensions, but it remains in homogeneous vacuum Kaluza–Klein universes in space–time dimensions between 4 and 10 [ 59 ] (the space–time dimension 11 has been called the ‘critical’ dimension for chaotic cosmology in [ 60 ]).

But two issues in all such models remained: What is that which makes some dimensions expanding while others are kept small, and second, how does one make the (small) size of the internal dimensions stable with respect to physically relevant perturbations? Both of these problems are addressed in more elaborate extensions of the interesting initial Kaluza–Klein cosmologies of the 1980s.

(g) String cosmology

A new chapter in mathematical and theoretical cosmology opened with the application and exploitation of the new duality symmetries between string-theoretic models and 11-dimensional supergravity, suggesting the existence of a still larger theory—M-theory—in which gravity being supersymmetric propagates in the 11th dimension while the remaining interactions are constrained on suitable 10-dimensional hypersurfaces. This new set-up requires in addition to the metric, other fields—for instance two more massless states, the dilaton and an antisymmetric tensor field (commonly called ‘the axion’).

For cosmology, all this new information translates into a huge variety of suitable gravitational Lagrangians including all sorts of other fields, leading to solutions which cannot exist in general relativistic or other similar contexts. The result is string and M-theoretic cosmology , a new and largely unexplored field of investigation (for excellent textbook introductions, see [ 61 ], and the last Part of [ 62 ]).

The duality symmetries when applied to a homogeneous Bianchi I cosmology lead to the so-called scale-factor dualities, which not only invert the scale factors but at the same time shift the dilaton, therefore making this a purely string-related effect. When combined to time-reversal symmetries, and applied to a Friedmannian background, one is led to a good result: In the pre-big-bang model of Gasperini & Veneziano [ 63 ], the singularity has moved to infinity, and its place is taken by a smooth evolution bouncing through it from a previous expanding to a post big bang contracting homogeneous and isotropic state. (More general results are possible in anisotropic contexts.)

The resulting universe-model is characteristically distinct from the hot big bang cosmology, in that the curvature has a maximum at the end of an initial cold, unstable and vacuum state. One may compare the quantum cosmological approaches to the hot big bang versus the string perturbative vacuum state of string cosmology in a quantum setting, where the latter overpasses some of the well-known problems of the standard approach to quantum cosmology, and introduces a tunnelling not ‘from nothing’ but from the initial string state (see [ 61 ] for a complete treatment of the various results in this approach). A potential issue with this model is, however, the possible instability of single semi-classical trajectories, an issue which could be bypassed in a path integral approach.

More generally, string cosmological models offer new possibilities for cyclic behaviour (cf. the interesting qualitative work [ 64 ] and references therein), exact solutions of Bianchi type made possible with new forms of the antisymmetric H -field [ 65 ], and a variety of inhomogeneous solutions with an initial Kasner era [ 66 ]. For more results of this type, see the comprehensive review [ 67 ].

(h) f ( R ) -cosmology

A rather different modification of the basic dynamical form of general relativity than the Brans–Dicke or more generally the scalar–tensor theories—higher-order gravity—appeared very early and continues in new forms until today, having major ties with early universe cosmology. Based on earlier impressive and original work of Lanczos (cf. [ 68 , 69 ] and references therein) and others on the influence of higher-order invariants of the Riemann tensor on the structure of general relativity, a particular choice eventually seemed simple and general enough: the gravitational Lagrangian be an arbitrary analytic function of the scalar curvature, f ( R ) . In fact, this leads under a metric variation to fourth-order field equations, not second order-like general relativity (while other types of variation may lead to second-order ones, see below). The result is a new theory of gravitation, f ( R ) -gravity .

Keeping f ( R ) analytic means that this type of theory will be expected to play a significant role in the extreme conditions of the early universe where higher-powers of the scalar curvature become important, but not for late-time evolution (where such powers become negligible). f ( R ) -gravity is hence expected to convey some of the importance of the influence of quantum gravitational effects in the early universe even though everything is classical.

Some first impressions of f ( R ) -gravity to cosmology were given in the period considered (e.g. [ 70 ,– 73 ]), but the field was meant to blow up in activity starting in the mid-1980s, and this continues until the present time (see the many reviews of this theory towards the end of this paper).

In 1983 in a seminal paper, Barrow & Ottewill [ 74 ] showed that under especially simple algebraic conditions, the whole family of theories in f ( R ) -gravity allows for inflation, as well as it provides stable FRWL, de Sitter cosmologies with respect to perturbations outside general relativity, that is in f ( R ) theories. In addition, it was shown a little later that f ( R ) -gravity is conformally equivalent to Einstein’s theory when another purely cosmological, self-interacting scalar field is added [ 75 ]. 1 This equivalence of the two dynamically different theories required the same type of matter as inflation did, but it also showed that f ( R ) -gravity leads to a symmetric-hyperbolic system, in contradistinction to other types of modified gravity. This equivalence also allowed to transfer a number of results from general relativity to the generalized framework of f ( R ) -gravity, including the singularity theorems (because conformal transformations respect causality).

With regard to conformal transformations in such contexts, there is an important geometric generalization of general relativity, conformal (Weyl) gravity. This theory has a unique place among all theories quadratic in the curvature invariants, since it is conformally invariant. (It is also closely related through the Gauss-Bonnet theorem to a particular Bach Lagrangian.) This leads to intriguing properties and connections with various important and largely unexplored issues, such as what breaks conformal invariance, and how this is related to a number of cosmological puzzles. For more on this theory cf. [ 76 ].

The development of f ( R ) -cosmology continues today at an accelerating pace. Two developments are of particular importance. The alternative Palatini formulation of the f ( R ) -gravity equations [ 77 ] leads to a reduction of order and can therefore lead to simplified treatments of a number of issues in cosmology (for a review of cosmology in Palatini theories, see several of the reviews cited at the end of this paper).

Second, there are new developments of no-scale f ( R ) -theory [ 78 ], that is Lagrangian f ( R ) theories in which the field equations are traceless versions of the standard ones. An important feature of these theories is that conformally they become GR plus a scalar field but with the crucial difference that the self-interacting potential is scale-invariant. This exact result implies different CMB parameter forms for all previous forms of f ( R ) -gravity. For the traceless version of the quadratic theory, the prediction for the tensor-to-scalar ratio is given by, r = 12 / ( b 2 N 2 ) , with b ≠ 1 is the new condition necessarily required in the traceless version [ 78 ]. (Here N stands for the e -fold function that measures the length of inflation, while b is the crucial new arbitrary constant related to the scale invariance of the potential when we scale the field in traceless theory.) This theory accommodates any r -value however small.

(i) Cosmological stability

We mentioned in Part A of this survey that the most important property of the Einstein static universe was its transient character. This is based on its instability, as in the Eddington–Lemaître cosmology. In fact, the issue of the instability of the Einstein static universe is much wider, and has been investigated by different authors who proved instability in various current contexts.

Starting with a radiation-filled Einstein universe, instability was shown in terms of inhomogeneous oscillatory modes [ 79 ], or in a fluid-filled model with respect to conformal metric perturbations (where the interesting result is that there are regions of stability depending on the sound speed) [ 80 , 81 ]. Studies of instability were then exploited by Ellis & Maartens to introduce the emergent universe [ 82 ], where in the context of inflationary cosmology, the Einstein static model serves as a prequel to the inflationary stage: an transient initial state with matter being a scalar field whose vacuum energy determines the cosmological constant of the model. This model has no singularity, no horizon problem and, most importantly, does not need a quantum era in its early evolution, it is past eternal. Its instability of the initial Einstein static state is proved [ 83 ], but the effects of other, inhomogeneous, nonlinear perturbations are not yet concluded (see, however, a proof against Bianchi-IX homogeneous perturbations in [ 84 ]). Last, the Einstein static universe, perhaps even as a transient model, does not seem to pass the finite action requirement [ 85 ].

The issue of cosmological stability is generally related to various geometric properties of the flow of a system of equations. For Bianchi universes in vacuum or filled with various fluids, exact solutions are known and so issues of stability have been studied by many authors (see [ 86 ] for a review of the exact solutions in this context). The systems are described by ordinary differential equations but the stability of most types (e.g. those of type V, VI, VII) becomes non-trivial to decide because of the typical appearance of zero eigenvalues in the case of future asymptotic evolution [ 87 ].

For Bianchi cosmologies with a positive λ , there is a result of Wald [ 88 ] to the effect that all (including B-IX with large enough λ ) approach the de Sitter solution, and are therefore isotropized. There were various such results in the 1980s and the 1990s pointing to the validity of a cosmic no-hair theorem for such space–times also in extended frameworks [ 89 ] such as higher-order gravity [ 90 ], or quantum cosmology [ 91 ].

Stability really depends on how one sets the problem, and there are various different and inequivalent definitions in the literature. It is closely related to the problem of describing the asymptotic states of a cosmology, and for this there exist various different approaches (see [ 92 , 93 ] for homogeneous cosmologies). This is a vast field within mathematical cosmology, rapidly expanding today. For inhomogeneous models, the situation is far less well understood; see the next section.

3.  Fourth period, 2000 until today

During the last 20 years in the evolution of mathematical cosmology, one sees an explosive mixture of joint developments in many of the aforementioned areas as well as the formation of many novel ones. It is fair to say that the whole field has matured to a degree beyond recognition as compared with, say, its image 50 years ago. In this last part of the development of the field, we shall focus primarily on the following topics:

• — M-theory and cosmology
• — Braneworlds
• — The landscape
• — Topological issues and dynamical evolution
• — Genericity in cosmology
• — Models of dark energy

(a) M-theoretic cosmology

It was a surprise to many that the quantum consistency of superstrings eventually required the existence of further (than strings) low-dimensional objects, the p -branes, with p taking ‘small integer values’. Once one allows for strings (that is p = 1 objects) into the theory, however, it is completely natural to expect that other such objects play an important role and consider these other possibilities. Branes are ubiquitous and largely unexplored, and given the various dualities between the original five string theories and 11-dimensional supergravity, it is only natural to explore them in this generalized context of interconnected theories coined M-theory . In fact, in the string or brane gas scenario of Brandenberger et al. in 2000 [ 94 ], the universe is supposed to be a ‘hot soup’ of branes of all p dimensions, topologies and spatial orientations, and all internal dimensions are assumed compact, in an attempt to explain why only three dimensions are surviving. In the simplest models of this kind, branes of larger dimensionality have higher energies and annihilate first, leaving only strings. Brane cosmology is a very rich subject, and some aspects of it are treated in §3b.

A most important aspect of M-theory cosmology is revealed in the study of chaotic Mixmaster behaviour in these frameworks. Initial results [ 95 ] pointed to the disappearance of the BKL chaotic oscillations on approach to the string cosmological singularity in homogeneous Mixmaster models, due to the combined effect of both the dilaton and the axion fields. A more elaborate treatment of this problem brings us into the realm of the general effects of p -form fields often coming from supergravity theories and M-theory.

A spectacular effect of these fields was shown to exist in the generic inhomogeneous case of the old Mixmaster universe but now considered in the context of superstring or M-theory cosmologies, where it was shown that the role of the p -form fields is similar to that of the curvature terms in the Einstein theory, namely they act like potential walls, thus preventing the possibility of free Kasner motions of the universe point [ 96 ]. The overall result in any space–time dimension in the general inhomogeneous case is again the BKL behaviour, even in the case of 11 or more space–time dimensions where that erratic behaviour was known to be absent in pure Einstein gravity [ 97 ]. This led to the interesting speculation of a possible de-emergence of a classical or even a quantum behaviour of space–time as we approach the initial singularity in these models, and the possibility of an effective, purely algebraic description of the dynamical behaviour of the universe near the singularity in terms of hyperbolic Kac–Moody algebras [ 98 ].

Today, about 20 years since its original conception, M-theoretic cosmology is only just beginning. In a series of interesting papers, Lucas et al. [ 99 ] (see also [ 100 ] and references therein) introduced and studied a general framework for doing cosmology in type I superstring and M-theory, with particular emphasis on the relation between supergravity p -brane solutions and cosmology. Because of an allowed exchange between the time coordinate and the transverse spatial coordinate in these solutions, the intriguing possibility opens to explaining a number of cosmological phenomena through stringy considerations.

For qualitative applications of dynamical systems techniques in the context of an FRWL model with six Ricci flat internal dimensions and the 11th dimension compactified on a circle, see [ 101 ]. A feature of M-theory cosmologies appears to be their transient acceleration, see [ 102 ] or many related references, and [ 103 ] for a more elaborate analysis of this property. An interesting ingredient used in these works is a correspondence between the space of flat FRWL cosmologies and that of geodesics of a suitable target space, with accelerating ones occupying a special subset of the lightcone [ 104 ].

For background necessary for string- and M-theoretic techniques particularly adapted for the relativist, see the relevant sections in [ 61 ] as well as [ 105 ].

(b) Braneworlds

Braneworlds, or p = 3 -branes, represent universes (i.e. four-dimensional space–times) lying inside a higher-dimensional space dictated by superstring theory, in which the three particle physics interactions ‘live on the brane’ while gravity propagates freely in all dimensions of space, and is much weaker than the other forces. This is in sharp contrast to the usual Kaluza–Klein cosmology wherein the extra dimensions are necessarily static and presumably compactified, hence unobservable.

Brane theory seriously elaborates further on this very original Kaluza–Klein idea. There is a set of consistency conditions of the quantum superstring theory that leads naturally to the exploration of the possibility of having ‘large extra dimensions’, dimensions that have a compactification scale not at Planckian energy but much lower, possibly comparable with the currently favourable ones (cf. [ 106 , 107 ] and references therein). A concrete realization of these ideas was originally introduced by Randall & Sundrum [ 108 ] in 2000, where the Einstein cosmological equations are modified by the addition of extra terms coming from the brane embedding in the bulk space, as well as the bulk space itself.

In the resulting set-up new possibilities are possible for inflation, gravity ‘induced’ on the brane by localizing matter, or more general cosmological dynamics (see [ 61 ], ch. 10 for a short review). One may imagine a number of such lower-dimensional universes coexisting in the parent space and moving in one or more of the extra dimensions. Using the mathematics of submanifolds, it is not very difficult to describe the geometric properties of this set-up as well as the modified Einstein equations, cf. [ 109 , 110 ].

In fact, there are several scenarios in the literature about possible brane models of the early universe, a particularly interesting one being the ekpyrotic universe proposed in 2001 by Khoury et al . [ 111 ] (see [ 112 ] for a review with many references). Here, two parallel branes approach each other, collide, and then rebound, moving in one of the spatial dimensions available. The big bang occurs as a bounce periodically an infinite number of times, each time there is a collision, and then there is a cyclic process of contraction, bounce and expansion, like in the old Tolman oscillating universe. There is a stage of early acceleration in this model that keeps the entropy from diverging in the cycle-to-cycle evolution after many cycles, and according to the authors there are no infinities in the defining quantities like in the standard cosmological model. The ekpyrotic model is but one of many possible bouncing cosmological models (see [ 113 ] for a related review).

Braneworld models nowadays abound. They have different motivations than the original brane models, but they all show the richness of brane cosmological ideas. Two such models are briefly noted below, one motivated by an attempt for a successful resolution of the cosmological constant problem, and the other by an adaptation of holographic ideas in cosmology. For a resolution of the λ problem in a higher-dimensional, brane setting, one uses a self-tuning mechanism and considers a single 3-brane universe in a five-dimensional bulk space with linear or nonlinear bulk-fluids (cf. [ 114 ] and related references therein). The main question here is whether there are regular solutions that satisfy a number of plausible physical criteria (finite Planck mass, energy conditions, etc.). In these braneworld models, ‘everything depends on the extra transverse Y -coordinate’, grossly violating the cylinder condition met in the original Kaluza–Klein universes. On the other hand, a particularly interesting feature of these models is the fact that a Wick-type of exchange between the time and the transverse spatial coordinates leads to cosmological models with many features having brane-theoretic origins.

The last brane model we discuss is ambient cosmology . This is an attempt to relate holographic techniques [ 115 ] in a braneworld setting with methods of conformal geometry to motivate the idea that the brane representing ‘our world’ has moved to the conformal infinity of the bulk, the ‘ambient space’. The resulting ambient cosmology has a number of novel characteristics that allow for previous problems such as the singularity problem and the question of cosmic censorship to be resolved very smoothly in this set-up [ 116 ].

In conclusion, braneworld cosmology presents interesting, well-posed problems for the future in terms of challenging the predictions of inflation as viable alternatives, as well as a variety of mathematical issues, which, in the face of the great number of unexplored possibilities in this part of cosmological model building, become particularly attractive to tackle.

(c) Measures in the landscape

Interestingly, the picture of the inflationary multiverse according to eternal inflation and developed in the period 1980–2000, was found to be strongly supported by a string- or M-theoretic prediction of a huge collection of allowed, or even predicted, different vacua known as the landscape [ 117 ].

Conversely, eternal inflation provides a mechanism to ‘populate the landscape’ [ 118 ], another being that of the sum-over-histories (no-boundary) approach [ 119 , 120 ].

These two versions of a multiverse are part of a broader classification given in [ 121 ], where many other speculative versions of the idea of a multiverse as discussed.

An open question here is in what sense all these different ‘universes’ are really distinct to each other and how one would be able to avoid counting same ones as different. The general problem of how such a structure may evolve is also unknown, but of course no one really knows the nature of what holds the multiverse together, or how M-theory operates in this ‘moduli space of supersymmetric vacua’ (to quote [ 117 ]). This is one of the frontiers of theoretical mathematical cosmology.

(d) Topology and cosmology

Another quantum possibility (or rather more like a speculation at the time) was suggested in 1973 by Tryon [ 122 ]. He imagined the universe as a quantum fluctuation of the vacuum, appearing accidentally so to speak ‘from time to time’ and obeying Heisenberg’s uncertainty principle. Thus an infinite lifetime would be associated with zero energy, but the unexplained issue with this proposal was why the universe had such a large age. But what would be the properties of a universe created from a fluctuation of the vacuum? A finitely born universe would have all possible shapes, and the Einstein equations only relate the local properties of space–time to the overall matter density. The issue of topology of the universe relates to global properties, possibly observable and in fact something like this could alter the images of observed galaxies by producing multiple, fainter copies of their images.

Sokolov & Shvartsman [ 123 ] and Gott [ 124 ] gave lower bounds on the size of a finite universe. Also Zeldovich & Starobinski [ 125 ] studied a flat, finite, universe as a quantum fluctuation and concluded that it must have an approximate spherical shape to avoid a singularity. Another issue with all these studies was how to create an infinite model with global non-trivial topology. It is difficult not to take seriously any model that allows for some mild form of non-trivial global topology. Today the problem of observationally detecting some aspect of large-scale topology is an active one [ 126 ].

As we discuss in more detail in §3f, the number of arbitrary spatial functions to describe the generality of a cosmology is four in vacuum for Einstein’s gravity and becomes 16 for higher-order gravity. This in turns becomes 4 ( 1 + F ) + 2 S and 16 + 4 F + 2 S , respectively, when a number F of fluids and a number S of scalar fields is added, cf. [ 127 ] (this counting assumes that dark energy is described by a cosmological constant).

It is an interesting result, which we now discuss that in the case of a Bianchi (homogeneous) cosmology having compact spatial topology—where because of the homogeneity assumption the arbitrary functions become constants—the corresponding numbers of constants require to determine the general solution generally increase without bound. This constitutes a major difference with respect to the corresponding situation of ‘trivial’ topologies. In the general inhomogeneous case, the situation is largely unknown.

The Einstein equations do not impose any restrictions on the spatial topological complexity of a solution, and this means that one may arbitrarily change the spatial topology of an original space–time-solution of the field equations and still keep the resulting configuration as a solution. Topological complexity, that is the complexity of a given topology of some solution to the field equations, is something that is measured by the number of the moduli degrees of freedom, namely, the number N M = 6 g + 2 k − 6 , where g denotes the genus and k the number of conical singularities of the underlying orbifold. (Although every manifold is trivially an orbifold, the converse is not true. To get an idea of what an orbifold very roughly looks like, take a properly discontinuous action of a group Γ acting on a manifold M , then an orbifold looks locally like the coordinate system chart M → M / Γ . It is an orbit-manifold.)

Returning to our discussion of Bianchi spatial topologies, it is an intriguing fact that when compact spatial topologies are admitted to the standard Bianchi universes, the well-known properties met in standard Bianchi cosmology change to such a degree that the situation becomes almost reversed (see [ 128 – 134 ] for more information). Some Bianchi universes (IV and VI   h ) no longer exist, while those that contained the FRWL universes and were the generic ones with trivial topologies, now are no longer generic. For example, the VII   h universe must be isotropic and hence not generic, and the Bianchi IX universe with compact topology of any complexity is non-generic, but B-III and B-VIII now become the most general types, although they do not contain FRWL universes as special cases and get arbitrarily close to them.

The conclusion of the consideration of anisotropic universes with compact topologies is that they become heavily restricted, while isotropic ones are non-generic. Compact open universes become necessarily isotropic if they are assumed homogeneous, and flat spaces are generally preferred than closed or open ones.

The consideration of inhomogeneities and/or higher dimensionality may lead to further restrictions in future cosmological theories that may not be obtained otherwise except by such topological considerations. This is because there is an intimate relationship between inhomogeneity on a cosmologically large scale and topology [ 135 ]. We recall that the degree of a manifold, deg M , equal to the dimension of its isometry group, is a number that shows the generality of it, and for compact manifolds (like the ones we have been considering in this section) deg M = 0 if and only if there is no non-zero global Killing field. Now according to Bochner’s theorem, compact manifolds having negative Ricci curvature admit no non-zero global Killing vectorfields, which in turn implies that they can only be locally homogeneous. We note that from local isotropy (say about us) one can only conclude local homogeneity (because of constant curvature), not a global one as it is usually assumed in the Bianchi class.

The broader class of locally homogeneous cosmologies becomes therefore a very interesting area of study in mathematical cosmology (cf. [ 136 ] and references therein). This subject closely ties and hugely extends the area of Bianchi topology through an analysis of Hamiltonian cosmology in this context. The results are truly remarkable and lead to a completely new picture of what topological structures may arise in a global situation under the Einstein evolution. A pivotal role is played by the mathematical theory of symplectic reduction giving in the present context a reduced Hamiltonian function for cosmology, such that asymptotically in the future direction of cosmological expansion the evolution is dominated by the so-called hyperbolizable components, on each one of which the conformal geometry described by a suitable metric becomes homogenous and isotropic, locally indistinguishable from a negatively curved FRWL domain, cf. [ 137 ] for a review and [ 138 ] for more recent work on this problem.

Understanding the global behaviour of solutions to any set of cosmological equations (such as the Einstein equations) and their dependence upon changes of spatial topology is one of the most important problems of mathematical cosmology.

(e) Dynamical singularities

As we have already indicated, the nature of cosmological singularities is a problem left out by the singularity theorems of general relativity, or by the corresponding ones in eternal inflation. The issue of the nature of singularities is indeed a very complex one, having many facets, and has recently received a further boost of activity, which we shall now briefly discuss.

There is a classification of homogeneous universes reviewed in Collins & Ellis [ 139 ] exploiting techniques used in the singularity theorems (e.g. the Raychaudhuri equation) as well as qualitative studies of the field equations themselves (for the purposes of this classification, the field equations are ordinary differential equations so that standard dynamical systems techniques may be applied). In this case, there arise infinite density singularities as well as infinities in certain curvature invariants in all FRWL and orthogonal Bianchi universes. An interesting aspect of this classification is, however, that the big bang is not necessarily a point singularity, but other types are possible, such as pancakes, cigars, etc.

The situation changes completely in tilted Bianchi models (except type IX) where, apart from big bang singularities, there are now finite density ones, where there is the intriguing possibility that the fluid flow may continue past the finite density singularity, as the flow lines turn null and a Cauchy horizon is developed where the evolutions comes to an end (cf. figure 1, and Section 8 of [ 139 ]). This behaviour may be very clearly seen in type V models (which contain the open FRWL universes), and the overall behaviour is very different from that occurring in the simplest isotropic models for a variety of fluids. For Bianchi-type IX universes instead, we have the closed universe recollapse theorem of R. M. Wald, which states that there do not exist any eternally expanding Bianchi IX universes with matter satisfying the dominant energy condition, and has non-negative average pressure [ 140 ].

There is however another type of singularity classification that is based on the work of Choquet–Bruhat and stems from theorems giving sufficient conditions for causal g-completeness, that is necessary conditions for the development of cosmological singularities (cf. [ 141 ], [ 142 , ch. 8]). This leads directly to a complete dynamical classification for isotropic cosmologies into many distinct types [ 143 , 144 ]. In fact, there are four types of this classification that are found to play an important role in current models, as they appear commonly in dark energy universes with phantom fluids [ 145 ].

This leads to a ‘zoo’ of cosmological singularities developing in finite time into the future, already in the isotropic category, to say nothing about possibilities in more general homogeneous universes. These singularities include not only the traditional ones discussed earlier (big bang and big crunch) but many other types, such as big rips, sudden singularities, or very mild soft ones, turnarounds, etc. (see [ 146 ] for a brief review). They can be studied by using generalized power series [ 147 , 148 ], or the method of dominant balance [ 149 ], and further classified using the notion of strength of singularities. These studies have provided a clear picture of the dynamical behaviours possible, but are limited only in the isotropic category.

(f) Generic universes

As we have already discussed earlier, a common property of most of the cosmological solutions met in Einstein’s theory is the occurrence of infinite curvatures and densities a finite time in their past, a ‘cosmological singularity’. Despite lacking a rigorous definition of what a singularity is at the time, Lifshitz and Khalatnikov in 1963 (LK hereafter) were able to show that the generic singularity present in typical solutions of the Einstein equations cannot have the usual simple, monotone, power-law character predicted by isotropic (or simple anisotropic) solutions [ 150 ]. Their analysis also extended the Lifshitz 1946 instability study to the more general situation where the examined perturbations were now comparable with the horizon scale (proportional to the scale factor in a Friedmann universe).

In their analysis, LK introduced a method of proof that was based on series expansions around some unperturbed state (vacuum, or simple radiation solutions), and then counting the arbitrary functions present in the resulting solution of the field equations considered in the synchronous reference system. If that number was equal to the maximum allowed number by the initial value problem, they concluded that the solution was a general one, otherwise the solution was a special one based on a smaller number of free initial data (cf. §3d). For instance, the number of free initial data required for a general solution is equal to 4 for vacuum general relativity.

This function counting method is more useful than it is expected naively. There are solutions with the required number of arbitrary functions (in terms of function counting) to quantify as general solutions of the field equations of a given theory, and others that have smaller such numbers. In the latter case, the solutions possess a ‘transient’ nature, they are unstable. In the former case, they are general solutions of the field equations, and consequently stable in the time intervals they are taken. For example, full functions counting solutions include the perturbed de Sitter space found in [ 151 ], the sudden finite-time singularity solution in general relativity [ 152 ], and in Brans–Dicke theory [ 153 ], and the ultrastiff perfect fluid solution having p > ρ near quasi-isotropic singularities [ 154 ]. On the other hand, unstable, transient solutions are more common, for example, the standard quasi-isotropic solutions in general relativity is unstable to perturbations within that theory, cf. [ 155 , p. 368], [ 156 , 157 ], and so are solutions containing one or more fluids in that theory [ 158 , 159 ]. For other approaches to the function counting problem, see [ 160 , 161 ] and references therein.

The functions counted in these problems have simple physical interpretations. For example, the four free parameters in general relativity specifying a general solution in vacuum describe two shear modes plus anisotropies in the spatial curvature. When matter is added, the extra functions are the density or pressure, and the three (non-comoving) fluid velocity components, and although these contribute to the temperature fluctuations of the CMB radiation, they can be usually ignored being too small to be detected presently. However, many of the more elaborate cosmological models discussed in this paper, e.g. eternal inflation or M-theoretic models, predict effects that are in principle described by many arbitrary functions of the sort appearing in function counting problems. For inflation, they are also unobservable lying beyond our particle horizon, albeit isotropic.

(g) Dark energy

Dark energy representing the major component of the current acceleration of the universe has become the prime focus of attention since 1998 when two groups [ 162 , 163 ] using different datasets and techniques discovered that observations showed that the speed of the expansion of distant supernovae curved upwards with relation to their distance. This discovery has had an immense impact on cosmology ever since, and confirmed the expectations of a cosmological constant—the so-called Λ CDM (CDM here stands for ‘cold dark matter’, cf. [ 164 , Section 7.2]) phenomenological model—but allowed for the existence of many more exotic stresses to describe this mysterious kind of energy.

Today models of dark energy span the whole range of possibilities, from a cosmological constant, to scalar fields—the so-called quintessence—to modified gravity theories. It is indeed an amazing feature of this hypothetical type of energy the fact that it has unified in a single quest the incredible spectrum of modified gravity theories and other exotic forms of energy to search for the missing explanation of this observed effect.

Dark energy appears as a property inherent in space–time because it is perfectly uniform and insensitive to space–time being empty or full of galaxies, or with respect to the direction we look, or the era in the universe history, or spatial location. The constraints from the supernovae observations, the CMB temperature fluctuations and the baryon acoustic oscillations (that is residual sound waves imprinted in the clustering patterns) all converge to the astonishing dark energy budget of about 72% in the overall matter energy content of the universe. Another component of the remaining material in the universe consists of dark matter with a percentage of about another 24%. The mysterious fact that the visible components of matter and radiation may constitute only about a tiny 4% of the overall distribution, represents perhaps the most unbelievable, unexplained result in the whole history of astronomy.

We thus see that the fundamental themes required for an adequate explanation of the cosmological constant, the energy of the vacuum and the nature of dark energy are all linked together as suggested by both theory and observations. The completely and seemingly disparate and independent fields such as scalar-tensor theory, higher-order gravity, theories with screening, Palatini cosmology, effective theories, Horndeski gravity, higher-dimensional cosmology, Born–Infeld type theories, holographic theory and many others, appear as one field having different facets in this sense; for various excellent reviews of this vast field, see [ 165 – 172 ].

4.  Contents and abstracts of Part B of the Theme Issue

The abstracts of the contributions to volume 2 of the Theme Issue are as follows.

Assuming that superstring theory is the fundamental theory which unifies all forces of Nature at the quantum level, I argue that there are key limitations on the applicability of effective field theory techniques in describing early universe cosmology.

We present a short introduction to a non-standard cosmological scenario motivated by the duality symmetries of string theory, in which the big bang singularity is replaced with a ‘big bounce’ at high but finite curvature. The bouncing epoch is prepared by a long (possibly infinitely extended) phase of cosmic evolution, starting from an initial state asymptotically approaching the string perturbative vacuum.

We review studies on the singularity structure and asymptotic analysis of a 3-brane (flat or curved) embedded in a five-dimensional bulk filled with a ‘perfect fluid’ with an equation of state p = γ ρ , where p is the ‘pressure’ and ρ is the ‘density’ of the fluid, depending on the fifth space coordinate.

Regular solutions satisfying positive energy conditions in the bulk exist only in the cases of a flat brane for γ = − 1 or of AdS branes for γ ∈ [ − 1 , − 1 / 2 ) . More cases can be found by gluing two regular brunches of solutions at the position of the brane. However, only a flat brane for γ = − 1 leads to finite Planck mass on the brane and thus localizes gravity. In a more recent work, we showed that a way to rectify the previous findings and obtain a solution for a flat brane and a range of γ , that is both free from finite-distance singularities and compatible with the physical conditions of energy and finiteness of four-dimensional Planck mass, is by introducing a bulk fluid component that satisfies a nonlinear equation of state of the form p = γ ρ λ with γ < 0 and λ > 1 .

The observation of gravitational waves emitted by binary systems has opened a new astronomical window into the Universe. We describe recent advances in the field of scattering amplitudes applied to the post-Minkowskian expansion, and the extraction of the effective two-body gravitational potential. The techniques presented here apply to any effective field theory of gravity and are not restricted to four-dimensional Einstein gravity.

It is well known that quantum field theory (QFT) induces a huge value of the cosmological constant, Λ , which is outrageously inconsistent with cosmological observations. We review here some aspects of this fundamental theoretical conundrum (the cosmological constant problem) and strongly argue in favour of the possibility that the cosmic vacuum density ρ vac may be mildly evolving with the expansion rate H . Such a ‘running vacuum model’ (RVM) proposal predicts an effective dynamical dark energy without postulating new ad hoc fields (quintessence and the like). Using the method of adiabatic renormalization within QFT in curved space–time we find that ρ vac ( H ) acquires a dynamical component O ( H 2 ) caused by the quantum matter effects. There are also O ( H n ) ( n = 4 , 6 , … ) contributions, some of which may trigger inflation in the early universe. Remarkably, the evolution of the adiabatically renormalized ρ vac ( H ) is not affected by dangerous terms proportional to the quartic power of the masses ( ∼ m 4 ) of the fields. Traditionally, these terms have been the main source of trouble as they are responsible for the extreme fine tuning feature of the cosmological constant problem. In the context under study, however, ρ vac ( H ) is currently dominated by a constant term plus the aforementioned mild dynamical component ∼ ν H 2 ( | ν | ≪ 1 ), which makes the RVM to mimic quintessence.

Reduction in effective space–time dimensionality can occur in field-theory models more general than the widely studied dimensional reductions based on technically consistent truncations. Situations where wave function factors depend non-trivially on coordinates transverse to the effective lower dimension can give rise to unusual patterns of gauge symmetry breaking. Leading-order gauge modes can be left massless, but naturally occurring Stueckelberg modes can couple importantly at quartic order and higher, thus generating a ‘covert’ pattern of gauge symmetry breaking. Such a situation is illustrated in a five-dimensional model of scalar electrodynamics in which one spatial dimension is taken to be an interval with Dirichlet/Robin boundary conditions on opposing ends. This simple model illuminates a mechanism which also has been found in gravitational braneworld scenarios.

The nineteenth century Aether died with Special Relativity but was resurrected by General Relativity in the form of dark energy; a tensile material with tension equal to its energy density. Such a material is provided by the D-branes of string-theory; these can support the fields of supersymmetric particle-physics, although their en-energy density is cancelled by orientifold singularities upon compactification. Dark energy can still arise from supersymmetry-breaking anti-D-branes but it is probably time-dependent. Recent results on time-dependent compactifications to an FLRW universe with late-time accelerated expansion are reviewed.

We include the single graviton loop contribution to the linearized Einstein equation. Explicit results are obtained for one loop corrections to the propagation of gravitational radiation. Although suppressed by a minuscule loop-counting parameter, these corrections are enhanced by the square of the number of inflationary e-foldings. One consequence is that perturbation theory breaks down for a very long epoch of primordial inflation. Another consequence is that the one loop correction to the tensor power spectrum might be observable, in the far future, after the full development of 21 cm cosmology.

We present qualitative arguments in favour of an extension of the theory of the gravitational interaction beyond that resulting from the Hilbert–Einstein action. To this end, we consider a locally conformal invariant theory of gravity, discussed some 30 years ago by Mannheim and Kazanas. We discuss its exact solution of the static, spherically symmetric configurations and, based on these, we revisit some of the outstanding problems associated with gravity, high energy interactions and sketch potential resolutions within the conformal gravity framework.

In this discourse, we would like to discuss some issues of concept and principle in the context of the following three aspects. One, how Λ arises as a constant of space–time structure on the same footing as the velocity of light. These are the two constants innate to space–time without reference to any force or dynamics whatsoever, and are interwoven in the geometry of ‘free’ homogeneous space–time. Two, how does vacuum energy gravitate? Could its gravitational interaction in principle be included in general relativity or a new theory of quantum space–time/gravity would be required? Finally, we would like to raise the fundamental question, how does physically the Universe expand? Since there does not lie anything outside, it cannot expand into, instead it has to expand of its own—may be by creating new space out of nothing at each instant! Thus not only was the Universe created at some instant in the past marking the beginning in the big-bang, and at its edge it is also continuously being created at each epoch as space expands. We thus need quantum theory of space–time/gravity at the both ends—ultraviolet as well as infrared.

1 In distinction to the case of the BD, or scalar-tensor, theory, this scalar field was defined as proportional to the ln ⁡ f ′ ( R ) . Although there are claims in the literature of a relation of f ( R ) -gravity to Brans–Dicke theory by pure redefinition of the fields, these are based on non-cosmological scalar fields (such as proportional to the scalar curvature thus becoming negligible at cosmological scales), and extra conditions like f ″ ( R ) ≠ 0 , which unnecessarily restrict the original theory. On the other hand, conformal equivalence does not require such relationship between the two classes of theory, and shows that both f ( R ) -gravity and Brans–Dicke type theories are directly conformally equivalent to GR plus suitable scalar fields.

Data accessibility

Authors' contributions.

S.C.: writing—original draft, writing—review and editing; A.Y.: writing—original draft, writing—review and editing.

Both authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Conflict of interest declaration

We declare we have no competing interests.

No funding has been received for this article.

Conceptualising the Cosmos: Development and Validation of the Cosmology Concept Inventory for High School

• Open access
• Published: 05 February 2022
• Volume 21 , pages 251–275, ( 2023 )

Cite this article

You have full access to this open access article

• Saeed Salimpour   ORCID: orcid.org/0000-0002-0387-3152 1 , 2 , 3 , 4 ,
• Russell Tytler   ORCID: orcid.org/0000-0003-0161-7240 1 ,
• Brian Doig   ORCID: orcid.org/0000-0001-8971-6619 1 ,
• Michael T. Fitzgerald   ORCID: orcid.org/0000-0001-6554-1826 5 , 6 &
• Urban Eriksson   ORCID: orcid.org/0000-0001-6638-1246 7  

2451 Accesses

4 Citations

1 Altmetric

Explore all metrics

Cosmology concepts encompass complex spatial and temporal relations that are counterintuitive. Cosmology findings, because of their intrinsic interest, are often reported in the public domain with enthusiasm, and students come to cosmology with a range of conceptions some aligned and some at variance with the current science. This makes cosmology concepts challenging to teach, and also challenging to evaluate students’ conceptual understanding. This study builds on previous research of the authors investigating the methodological challenges for characterising students’ cosmology conceptions and the reasoning underlying these. Insights from student responses in two iterations of an open-ended instrument were used to develop a concept inventory that combined cosmological conceptions with reasoning levels based on the SOLO taxonomy. This paper reports on the development and validation of the Cosmology Concept Inventory (CosmoCI) for high school. CosmoCI is a 28-item multiple-choice instrument that was implemented with grade 10 and 11 school students ( n  = 234) in Australia and Sweden. Using Rasch analysis in the form of a partial credit model (PCM), the paper describes a validated progression in student reasoning in cosmology across four conceptual dimensions, supporting the utility of CosmoCI as an assessment tool which can also instigate rich discussions in the science classroom.

Similar content being viewed by others

Is the Universe Infinite? Characterising a Hierarchy of Reasoning in Student Conceptions of Cosmology Concepts Using Open-Ended Surveys

Saeed Salimpour, Russell Tytler, … Urban Eriksson

The Cosmic Interaction

Saeed Salimpour & Michael T. Fitzgerald

The Science of the Universe: Cosmology and Science Education

Avoid common mistakes on your manuscript.

Introduction

Cosmology as a field of inquiry has roots in mythology, philosophy, and religion. Cosmology pursues answers to some of the biggest and most fundamental questions about the Universe. As a precision observational science cosmology aims to tell the evolutionary history of the universe and predict its future. Cosmology topics are prevalent and consistent across most curricula at upper secondary level (Salimpour et al., 2020a ). The cosmology curriculum, because of the fundamental questions raised about our place in a mysterious universe, has enormous potential to engage the curiosity of students and create rich discussions in the classroom. Simultaneously, these topics encompass complex space–time relations which are innately counterintuitive and require reasoning beyond everyday experiences (Salimpour et al., 2021b , in review).

Conceptions and Reasoning

The history of research into student alternative/misconceptions in astronomy is rich and diverse. Over the years, various misconceptions have been identified and various evidence-based interventions proposed to scaffold students towards conceptual change. The iSTAR database (Slater et al., 2016 ) contains 186 articles focussing on some aspect of misconceptions in astronomy. Some examples of alternative conception studies include topics such as night/day (e.g.: Vosniadou & Brewer, 1994 ), seasons (e.g.: Slater et al., 2018 ), moon phases (e.g.: Trundle et al., 2007 ), cosmology (e.g.: Prather et al., 2002 ), size/distances (e.g.: Miller & Brewer, 2010 ), and astrobiology (e.g.: Offerdahl et al., 2002 ). One of the underlying challenges in addressing student conceptions is that they are based on intuition grounded in everyday experiences and language (e.g.: Nussbaum & Novak, 1976 ; Vosniadou & Brewer, 1992 , 1994 ), making them resistant to change (Driver & Easley, 1978 ). Furthermore, although studies have been extremely valuable in identifying alternative conceptions, there is much work that can be done in characterising the reasoning that underpins these conceptions.

Reasoning is one of the foundations of science, and one of the thrusts of science education has been to “instil the disciplinary habits of the mind of the scientist” (Kind & Osborne, 2017 , p. 9). However, as argued by Kind and Osborne ( 2017 ), despite the importance and richness of reasoning in science, science education has yet to conceptualise and characterise scientific reasoning in the classroom in a way that is reflective of the epistemic practices of science. Following Driver and Easley ( 1978 ) in order to characterise alternative conceptions in a way that allows them to be addressed effectively requires an understanding of the underlying reasoning patterns. Alternative conceptions research has in essence been of two varieties –— nomothetic and ideographic (Driver & Easley, 1978 ). While nomothetic studies have their place and compare student understanding to a standard, ideographic studies can productively explore the reasoning underpinning students’ conceptions (e.g.: Vosniadou & Brewer, 1994 ).

Previous Work on Concept Inventories

Concept Inventories (CIs) have gained popularity as a basis for formative and summative assessment processes, particularly in astronomy education. CIs are diagnostic tests consisting of multiple-choice questions designed to explore a student’s understandings of a particular construct or a series of constructs/concepts (Bailey, 2009 ; Sadler et al., 2009 ; Wilson, 2005 ). There has been much research into the benefits of using CIs (Bailey, 2009 ; Wallace & Bailey, 2010 ), and the methodologies used to create them (Lindell et al., 2007 ). As of this reading, a range of validated CIs exist in astronomy (Table 1 ), which have mostly been of the nomothetic type aimed at undergraduate level and focus on levels in conceptual understanding and do not necessarily privilege reasoning.

Validated CIs focussing on cosmology education include those of Wallace ( 2011 ), which is aimed at undergraduate students in an introductory astronomy course. The CI consists of conceptual questions on very focussed topics in cosmology: expansion and evolution of the universe, the Big Bang, and the evidence for dark matter in spiral galaxies, which are aligned to the level the concepts are taught at undergraduate level. The questions do explore student reasoning informed by construct (concept) maps for each of the topics; however, that is not the primary focus. The CI is designed to be a pre-/post-test to measure student learning gains via Lecture-Tutorials in undergraduate introductory astronomy. The work of Aretz et al. ( 2016 ) focuses on exploring student pre-instructional ideas about the Big Bang Theory, while Aretz et al. ( 2017 ) used student responses and the work of Wallace ( 2011 ) to refine a construct map about the expansion of the universe. As such, there is no CI in cosmology developed specifically for high school students that privileges a progression in reasoning combined with conceptual and declarative knowledge. Given the complex and counterintuitive nature of much of cosmology, understanding and supporting students’ reasoning are important as it helps unpack the complex space–time relations, the epistemic practices of the discipline, and the rich narrative of how we have uncovered the mysteries of the Cosmos. Characterising hierarchies of reasoning can also provide teachers with guidance on how to frame their teaching to effectively address alternative conceptions, in a way that scaffolds students to unpack the concepts in cosmology.

In our previous work (Salimpour et al., 2021b , in review) using student responses from an open-ended survey, we identified alternative conceptions which aligned with previous studies (Aretz et al., 2016 ; Hansson & Redfors, 2006 ; Prather et al., 2002 ; Trouille et al., 2013 ; Wallace, 2011 ), but extended these to identify the underlying reasoning patterns. Looking deeper at the alternative conceptions revealed that they were linked to three fundamental reasoning challenges associated with the following:

Navigating spatial and temporal relations over enormous scales

The counterintuitive nature of cosmological concepts

Intuition based on everyday language and experience

Using the above reasoning challenges, we were able to construct a preliminary progression scale based on the SOLO taxonomy (Collis & Biggs, 1979 ), which combined with the quality of conceptions, provided a potential basis for a concept inventory. This current paper describes the development and validation of a concept inventory for cosmology in high school. The paper begins by introducing the research aim, then an explanation of the framing underpinning the study. Next, the paper highlights the methodological approach to the study, the results, and subsequent analysis. The paper concludes with a brief discussion of the findings, implications of the concept inventory, and concluding remarks.

Research Aim

Effective instruments to measure student understanding need to extend beyond declarative content knowledge or base-level comprehension to characterise the reasoning associated with deeper levels of conceptual knowledge. The aim of the research described in this paper is to develop and validate a concept inventory that can be used to appropriately characterise and monitor progression in student reasoning and learning in cosmology. The Cosmology Concept Inventory (CosmoCI) is a multi-dimensional concept inventory aimed at high school students, that moves beyond characterising lists of conceptions to enable exploration of progression in sophistication of student reasoning.

Framing This Study

Given this study aims to highlight the development and validation of a concept inventory for cosmology, we describe the framing of the study with regard to validity. The notion of validity is complex, and over many decades, there have been a range of debates about the various aspects of validity (e.g.: Cronbach, 1971 ; Cronbach & Meehl, 1955 ; Lissitz & Samuelsen, 2007 ; Messick, 1989 ; Sireci, 2007 ; Sireci & Parker, 2006 ). Traditionally, validity has been considered to be of three types: criterion, content, and construct. This has evolved into a unified theory of construct validity which has subsumed criterion and content validity as evidence for a more general framing of construct validity (Messick, 1989 ). What is considered valid depends on the context and aim and has to include expert judgement of the items in terms of their alignment with canonical/consensus ideas. Also relevant is the internal coherence across the levels, and alignment with students’ thinking.

The American Educational Research Association, American Psychological Association, and National Council on Measurement, in the most recent version of the Standards for Educational and Psychological testing ( 2014 ), define validity as the “degree to which evidence and theory support the interpretations of test scores for proposed uses of tests” (p. 11).

From an educational perspective, Lissitz and Samuelsen ( 2007 ) emphasise the importance of content validity; however, Sireci ( 2007 ) states that “A serious effort to validate use of an educational test should involve both subjective analysis of test content and empirical analysis of test score and item response data.” (p.481). Therefore, content validity on its own is not adequate. More recently, Sireci ( 2016 ) argues that the interpretation of test scores “is part of validation, and partly what validity refers to. Validating interpretations of test scores is a necessary component of any validation endeavour. However, it is not sufficient for defending the use of a test for a particular purpose” (p. 231).

This study aims to develop a concept inventory tool that will tap into students’ knowledge and reasoning in cosmology concepts, aligned with the four dimensions of cosmology developed by Salimpour et al. ( 2020b ): size and scale, spacetime location, composition of the universe, and evolution of the universe. This tool is intended to.

act as a pre-test to explore students’ knowledge in relation to key concepts in cosmology

alert teachers to the key ideas in cosmology and provide them with an understanding of student thinking and reasoning

provide a stimulus for classroom discussion

provide a tool to monitor student learning

Methodology

The methodological approach in this study consists of two parts; the first is the process undertaken for developing the cosmology concept inventory (CosmoCI). The second involves using Rasch analysis in the form of a partial credit model (PCM) (Masters, 1982 ) to establish a scale, and evaluate the internal coherence and utility of the instrument.

Development of CosmoCI

The development of CosmoCI is underpinned by a Design-Based Research (DBR) framework (Anderson & Shattuck, 2012 ; Collins, 1992 ; Collins et al., 2004 ). The DBR cycle used in this study is visualised in Fig.  1 .

Visualisation showing the different aspect of the DBR cycle employed in this study. As is noted, each step is iterative, allowing insights to be used in the next step

The first iteration of CosmoCI consisted of 23 open-ended and five multiple choice questions. The questions were developed by reviewing curriculum statements related to cosmology in 52 curricula, which covered the OECD countries, China, and South Africa (Salimpour et al., 2020a ) and the International Baccalaureate (IB) Diploma programme, and using the curriculum statements to extract key concepts in cosmology that were prevalent across most curricula. These were then categorised into four overarching conceptual dimensions of cosmology: size and scale, spacetime location, composition of the universe, and evolution of the universe (Salimpour et al., 2020b ). The questions drew on previous research carried out at an undergraduate level (Wallace, 2011 ), filtered through the research team’s experience in both cosmology and teaching cosmology. Mostly open-ended questions were used to allow students to express their reasoning without being restricted. The first iteration of CosmoCI was implemented with a pilot group of students ( n  = 75). The analysis provided preliminary insights into students’ knowledge and reasoning in relation to concepts across the four dimensions and allowed for the preliminary development of a universal rubric for characterising student responses (Salimpour et al., 2020b ). On this basis, also, the questions were refined.

The second iteration used a slightly refined version in the wording of questions based on student responses. This is because student responses for some questions hinted that (a) some students may not have understood the question and (b) students were not sufficiently prompted to explain their reasoning. In addition, for the five multiple-choice questions, students were now asked to explain the reasoning for their choice. This second iteration was implemented with a larger group of participants ( n  = 286). The analysis of the student responses allowed for the refinement of the grading rubric to include finer level distinctions (initially 16 levels and then 14 levels) that attempted to capture the levels of student reasoning, while encompassing the variety of responses (Salimpour et al., 2021b , in review). The underlying framework for building the levels of student responses was based on the SOLO taxonomy (Collis & Biggs, 1979 ). This was a natural outcome that had developed during the first round of analysis, except finer levels within each SOLO level were included to capture the range of student responses. The finer-grained analysis, although helpful from a research perspective, we felt would be challenging for teachers to use to gain a big picture view of student reasoning at various levels of progression. Further, the patterns of responses across the questions and dimensions were extremely complex to analyse. Therefore, the finer levels were eventually collapsed into four of the five SOLO levels: relational, multi-structural, uni-structural, and pre-structural (Salimpour et al., 2021b , in review). This approach allowed broader patterns of student reasoning to be extracted, mapped to the SOLO levels. The reason the fifth SOLO level — extended abstract — was not included is that the nature of the questions being asked and the type of responses being canvassed did not prompt this extended form of reasoning.

The concept inventory idea is essentially based on the distractor-driven multiple-choice test (DDMC) (Sadler et al., 2009 ). The use of a multiple-choice format allows student understanding to be objectively assessed because it is practically efficient for teachers to use in the classroom environment. The task in this study was to take the variety of student responses for each question to construct multiple choice options that were exemplars of the responses at each of the four SOLO levels. That is, for each question, each option represented reasoning at a different SOLO level, constructed through thematic analyses of the open responses. Several cycles of refinement to the wording were made by the research team. The options were carefully designed not to be identifiable as higher level based on the use of abstracted disciplinary language and/or the length of the option. The mapping to SOLO levels provides teachers with a framework to characterise and appreciate the level of sophistication in student reasoning. An example of this categorisation approach is shown in Table 2

Brief Overview of CosmoCI

The question structure of CosmoCI (Appendix) is based on four overarching conceptual dimensions (Fig.  2 ) each focussing on a particular aspect of Cosmology. Each dimension encompasses key concepts and discoveries in cosmology, for example the large-scale structure, dark energy, dark matter, and the cosmic microwave background, all of which are present in curricula and found in high school physics textbooks. CosmoCI encompasses both declarative knowledge and higher-level conceptual knowledge, placing the progression of student reasoning at the core of its structure. The content coverage is organised under the four overarching, fundamental dimensions described above (Fig.  2 ).

Characterisation of the four conceptual dimensions of cosmology

To illustrate the scope of CosmoCI and how the multiple-choice options are aligned to the SOLO taxonomy, Table 3 provides an example of a question from each dimension. It can be noted that at each SOLO level fundamental reasoning similarities can be seen which are explained in the “Essence of levels” as shown in Table 2 .

Validation of CosmoCI

This third iteration of CosmoCI (Appendix) was implemented with a cohort of students in Australia and Sweden. The participants included high school students in grades 10 and 11 ( n  = 234). The sample selection was based on random opportunistic sampling (Newby, 2014 ). Australia and Sweden are used as instances, given that curriculum statements related to cosmology are relatively homogeneous across curricula (Salimpour et al., 2020a ), and the authors have knowledge of the curriculum and access to schools in Australia and Sweden.

This study uses an item response theory (IRT) approach to validation. IRT is an item level approach and in essence aims to explore the relationship between test item (question) difficulty, and student ability (e.g.: Boone et al., 2014 ; Hambleton & Jones, 1993 ). Basically, easier questions are accessible by most students, and higher ability students are more likely to answer correctly difficult questions compared to a lower ability student. One aspect of IRT models is that results are independent of the participant group. IRT and its associated models (1-, 2-, 3-parameter) are independent of the participants taking the test. It should be emphasised that although the Rasch Model in some instances is referred to as being a type of IRT (specifically 1-parameter IRT model), there is a fundamental philosophical difference “…in that one model, IRT, is altered to fit data and one model, Rasch, is not altered to fit data” (Boone et al., 2014 , p. 453). This current study uses Masters’ ( 1982 ) partial credit model (PCM), which is a development of the basic Rasch model, and shares the defining characteristics associated with other Rasch models. The PCM is used for polytomously scored items, which is to say that the distractors in a question are given different levels of credit because they demonstrate a particular level of knowledge or reasoning (Masters, 1988 ). Therefore, multiple-choice questions are not solely marked as “correct” or “incorrect.” For tests designed for the PCM model, the reasoning underpinning every multiple-choice option is distinct, with responses providing teachers with insights into the fundamental challenges that students face with regards to complex concepts (see for example, Briggs et al., 2006 ). This principle of identifying student reasoning is at the heart of this study, and thus using the PCM offers a framework for pursuing this line of inquiry.

The raw data from the CosmoCI was run through a custom Python script to clean the data, and format it for use with the QUEST software package (Adams & Khoo, 1993 ). QUEST is an analysis package that implements Rasch analysis on both dichotomous and polytomous data.

Results and Analysis

The statistical analysis reveals a reasonable fit to the Rasch model within the acceptable range set by literature (Adams & Khoo, 1993 ). Figure  3 shows that the item scores fit well within the “tram lines” (dotted lines).

Analysis of the item fit to the Rasch model. Dotted lines represent the boundaries of the model fit

One of the key outputs from the analysis is a set of Wright Maps (Wilson, 2005 ). Wright Maps allow researchers to quickly see the relationship between item difficulty and student ability, by placing both on the same measurement scale (Logit scale – log of the odds) (Fig.  4 ). This scale is a probabilistic measure and not an actual measure. Wright Maps were generated from the data analysis for each of the four conceptual dimensions in cosmology: size and scale, spacetime location, composition of the universe, and evolution of the universe (Salimpour et al., 2020b ). The right side of the Wright Map lists the items, with the notation used being a three-letter word (Siz, Loc, Com, Evo), followed by ‘x.y’, where x is question number in that dimension and y is the multiple-choice level. Therefore, Siz1.2, refers to question 1, multiple-choice level 2 option (uni-structural) in the dimension size and scale. The order of items increases in difficulty (bottom to top). The left side of the Wright Map lists the students represented by X (which can be any number of students), in order of increasing ability (bottom to top). A student located in the same line as an item indicates that the student has a 50% chance of choosing that item option. Items above the student’s position are harder for that student (students have less than 50% chance of choosing that reasoning option), and items below that student’s position are easier (students have greater than 50% chance of choosing that reasoning option).

Wright map showing all the questions and choice options. Each X represents 3 students. The variation in font thickness differentiates between the four SOLO levels

Looking at the Wright Map (Fig.  4 ), it can be seen that the multiple-choice options for each question line up in the predicted SOLO reasoning order, providing a validation of the identification of the levels of reasoning underpinning the different choices in each question. There are, however, some outliers where the SOLO levels are inconsistent across questions which will be discussed below. Overall, the Wright Map also reveals that the multiple-choice options satisfactorily align with the ability of the students; i.e. the highest ability students are able to pick the multiple-choice options which are at a relational level (4).

There are some outliers in the choice options. For example, items Evo1.3 and Evo3.3 were both assigned to a multi-structural level in design of the instrument, yet Fig.  4 shows that they are among the least difficult items when implemented with students. Item Evo1.3 gives the age of the universe as “more than 100 billion years,” and item Evo3.3 states that the Big Bang Theory “is a theory for the origin/creation of the Universe, that proves an explosion of a tiny singularity led to the formation of the Universe.” The solution to this anomaly lies in the notion of student alternative conceptions. With regard to item Evo1.3, previous work shows that students reason that because the universe is so large, it must be extremely old (Salimpour et al., 2021b , in review). While for item Evo3.3, there is a prevalent alternative conception that the Big Bang is an explosion a point in space; this has been shown in other studies as well (Aretz et al., 2016 ; Wallace, 2011 ), and is perhaps owing to the way representations depict the Big Bang Theory (Salimpour et al., 2021a ). Perhaps, it is not surprising that students find this option attractive due to its pervasiveness as a popular metaphor, distinct from choosing the response through the reasoning process it seems to represent. The reason these items are deemed multi-structural lies in the fact that students need to bring together different lines of reasoning which are sophisticated, albeit alternative.

In addition to the above, the outliers are also an indication of a more fundamental challenge when collapsing the SOLO levels. The fine-grained expanded (14 and 16) SOLO categories made distinctions that took into account the following aspects present in student responses:

the sophistication of reasoning;

whether students’ ideas were scientifically correct;

whether students were expressing alternative conceptions in a considered way;

the amount of detail/justification students providing in their responses; and

whether the multiple-choice component (if present) of a question was correct.

Some of these distinctions were lost in collapsing the data. However, this was justified since the complexity of the open responses represented by those categories masked the broader patterns of reasoning seen more clearly when the number of categories was reduced. We argue that the simplification offered by SOLO allows the instrument to capture patterns in students’ levels of thinking across questions and the four conceptual dimensions (size and scale, spacetime location, composition and evolution of the universe). Nevertheless, we acknowledge that the SOLO levels cannot capture all elements of students’ reasoning (Biggs & Collis, 1989 ; Watson et al., 1995 ).

This study highlighted the process of developing and validating a cosmology concept inventory — CosmoCI — targeted at the high school level. The Rasch analysis in the form of a PCM shows a good alignment of the multiple-choice items in terms of increasing levels of sophistication and difficulty in line with student ability. For every question, the levels line up in the predicted order. The iterative coding of student responses naturally fit the SOLO taxonomy which provided a general framework for characterising the level of sophistication of the reasoning underpinning student responses. One of the key challenges of this study was unpicking knowledge and reasoning, and their interaction in framing student responses. The use of two iterations of open-ended questions allowed relations between “level of knowledge” and “pattern of thinking” to be explored (Salimpour et al., 2020b ) and subsequently coordinated in CosmoCI.

The complexities in student responses at first warranted a fine-grained approach and so the SOLO taxonomy was expanded to capture these; however, to capture broad parameters of reasoning collapsing to the four SOLO levels provided a suitable characterisation. While the SOLO taxonomy theoretically represents distinct levels, in practice, these have blurred interfaces that allow characteristics from one level to manifest in adjoining levels. This is particularly evident in the clustering of multiple-choice options in the Wright map (Fig.  4 ). For example, among the level 4 options, there are some level 3 options with the same Logit score. Nevertheless, the consistencies in ordering of levels in the map demonstrate that the SOLO taxonomy as used in this study provides a valid and useful guide to anchor the progression in sophistication of student reasoning and knowledge in cosmology.

CosmoCI, through the situating of responses in a progression of reasoning, can be used as an assessment tool pre- and post-instruction. In addition, representation of the narrative of how scientists have come to know that the dark energy makes up the majority of the universe, that the universe is 13.8 billion years old, or that the universe is undergoing accelerated expansion, coupled with the innate interest it piques in students, means the CosmoCI can be a powerful stimulus to opening up rich discussions in the classroom. This latter aspect of instigating discussions was supported by the feedback from teachers who implemented CosmoCI in the classroom. The collection of questions can set the stage for learning to begin and support teachers to frame learning activities, as much as it can evaluate student conceptual understanding and reasoning in cosmology. This idea of determining what the student knows, so that teaching can be framed accordingly, echoes the views of Ausubel ( 1968 ).

It could be argued that sustaining such discussions in the classroom by teachers who may not be confident with the subject area could prove challenging. However, with support, teachers could extend discussions of the questions raised by CosmoCI to consider the epistemic practices of cosmology — the way that ideas are built on evidence. The discussion of ideas, views, theories, and hypotheses form a vital part of the epistemic practices of science. The questions in CosmoCI and their categorisation into the four conceptual dimensions of cosmology provide the scaffolding needed to focus and instigate such discussions. With that in mind, the authors of this study are in the process of developing a teaching sequence for cosmology that incorporates an extensive guide for teachers, which includes a guide on unpacking the CosmoCI instrument.

Given that CosmoCI is developed through a design-based research (DBR) approach, the next stage will be the refinement of CosmoCI over various classroom implementations and more structured feedback from teachers.

Conclusions

This study aimed to develop and validate a Cosmology Concept Inventory (CosmoCI) for high school that can be used to monitor progression in reasoning and learning in cosmology. The validation process, through the application of a partial credit model IRT, shows that it is possible to capture the reasoning levels of students in cosmology using a multiple-choice instrument. The SOLO taxonomy proved versatile in capturing levels of reasoning associated with conceptions in cosmology. The instrument has an educative purpose through this reasoning focus, allowing teachers to discern the types of reasoning associated with cosmological declarative knowledge and concepts, acting as a formative and summative assessment tool to capture student thinking. It can open up discussions for teachers and students, and the possibility of informed support for moving students’ thinking in cosmology forward. The inclusion within the instrument of aspects of the evidence bases for cosmological knowledge also aligns it with current thinking about the need to represent scientific practices in teaching and learning science, and with increasing attention to epistemic knowledge as an appropriate outcome. A beneficial outcome from implementing CosmoCI in the first author’s classroom and those of other teachers who were part of the study was the rich discussions instigated between students and the teacher, providing insights into their thinking and the opportunity to frame their learning.

Adams, R. J., & Khoo, S.-T. (1993). Quest: The interactive test analysis system . Quest, Australian Council for Educational Research Press.

American Educational Research Association. (2014). Standards for educational and psychological testing, 2014 Edition.

Anderson, T., & Shattuck, J. (2012). Design-based research: A decade of progress in education research? Educational Researcher, 41 (1), 16–25. https://doi.org/10.3102/0013189X11428813

Article   Google Scholar  

Aretz, S., Borowski, A., & Schmeling, S. (2016). A fairytale creation or the beginning of everything: Students’ pre-instructional conceptions about the Big Bang Theory. Perspectives in Science, 10 , 46–58. https://doi.org/10.1016/j.pisc.2016.08.003

Aretz, S., Borowski, A., & Schmeling, S. (2017). Development and evaluation of a construct map for the understanding of the expansion of the Universe. Science Education Review Letters, 2017 , 1–8. https://doi.org/10.18452/8216

Ausubel, D. P. (1968). Educational psychology: A cognitive view . Holt Rinehart and Winston.

Bailey, J. M. (2009). Concept inventories for ASTRO 101. The Physics Teacher, 47 (7), 439–441. https://doi.org/10.1119/1.3225503

Bailey, J. M., Johnson, B., Prather, E. E., & Slater, T. F. (2012). Development and validation of the star properties concept inventory. International Journal of Science Education, 34 (14), 2257–2286. https://doi.org/10.1080/09500693.2011.589869

Biggs, J., & Collis, K. (1989). Towards a model of school-based curriculum development and assessment using the SOLO taxonomy. Australian Journal of Education, 33 (2), 151–163. https://doi.org/10.1177/168781408903300205

Boone, W. J., Staver, J. R., & Yale, M. S. (2014). Rasch analysis in the human sciences . Springer. https://doi.org/10.1007/978-94-007-6857-4

Briggs, D. C., Alonzo, A. C., Schwab, C., & Wilson, M. (2006). Diagnostic assessment with ordered multiple-choice items. Educational Assessment, 11 (1), 33–63. https://doi.org/10.1207/s15326977ea1101_2

Chastenay, P., & Riopel, M. (2020). Development and validation of the moon phases concept inventory for middle school. Physical Review Physics Education Research, 16 (2), 020107. https://doi.org/10.1103/PhysRevPhysEducRes.16.020107

Collins, A. (1992). Toward a design science of education. In E. Scanlon & T. O’Shea (Eds.), New directions in educational technology (pp. 15–22). Springer.

Chapter   Google Scholar  

Collins, A., Joseph, D., & Bielaczyc, K. (2004). Design research: Theoretical and methodological issues. Journal of the Learning Sciences, 13 (1), 15–42. https://doi.org/10.1207/s15327809jls1301_2

Collis, K. F., & Biggs, J. B. (1979). Classroom examples of cognitive development phenomena: The SOLO taxonomy . Education Department, University of Tasmania.

Cronbach, L. J. (1971). Test validation. In Educational measurement (2nd ed., p. 443). American Council on Education.

Cronbach, L. J., & Meehl, P. E. (1955). Construct validity in psychological tests. Psychological Bulletin, 52 (4), 281–302. https://doi.org/10.1037/h0040957

Driver, R., & Easley, J. (1978). Pupils and paradigms: A review of literature related to concept development in adolescent science students. Studies in Science Education, 5 (1), 61–84. https://doi.org/10.1080/03057267808559857

Finegold, M., & Pundak, D. (1991). A study of change in students’ conceptual frameworks in Astronomy. Studies in Educational Evaluation, 17 (1), 151–166.

Gingrich, E. C., Ladd, E. F., Nottis, K. E. K., Udomprasert, P., & Goodman, A. A. (2015). The Size, Scale, and Structure Concept Inventory (S3CI) for astronomy. In G. Schultz, S. Buxner, L. Shore, & J. Barnes (Eds.), Celebrating science: Putting education best practices to work (Vol. 500, pp. 269–279). Astronomical Society of the Pacific Conference Series. Retrieved from http://www.aspbooks.org/a/volumes/article_details/?paper_id=37504

Hambleton, R. K., & Jones, R. W. (1993). Comparison of classical test theory and item response theory and their applications to test development. Educational Measurement: Issues and Practice, 12 (3), 38–47. https://doi.org/10.1111/j.1745-3992.1993.tb00543.x

Hansson, L., & Redfors, A. (2006). Swedish upper secondary students’ views of the origin and development of the universe. Research in Science Education, 36 (4), 355–379. https://doi.org/10.1007/s11165-005-9009-y

Kind, P., & Osborne, J. F. (2017). Styles of scientific reasoning: A cultural rationale for science education? Science Education, 101 (1), 8–31. https://doi.org/10.1002/sce.21251

Ladd, E. (Ned), Nottis, K., Udomprasert, P., & Goodman, A. A. (2015). Initial development of a concept inventory to assess size, scale, and structure in introductory astronomy. US-China Education Review B , 5 (11), 689–700. https://doi.org/10.17265/2161-6248/2015.11.001

Lazendic-Galloway, J., Fitzgerald, M., & McKinnon, D. H. (2017). Implementing a studio-based flipped classroom in a first year Astronomy course. International Journal of Innovation in Science and Mathematics Education (Formerly CAL-Laborate International ), 24 (5), 35–47. https://openjournals.library.sydney.edu.au/index.php/CAL/article/view/10670

Lindell, R. S. (2001). Enhancing college students’ understanding of lunar phases [Doctoral dissertation, University of Nebraska - Lincoln]. ETD Collection for University of Nebraska - Lincoln.

Lindell, R. S., Peak, E., & Foster, T. M. (2007). Are they all created equal? A comparison of different concept inventory development methodologies. AIP Conference Proceedings, 883 (1), 14–17. https://doi.org/10.1063/1.2508680

Lissitz, R. W., & Samuelsen, K. (2007). A suggested change in terminology and emphasis regarding validity and education. Educational Researcher, 36 (8), 437–448. https://doi.org/10.3102/0013189X07311286

Masters, G. N. (1982). A rasch model for partial credit scoring. Psychometrika, 47 (2), 149–174. https://doi.org/10.1007/BF02296272

Masters, G. N. (1988). The analysis of partial credit scoring. Applied Measurement in Education, 1 (4), 279–297. https://doi.org/10.1207/s15324818ame0104_2

Messick, S. (1989). Meaning and values in test validation: The science and ethics of assessment. Educational Researcher, 18 (2), 5–11. https://doi.org/10.3102/0013189X018002005

Miller, B. W., & Brewer, W. F. (2010). Misconceptions of astronomical distances. International Journal of Science Education, 32 (12), 1549–1560. https://doi.org/10.1080/09500690903144099

Newby, P. (2014). Research methods for education (2nd ed.). Routledge. http://ebookcentral.proquest.com/lib/deakin/detail.action?docID=1734204

Nussbaum, J., & Novak, J. D. (1976). An assessment of children’s concepts of the earth utilizing structured interviews. Science Education, 60 (4), 535–550. https://doi.org/10.1002/sce.3730600414

Offerdahl, E. G., Prather, E. E., & Slater, T. F. (2002). Students’ pre-instructional beliefs and reasoning strategies about astrobiology concepts. Astronomy Education Review, 1 (2), 5–27. https://doi.org/10.3847/AER2002002

Prather, E. E., Slater, T. F., & Offerdahl, E. G. (2002). Hints of a fundamental misconception in cosmology. Astronomy Education Review, 1 (2), 28–34. https://doi.org/10.3847/AER2002003

Pundak, D. (2016). Evaluation of conceptual frameworks in Astronomy. Problems of Education in the 21st Century , 69 (1), 57–75.

Sadler, P. M., Coyle, H., Miller, J. L., Cook-Smith, N., Dussault, M., & Gould, R. R. (2009). The astronomy and space science concept inventory: Development and validation of assessment instruments aligned with the K-12 national science standards. Astronomy Education Review, 8 (1), 010111. https://doi.org/10.3847/AER2009024

Salimpour, S., Bartlett, S., Fitzgerald, M. T., McKinnon, D. H., Cutts, K. R., James, … Ortiz-Gil, A. (2020a). The gateway science: A review of astronomy in the OECD school curricula, including China and South Africa. Research in Science Education , 51 (4), 975–996. https://doi.org/10.1007/s11165-020-09922-0

Salimpour, S., Tytler, R., & Fitzgerald, M. T. (2020b). Exploring the cosmos: The challenge of identifying patterns and conceptual progressions from student survey responses in cosmology. In R. Tytler, P. White, J. Ferguson, & J. C. Clark (Eds.), Methodological Approaches to STEM Education Research (Vol. 1, pp. 203–228). Cambridge University Press.

Salimpour, S., Tytler, R., Eriksson, U., & Fitzgerald, M. T. (2021a). Cosmos visualized: Development of a qualitative framework for analyzing representations in cosmology education. Physical Review Physics Education Research , 17 (1), 013104. https://doi.org/ https://doi.org/10.1103/PhysRevPhysEducRes.17.013104

Salimpour, S., Tytler, R., Fitzgerald, M. T., & Eriksson, U. (2021b). Is the Universe infinite? Exploring high student conceptions of cosmology concepts using open-ended surveys. (In Review).

Simon, M. N., Prather, E. E., Buxner, S. R., & Impey, C. D. (2019). The development and validation of the Planet Formation Concept Inventory. International Journal of Science Education, 41 (17), 2448–2464. https://doi.org/10.1080/09500693.2019.1685140

Sireci, S. G. (2007). On validity theory and test validation. Educational Researcher, 36 (8), 477–481.

Sireci, S. G. (2016). On the validity of useless tests. Assessment in Education: Principles, Policy & Practice, 23 (2), 226–235. https://doi.org/10.1080/0969594X.2015.1072084

Sireci, S. G., & Parker, P. (2006). Validity on trial: Psychometric and legal conceptualizations of validity. Educational Measurement: Issues and Practice, 25 (3), 27–34. https://doi.org/10.1111/j.1745-3992.2006.00065.x

Slater, E., Morris, J., & Mckinnon, D. H. (2018). Astronomy alternative conceptions in pre-adolescent students in Western Australia. International Journal of Science Education , 40 (17), 2158–2180. https://doi.org/10.1080/09500693.2018.1522014

Slater, S. J. (2014). The development and validation of the test of astronomy standards (TOAST). Journal of Astronomy & Earth Sciences Education (JAESE), 1 (1), 1–22.  https://doi.org/10.19030/jaese.v1i1.9102

Slater, S. J., Tatge, C. B., Bretones, P. S., Slater, T. F., Schleigh, S. P., McKinnon, D. H., & Heyer, I. (2016). iSTAR first light: Characterizing astronomy education research dissertations in the iSTAR database. Journal of Astronomy & Earth Sciences Education (JAESE), 3 (2), 125–140.  https://doi.org/10.19030/jaese.v3i2.9845

Trouille, L. E., Coble, K., Cochran, G. L., Bailey, J. M., Camarillo, C. T., Nickerson, M. D., & Cominsky, L. R. (2013). Investigating student ideas about cosmology III: Big Bang Theory, expansion, age, and history of the Universe. Astronomy Education Review , 12 (1), 010110. https://doi.org/10.3847/AER2013016

Trundle, K. C., Atwood, R. K., & Christopher, J. E. (2007). Fourth-grade elementary students’ conceptions of standards-based lunar concepts. International Journal of Science Education, 29 (5), 595–616. https://doi.org/10.1080/09500690600779932

Vosniadou, S., & Brewer, W. F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive Psychology, 24 (4), 535–585. https://doi.org/10.1016/0010-0285(92)90018-W

Vosniadou, S., & Brewer, W. F. (1994). Mental models of the day/night cycle. Cognitive Science, 18 (1), 123–183. https://doi.org/10.1207/s15516709cog1801_4

Wallace, C. S. (2011). An investigation into introductory astronomy students’ difficulties with cosmology, and the development, validation, and efficacy of a new suite of cosmology lecture-tutorials. Astrophysical & Planetary Sciences Graduate Theses & Dissertations . http://scholar.colorado.edu/astr_gradetds/9

Wallace, C. S., & Bailey, J. M. (2010). Do concept inventories actually measure anything? Astronomy Education Review , 9 (1), 010116. https://doi.org/10.3847/AER2010024

Watson, J. M., Collis, K. F., Callingham, R. A., & Moritz, J. B. (1995). A model for assessing higher order thinking in statistics. Educational Research and Evaluation, 1 (3), 247–275. https://doi.org/10.1080/1380361950010303

Wilson, M. (2005). Constructing measures: An item response modeling approach . Routledge.

Download references

Acknowledgements

The authors are very grateful to all the teachers and students from schools in Australia and Sweden who participated in this study. The fruition of this project would not have been possible without your keen and enthusiastic support. The authors would like to thank the reviewers for their constructive feedback in preparing this manuscript.

Open Access funding enabled and organized by CAUL and its Member Institutions. Dr. Michael Fitzgerald is the recipient of an Australian Research Council Discovery Early Career Award (project number DE180100682) funded by the Australian Government.

Author information

Authors and affiliations.

Deakin University, Victoria, Burwood, Australia

Saeed Salimpour, Russell Tytler & Brian Doig

Office of Astronomy for Education, International Astronomical Union, Heidelberg, Germany

Saeed Salimpour

Haus Der Astronomie, Heidelberg, Germany

Max Planck Institute for Astronomy, Heidelberg, Germany

Deakin University, Burwood, Victoria, Australia

Michael T. Fitzgerald

Las Cumbres Observatory, Goleta, CA, USA

National Resource Centre for Physics Education, Department of Physics, Lund University, Lund, Sweden

Urban Eriksson

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Saeed Salimpour .

Ethics declarations

This project was approved by Faculty of Arts and Education Human Ethics Advisory Group (HEAG) under the terms of Deakin University’s Human Research Ethics Committee (DUHREC): HAE-19–049.

Conflict of Interest

The authors declare no competing interests.

Cosmology Concept Inventory (CosmoCI).

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Salimpour, S., Tytler, R., Doig, B. et al. Conceptualising the Cosmos: Development and Validation of the Cosmology Concept Inventory for High School. Int J of Sci and Math Educ 21 , 251–275 (2023). https://doi.org/10.1007/s10763-022-10252-y

Download citation

Received : 31 May 2021

Accepted : 21 January 2022

Published : 05 February 2022

Issue Date : January 2023

DOI : https://doi.org/10.1007/s10763-022-10252-y

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Cosmology education
• Concept inventory
• Student conceptions
• Partial credit model
• Find a journal
• Publish with us
• Track your research

• CTC structure
• Job/PhD opportunities
• Mathematics at the University of Cambridge
• Collaborators
• News archive
• How to find us
• Information for newcomers
• Contact details

Fundamental Theory and Cosmology

• Critical Tests of the Inflationary Paradigm and the Cosmic Microwave Background
• Gravitational Waves and Signatures of the Early Universe
• Mutability of the Laws of Physics

Black Holes

• Other Research
• Upcoming Conferences and Workshops
• Past Conferences and Workshops
• Public Lecture Series
• Ultra-High-Frequency Gravitational Waves Initiative

The Origins of the Universe

• Public Events
• Stephen Hawking
• Studying at DAMTP
• A Message from Professor Stephen Hawking
• Current supporters
• How to give

Research Topics

Fundamental theory suggests that when we survey our Universe we discern only a shadow of a much vaster topologically complex higher-dimensional world. Almost all theorists are agreed that Einstein's four-dimensional spacetime is only part of an as yet only dimly envisaged, more fundamental structure, in which space, time and matter exist on the same footing.

Cosmology is a rapidly changing field and the most exciting innovations cannot be foreseen with certainty. For this reason, CTC will operature flexibly and respond rapidly to new developments. Nevertheless, we believe we can identify ambitious and timely fields of research where important progess is likely in the near future.

Research Overview

The purpose of the Centre for Theoretical Cosmology is to advance the scientific understanding of our universe, developing cosmological theories that are both mathematically consistent and observationally testable.

Read more »

One of the central problems in connecting fundamental theory with cosmology is how inflation emerges from within a higher-dimensional spacetime.

Critical tests of the inflationary paradigm

The cosmic microwave background radiation, left over from the Big Bang, has recently been mapped over the whole sky. To date, the small fluctuations measured have been in impressive agreement with predictions.

Gravitational waves and signiatures of the early Universe

The Advanced LIGO interferometer, which will begin to operate at high sensitivity in 2013, will herald a new era of gravitational wave astronomy.

Mutability of the laws of physics

These are subjects of major international interest where CTC has a history of leading contributions and a network of world-class collaborators.

Building on our pioneering work on the pivotal role of black holes and other extended objects in fundamental theories which seek to unify gravity and the strong and electroweak forces.

Other research: dark energy and dark matter

What is the dark matter that makes up about 25% of the Universe and which holds together galaxies?

Useful links

Find out more about the conditions in the early Universe, what happens inside a black hole, and string theory on our outreach pages.

The Large Hadron Collider and the Search for the Higgs Boson

View the Large Hadron Collider's webpage to find out more about the exotic particles that it hopes to find, including the famously hypothesised Higgs Boson.

Research Groups Within DAMTP

Discover what other research groups there are within DAMTP, including the High Energy Physics and Relativity and Gravitation groups.

COSMOS, the UK's national cosmology supercomputer

Learn more about COSMOS, the UK's national cosmology supercomputer and supercomputer of the COSMOS@DiRAC Consortium, hosted by the Centre for Theoretical Cosmology.

• Accessibility
• Privacy policy
• Return to top

Accessibility Links

• Skip to content
• Skip to search IOPscience
• Skip to Journals list
• Accessibility help
• Accessibility Help

Click here to close this panel.

Journal of Cosmology and Astroparticle Physics

The International School for Advanced Studies (SISSA) was founded in 1978 and was the first institution in Italy to promote post-graduate courses leading to a Doctor Philosophiae (or PhD) degree. A centre of excellence among Italian and international universities, the school has around 65 teachers, 100 post docs and 245 PhD students, and is located in Trieste, in a campus of more than 10 hectares with wonderful views over the Gulf of Trieste.

SISSA hosts a very high-ranking, large and multidisciplinary scientific research output. The scientific papers produced by its researchers are published in high impact factor, well-known international journals, and in many cases in the world's most prestigious scientific journals such as Nature and Science. Over 900 students have so far started their careers in the field of mathematics, physics and neuroscience research at SISSA.

Journal of Cosmology and Astroparticle Physics (JCAP) covers all aspects of cosmology and particle astrophysics and encompasses theoretical, observational and experimental areas as well as computation and simulation. An electronic-only journal, JCAP is jointly owned by IOP Publishing and SISSA .

Open all abstracts , in this tab

J. Ambjørn and Y. Watabiki JCAP12(2023)011

We show that by allowing our Universe to merge with other universes one is lead to modified Friedmann equations that explain the present accelerated expansion of our Universe without the need of a cosmological constant.

Ido Ben-Dayan and Utkarsh Kumar JCAP12(2023)047

Addressing the discrepancy between the late and early time measurements of the Hubble parameter, H 0 , and the so-called S 8 parameter has been a challenge in precision cosmology. Several models are present to address these tensions, but very few of them can do so simultaneously. In the past, we have suggested Banks-Zaks/Unparticles as an emergent Dark Energy model, and claimed that it can ameliorate the Hubble tension. In this work, we test this claim, and perform a likelihood analysis of the model and its parameters given current data, and compare it to ΛCDM. The model offers a possible resolution of Hubble tension and softens the Large Scale Structure (LSS) tension without employing a scalar field or modifying the gravitational sector. Our analysis shows a higher value of H 0 ∼ 70 – 73 km/sec/Mpc and a slightly lower value of S 8 for certain combinations of data sets. Consideration of Planck CMB data combined with the Pantheon sample and SH0ES priors lowers the H 0 and S 8 tension to 0.96 σ and 0.94 σ respectively with best-fit Δ χ 2 ≈ -11 restoring cosmological concordance. Significant improvement in the likelihood persists for other combinations of data sets as well. Evidence for the model is given by inferring one of its parameters to be x 0 ≃ -4.46. The improvement in the fit is driven by the inclusion of the SH0ES prior. In its absence most of the improvement is due to larger error bars in the Emergent Unparticles Dark Energy model.

Marco Cirelli et al JCAP03(2011)051

Peter Ade et al JCAP02(2019)056

The Simons Observatory (SO) is a new cosmic microwave background experiment being built on Cerro Toco in Chile, due to begin observations in the early 2020s. We describe the scientific goals of the experiment, motivate the design, and forecast its performance. SO will measure the temperature and polarization anisotropy of the cosmic microwave background in six frequency bands centered at: 27, 39, 93, 145, 225 and 280 GHz. The initial configuration of SO will have three small-aperture 0.5-m telescopes and one large-aperture 6-m telescope, with a total of 60,000 cryogenic bolometers. Our key science goals are to characterize the primordial perturbations, measure the number of relativistic species and the mass of neutrinos, test for deviations from a cosmological constant, improve our understanding of galaxy evolution, and constrain the duration of reionization. The small aperture telescopes will target the largest angular scales observable from Chile, mapping ≈ 10% of the sky to a white noise level of 2 μK-arcmin in combined 93 and 145 GHz bands, to measure the primordial tensor-to-scalar ratio, r , at a target level of σ( r )=0.003. The large aperture telescope will map ≈ 40% of the sky at arcminute angular resolution to an expected white noise level of 6 μK-arcmin in combined 93 and 145 GHz bands, overlapping with the majority of the Large Synoptic Survey Telescope sky region and partially with the Dark Energy Spectroscopic Instrument. With up to an order of magnitude lower polarization noise than maps from the Planck satellite, the high-resolution sky maps will constrain cosmological parameters derived from the damping tail, gravitational lensing of the microwave background, the primordial bispectrum, and the thermal and kinematic Sunyaev-Zel'dovich effects, and will aid in delensing the large-angle polarization signal to measure the tensor-to-scalar ratio. The survey will also provide a legacy catalog of 16,000 galaxy clusters and more than 20,000 extragalactic sources.

Marica Branchesi et al JCAP07(2023)068

The Einstein Telescope (ET), the European project for a third-generation gravitational-wave detector, has a reference configuration based on a triangular shape consisting of three nested detectors with 10 km arms, where each detector has a 'xylophone' configuration made of an interferometer tuned toward high frequencies, and an interferometer tuned toward low frequencies and working at cryogenic temperature. Here, we examine the scientific perspectives under possible variations of this reference design. We perform a detailed evaluation of the science case for a single triangular geometry observatory, and we compare it with the results obtained for a network of two L-shaped detectors (either parallel or misaligned) located in Europe, considering different choices of arm-length for both the triangle and the 2L geometries. We also study how the science output changes in the absence of the low-frequency instrument, both for the triangle and the 2L configurations. We examine a broad class of simple 'metrics' that quantify the science output, related to compact binary coalescences, multi-messenger astronomy and stochastic backgrounds, and we then examine the impact of different detector designs on a more specific set of scientific objectives.

Wendy L. Freedman and Barry F. Madore JCAP11(2023)050

One of the most exciting and pressing issues in cosmology today is the discrepancy between some measurements of the local Hubble constant and other values of the expansion rate inferred from the observed temperature and polarization fluctuations in the cosmic microwave background (CMB) radiation. Resolving these differences holds the potential for the discovery of new physics beyond the standard model of cosmology: Lambda Cold Dark Matter (ΛCDM), a successful model that has been in place for more than 20 years. Given both the fundamental significance of this outstanding discrepancy, and the many-decades-long effort to increase the accuracy of the extragalactic distance scale, it is critical to demonstrate that the local measurements are convincingly free from residual systematic errors. We review the progress over the past quarter century in measurements of the local value of the Hubble constant, and discuss remaining challenges. Particularly exciting are new data from the James Webb Space Telescope ( JWST ), for which we present an overview of our program and first results. We focus in particular on Cepheids and the Tip of the Red Giant Branch (TRGB) stars, as well as a relatively new method, the JAGB (J-Region Asymptotic Giant Branch) method, all methods that currently exhibit the demonstrably smallest statistical and systematic uncertainties. JWST is delivering high-resolution near-infrared imaging data to both test for and to address directly several of the systematic uncertainties that have historically limited the accuracy of extragalactic distance scale measurements (e.g., the dimming effects of interstellar dust, chemical composition differences in the atmospheres of stars, and the crowding and blending of Cepheids contaminated by nearby previously unresolved stars). For the first galaxy in our program, NGC 7250, the high-resolution JWST images demonstrate that many of the Cepheids observed with the Hubble Space Telescope (HST) are significantly crowded by nearby neighbors. Avoiding the more significantly crowded variables, the scatter in the JWST near-infrared (NIR) Cepheid PL relation is decreased by a factor of two compared to those from HST, illustrating the power of JWST for improvements to local measurements of H 0 . Ultimately, these data will either confirm the standard model, or provide robust evidence for the inclusion of additional new physics.

Simone Aiola et al JCAP12(2020)047

We present new arcminute-resolution maps of the Cosmic Microwave Background temperature and polarization anisotropy from the Atacama Cosmology Telescope, using data taken from 2013–2016 at 98 and 150 GHz. The maps cover more than 17,000 deg 2 , the deepest 600 deg 2 with noise levels below 10μK-arcmin. We use the power spectrum derived from almost 6,000 deg 2 of these maps to constrain cosmology. The ACT data enable a measurement of the angular scale of features in both the divergence-like polarization and the temperature anisotropy, tracing both the velocity and density at last-scattering. From these one can derive the distance to the last-scattering surface and thus infer the local expansion rate, H 0 . By combining ACT data with large-scale information from WMAP we measure H 0 =67.6± 1.1 km/s/Mpc, at 68% confidence, in excellent agreement with the independently-measured Planck satellite estimate (from ACT alone we find H 0 =67.9± 1.5 km/s/Mpc). The ΛCDM model provides a good fit to the ACT data, and we find no evidence for deviations: both the spatial curvature, and the departure from the standard lensing signal in the spectrum, are zero to within 1σ; the number of relativistic species, the primordial Helium fraction, and the running of the spectral index are consistent with ΛCDM predictions to within 1.5–2.2σ. We compare ACT, WMAP , and Planck at the parameter level and find good consistency; we investigate how the constraints on the correlated spectral index and baryon density parameters readjust when adding CMB large-scale information that ACT does not measure. The DR4 products presented here will be publicly released on the NASA Legacy Archive for Microwave Background Data Analysis.

A. Abdul Halim et al JCAP01(2024)022

The combined fit of the measured energy spectrum and shower maximum depth distributions of ultra-high-energy cosmic rays is known to constrain the parameters of astrophysical models with homogeneous source distributions. Studies of the distribution of the cosmic-ray arrival directions show a better agreement with models in which a fraction of the flux is non-isotropic and associated with the nearby radio galaxy Centaurus A or with catalogs such as that of starburst galaxies. Here, we present a novel combination of both analyses by a simultaneous fit of arrival directions, energy spectrum, and composition data measured at the Pierre Auger Observatory. The model takes into account a rigidity-dependent magnetic field blurring and an energy-dependent evolution of the catalog contribution shaped by interactions during propagation. We find that a model containing a flux contribution from the starburst galaxy catalog of around 20% at 40 EeV with a magnetic field blurring of around 20° for a rigidity of 10 EV provides a fair simultaneous description of all three observables. The starburst galaxy model is favored with a significance of 4.5σ (considering experimental systematic effects) compared to a reference model with only homogeneously distributed background sources. By investigating a scenario with Centaurus A as a single source in combination with the homogeneous background, we confirm that this region of the sky provides the dominant contribution to the observed anisotropy signal. Models containing a catalog of jetted active galactic nuclei whose flux scales with the γ-ray emission are, however, disfavored as they cannot adequately describe the measured arrival directions.

Avik De et al JCAP03(2024)050

We formulate f ( Q,C ) gravity and cosmology. Such a construction is based on the symmetric teleparallel geometry, but apart form the non-metricity scalar Q we incorporate in the Lagrangian the boundary term C of its difference from the standard Levi-Civita Ricci scalar   R̊ . We extract the general metric and affine connection field equations, we apply them at a cosmological framework, and adopting three different types of symmetric teleparallel affine connections we obtain the modified Friedmann equations. As we show, we acquire an effective dark-energy sector of geometrical origin, which can lead to interesting cosmological phenomenology. Additionally, we may obtain an effective interaction between matter and dark energy. Finally, examining a specific model, we show that we can obtain the usual thermal history of the universe, with the sequence of matter and dark-energy epochs, while the effective dark-energy equation-of-state parameter can be quintessence-like, phantom-like, or cross the phantom-divide during evolution.

A. Abdul Halim et al JCAP05(2023)024

In this work we present the interpretation of the energy spectrum and mass composition data as measured by the Pierre Auger Collaboration above 6 × 10 17 eV. We use an astrophysical model with two extragalactic source populations to model the hardening of the cosmic-ray flux at around 5 × 10 18 eV (the so-called "ankle" feature) as a transition between these two components. We find our data to be well reproduced if sources above the ankle emit a mixed composition with a hard spectrum and a low rigidity cutoff. The component below the ankle is required to have a very soft spectrum and a mix of protons and intermediate-mass nuclei. The origin of this intermediate-mass component is not well constrained and it could originate from either Galactic or extragalactic sources. To the aim of evaluating our capability to constrain astrophysical models, we discuss the impact on the fit results of the main experimental systematic uncertainties and of the assumptions about quantities affecting the air shower development as well as the propagation and redshift distribution of injected ultra-high-energy cosmic rays (UHECRs).

Latest articles

Lang Liu et al JCAP04(2024)011

Recently, several major pulsar timing array (PTA) collaborations have assembled strong evidence for the existence of a gravitational-wave background at frequencies around the nanohertz regime. Assuming that the PTA signal is attributed to scalar-induced gravitational waves, we jointly employ the PTA data from the NANOGrav 15-year data set, PPTA DR3, and EPTA DR2 to probe the conditions of the early Universe. Specifically, we explore the equation of state parameter ( w ), the reheating temperature ( T rh ), and the sound speed ( c s ), finding w = 0.59 +0.36 -0.40 (median + 90% credible interval), and T rh ≲ 0.2 GeV at the 95% credible interval for a lognormal power spectrum of the curvature perturbation. Furthermore, we compute Bayes factors to compare different models against the power-law spectrum model, effectively excluding the pressure-less fluid domination model. Our study underscores the significance of scalar-induced gravitational waves as a powerful tool to explore the nature of the early Universe.

Xun-Jie Xu et al JCAP04(2024)012

Right-handed neutrinos ( v R ) offer an intriguing portal to new physics in hidden sectors where dark matter (DM) may reside. In this work, we delve into the simplest hidden sector involving only a real scalar exclusively coupled to v R , referred to as the v R -philic scalar. We investigate the viability of the v R -philic scalar to serve as a DM candidate, under the constraint that the coupling of v R to the standard model is determined by the seesaw relation and is responsible for the observed DM abundance. By analyzing the DM decay channels and solving Boltzmann equations, we identify the viable parameter space. In particular, our study reveals a lower bound (2.6 × 10 5 GeV) on the mass of v R for the v R -philic scalar to be DM. The DM mass may vary from sub-MeV to sub-GeV. Within the viable parameter space, monochromatic neutrino lines from DM decay can be an important signal for DM indirect detection.

Antonio De Felice et al JCAP04(2024)013

In this work, we derive for the first time observational constraints on the extended Minimal Theory of Massive Gravity (eMTMG) framework in light of Planck-CMB data, geometrical measurements from Baryon Acoustic Oscillation (BAO), Type Ia supernovae from the recent Pantheon+ samples, and also using the auto and cross-correlations cosmic shear measurements from KIDS-1000 survey. Given the great freedom of dynamics choice for the theory, we consider an observationally motivated subclass in which the background evolution of the Universe goes through a transition from a (positive or negative) value of the effective cosmological constant to another value. From the statistical point of view, we did not find evidence of such a transition, i.e. deviation from the standard ΛCDM behavior, and from the joint analysis using Planck + BAO + Pantheon+ data, we constrain the graviton mass to < 6.6 × 10 -34 eV at 95% CL. We use KIDS-1000 survey data to constrain the evolution of the scalar perturbations of the model and its limits for the growth of structure predicted by the eMTMG scenario. In this case, we find small evidence at 95% CL for a non-zero graviton mass. We interpret and discuss these results in light of the current tension on the S 8 parameter. We conclude that, within the subclass considered, the current data are only able to impose upper bounds on the eMTMG dynamics. Given its potentialities beyond the subclass, eMTMG can be classified as a good candidate for modified gravity, serving as a framework in which observational data can effectively constrain (or confirm) the graviton mass and deviations from the standard ΛCDM behavior.

Zirui Zhang et al JCAP04(2024)014

The Internal Linear Combination (ILC) method is commonly employed to extract the cosmic microwave background (CMB) signal from multi-frequency observation maps. However, the performance of the ILC method tends to degrade when the signal-to-noise ratio (SNR) is relatively low, particularly when measuring the primordial B -modes to detect the primordial gravitational waves. To address this issue, an enhanced version of the ILC method, known as constrained ILC, is proposed. This method is designed to be more suitable for situations with low signal-to-noise ratio (SNR) by incorporating additional prior foreground information. In our study, we have modified the constraint Needlet ILC method and successfully improved its performance at low SNR. We illustrate our methods using mock data generated from the combination of WMAP, Planck and a ground-based experiment in the northern hemisphere, and the chosen noise level for the ground-based experiment are very conservative which can be easily achieved in the very near future. The results show that the level of foreground residual can be well controlled. In comparison to the standard NILC method, which introduces a bias to the tensor-to-scalar ratio ( r ) of approximately 0.05, the constrained NILC method exhibits a significantly reduced bias of only around 5 × 10 -3 towards r which is much smaller than the statistical error.

Himanish Ganjoo and M. Sten Delos JCAP04(2024)015

In cosmologies with an early matter-dominated era (EMDE) prior to Big Bang nucleosynthesis, the boosted growth of small-scale matter perturbations during the EMDE leads to microhalo formation long before halos would otherwise begin to form. For a range of models, halos can even form during the EMDE itself. These halos would dissipate at the end of the EMDE, releasing their gravitationally heated dark matter and thereby imprinting a free-streaming cut-off on the matter power spectrum. We conduct the first cosmological N-body simulations of the formation and evaporation of halos during and after an EMDE. We show that in these scenarios, the free-streaming cut-off after the EMDE can be predicted accurately from the linear matter power spectrum. Although the free streaming can erase much of the EMDE-driven boost to density perturbations, we use our findings to show that the (re-)formation of halos after the EMDE nevertheless proceeds before redshift ∼ 1000. Early-forming microhalos are a key observational signature of an EMDE, and our prescription for the impact of gravitational heating will allow studies of the observational status and prospects of EMDE scenarios to cover a much wider range of parameters.

Open access

K. Boutivas et al JCAP04(2024)017

We compute the evolution of the entanglement entropy for a massless field within a spherical region throughout the inflationary period and the subsequent era of radiation domination, starting from the Bunch-Davies vacuum. In order to focus on the entanglement of modes that are directly accessible to observations, we impose an ultraviolet cutoff set by the wavelength of the last mode that exited the horizon at the end of inflation. The transition of each mode towards a squeezed state upon horizon exit during inflation and the additional squeezing when radiation domination sets in enhance the entanglement entropy. Shortly after the transition to the radiation-dominated era, a volume term develops and becomes the leading contribution to the entropy at late times, as is common for systems lying in squeezed states. We estimate the magnitude of the entropy and discuss its interpretation in the light of the quantum to classical transition for modes exiting the horizon during inflation. Our results raise the possibility that the quantum nature of weakly interacting fields, such as gravitational waves resulting from tensor modes during inflation, may be detectable in today's universe. On the other hand, an observer with no knowledge of the degrees of freedom beyond the horizon would interpret the entropy as thermal. From this point of view, the reheating after inflation would be a result of quantum entanglement.

Oksana Iarygina et al JCAP04(2024)018

We consider the effects of backreaction on axion-SU(2) dynamics during inflation. We use the linear evolution equations for the gauge field modes and compute their backreaction on the background quantities numerically using the Hartree approximation. We show that the spectator chromo-natural inflation attractor is unstable when back-reaction becomes important. Working within the constraints of the linear mode equations, we find a new dynamical attractor solution for the axion field and the vacuum expectation value of the gauge field, where the latter has an opposite sign with respect to the chromo-natural inflation solution. Our findings are of particular interest to the phenomenology of axion-SU(2) inflation, as they demonstrate the instability of the usual trajectory due to large backreaction effects. The viable parameter space of the model becomes significantly altered, provided future non-Abelian lattice simulations confirm the existence of the new dynamical attractor. In addition, the backreaction effects lead to characteristic oscillatory features in the primordial gravitational wave background that are potentially detectable with upcoming gravitational wave detectors.

T. Mistele et al JCAP04(2024)020

We combine kinematic and gravitational lensing data to construct the Radial Acceleration Relation (RAR) of galaxies over a large dynamic range. We improve on previous weak-lensing studies in two ways. First, we compute stellar masses using the same stellar population model as for the kinematic data. Second, we introduce a new method for converting excess surface density profiles to radial accelerations. This method is based on a new deprojection formula which is exact, computationally efficient, and gives smaller systematic uncertainties than previous methods. We find that the RAR inferred from weak-lensing data smoothly continues that inferred from kinematic data by about 2.5 dex in acceleration. Contrary to previous studies, we find that early- and late-type galaxies lie on the same joint RAR when a sufficiently strict isolation criterion is adopted and their stellar and gas masses are estimated consistently with the kinematic RAR.

Nicole F. Bell et al JCAP04(2024)006

The capture of dark matter, and its subsequent annihilation, can heat old, isolated neutron stars. In order for kinetic heating to be achieved, the captured dark matter must undergo sufficient scattering to deposit its kinetic energy in the star. We find that this energy deposit typically occurs quickly, for most of the relevant parameter space. In order for appreciable annihilation heating to also be achieved, the dark matter must reach a state of capture-annihilation equilibrium in the star. We show that this can be fulfilled for all types of dark matter-baryon interactions. This includes cases where the scattering or annihilation cross sections are momentum or velocity suppressed in the non-relativistic limit. Importantly, we find that capture-annihilation equilibrium, and hence maximal annihilation heating, can be achieved without complete thermalization of the captured dark matter. For scattering cross sections that saturate the capture rate, we find that capture-annihilation equilibrium is typically reached on a timescale of less than 1 year for vector interactions and 10 4 years for scalar interactions.

Alan B.H. Nguyen et al JCAP04(2024)008

Baryon Acoustic Oscillation (BAO) observations offer a robust method for measuring cosmological expansion. However, the BAO signal in a sample of galaxies can be diluted and shifted by interlopers — galaxies that have been assigned the wrong redshifts. Because of the slitless spectroscopic method adopted by the Roman and Euclid space telescopes, the galaxy samples resulting from single line detections will have relatively high fractions of interloper galaxies. Interlopers with a small displacement between true and false redshift have the strongest effect on the measured clustering. In order to model the BAO signal, the fraction of such interlopers and their clustering need to be accurately known. We introduce a new method to self-calibrate these quantities by shifting the contaminated sample towards or away from us along the line of sight by the interloper offset, and measuring the cross-correlations between these shifted samples. The contributions from the different components are shifted in scale in this cross-correlation compared to the auto-correlation of the contaminated sample, enabling the decomposition and extraction of the component terms. We demonstrate the application of the method using numerical simulations and show that an unbiased BAO measurement can be extracted. Unlike previous attempts to model the effects of contaminants, self-calibration allows us to make fewer assumptions about the form of the contaminants such as their bias.

Clare Burrage et al JCAP04(2024)004

Screening mechanisms allow light scalar fields to dynamically avoid the constraints that come from our lack of observation of a long-range fifth force. Galactic scale tests are of particular interest when the light scalar is introduced to explain the dark matter or dark energy that dominates our cosmology. To date, much of the literature that has studied screening in galaxies has described screening using simplifying approximations. In this work, we calculate numerical solutions for scalar fields with screening mechanisms in galactic contexts, and use these to derive new, precise conditions governing where fifth forces are screened. We show that the commonly used binary screened/unscreened threshold can predict a fifth force signal in situations where a fuller treatment does not, leading us to conclude that existing constraints might be overestimated. We show that various other approximations of the screening radius provide a more accurate proxy to screening, although they fail to exactly reproduce the true screening surface in certain regions of parameter space. As a demonstration of our scheme, we apply it to an idealised Milky Way and thus identify the region of parameter space in which the solar system is screened.

J. Egge et al JCAP04(2024)005

The reciprocity approach is a powerful method to determine the expected signal power of axion haloscopes in a model-independent way. Especially for open and broadband setups like the MADMAX dielectric haloscope the sensitivity to the axion field is difficult to calibrate since they do not allow discrete eigenmode analysis and are optically too large to fully simulate. The central idea of the reciprocity approach is to measure a reflection-induced test field in the setup instead of trying to simulate the axion-induced field. In this article, the reciprocity approach is used to determine the expected signal power of a dish antenna and a minimal dielectric haloscope directly from measurements. The results match expectations from simulation but also include important systematic effects that are too difficult to simulate. In particular, the effect of antenna standing waves and higher order mode perturbations can be quantified for the first time in a dielectric haloscope.

Andrea Addazi et al JCAP03(2024)E01

We rectify a typographical error in equation (3.14) from the original version of this article, pertaining to the effective Higgs-Majoron coupling, λ (0) JJh 1 , expressed in the mass eigenbasis. Notably, the same error persisted in the computational routines used in our work. This oversight resulted in a discrepancy in the numerical calculation of the invisible Higgs decay branching fraction, Br( h 1 → JJ ), affecting a subset of the sampled points. While the main conclusions remain unaltered, we provide an updated version of our results.

Konstantinos Tanidis et al JCAP03(2024)058

More Open Access articles

Journal links

• Submit an article
• About the journal
• Editorial Board
• Author guidelines
• Publication charges
• News and editorial
• Journal collections
• Pricing and ordering

Journal information

• 2003-present Journal of Cosmology and Astroparticle Physics doi: 10.1088/issn.1475-7516 Online ISSN: 1475-7516

• Interact with NASA APPEL on LinkedIn
• Interact with NASA APPEL on Twitter
• Interact with NASA APPEL on Facebook
• View NASA APPEL Images on Flickr
• View NASA APPEL Videos on YouTube
• Subscribe to NASA APPEL's RSS Feed

Subscribe to INSIGHT

Expanding perspectives every month.

• Curated Curricula
• Competency Models
• Development Frameworks
• Maximize Your Learning Experience
• Systems Engineering Leadership Program (SELP)
• Accreditations & Affiliations
• Defense Acquisition University
• Course Support
• Registration Overview
• Virtual Backgrounds
• INSIGHT Publication
• Apollo Era Resources
• Case Studies
• Knowledge Capture and Transfer
• Knowledge Sharing Tools
• NASA Knowledge Community
• Shuttle Era Resources
• Spotlight on Lessons Learned Series
• Lessons Learned Lifecycle and Highlights
• Lessons Learned Bot
• Project Management Courses
• Program Management Series
• NPR 7120.5 Revision F Rollout Briefing (NASA Only)
• NPR 7120.5 Tailoring Resources
• NASA FAC-P/PM Certification Program
• Office of the Chief Engineer Handbooks
• Relevant Documents
• Affiliations
• Small Steps, Giant Leaps Podcast
• Quick Webinars
• On-Demand Courses
• Project Knowledge Expo
• NASA Knowledge on Video
• Knowledge Inventory
• Technical Authority

This Month in NASA History: A Turning Point in Cosmology

This detailed, all-sky picture of the infant universe was created from nine years of data gathered by the Wilkinson Microwave Anisotropy Probe. The image reveals 13.77 billion year old temperature fluctuations (shown as color differences) that correspond to the seeds that grew to become the galaxies. Credit: NASA

WMAP mission releases stunning map of the Cosmic Microwave Background, a “baby picture” of the Universe.

To the untrained eye, it was an unassuming dark blue oval with layers of green, yellow, and red. But the image released by NASA on February 11, 2003—21 years ago this month—represented nothing short of a turning point in cosmology. The swirling colors in the image were the most detailed representation yet of the Cosmic Microwave Background (CMB), the faint afterglow of the Big Bang that astronomers see between stars and galaxies when using powerful telescopes.

The image was the product of the first year of science by the Wilkinson Microwave Anisotropy Probe (WMAP), launched by NASA on June 30, 2001. The WMAP carried sophisticated instruments that were approximately 45 times more sensitive than NASA’s previous mission to examine the CMB a decade earlier. It was immediately apparent that WMAP represented a bold step forward in the field.

The Wilkinson Microwave Anisotropy Probe. Credit: NASA/WMAP Science Team

“We’ve captured the infant Universe in sharp focus, and from this portrait we can now describe the Universe with unprecedented accuracy,” said Dr. Charles L. Bennett of the Goddard Space Flight Center, Greenbelt Md., in a NASA press release . Bennett was the Principal Investigator for WMAP. “The data are solid, a real gold mine.”

WMAP was about 12 feet tall and 16.5 feet wide once the combined solar array and sun shield was deployed in space. The spacecraft carried a differential pseudo-correlation radiometer with polarization that could measure the temperature difference between two points in the sky to an accuracy of one millionth of a degree. The instrument operated in five frequency bands from 22 to 90 GHz to better separate foreground signals from the CMB.

The spacecraft orbited the Sun at a spot 1 million miles from Earth, the second LaGrange point (L2) in Earth’s orbit around the Sun. L2 has a cold, stable thermal environment, which was important for WMAP to accurately measure the CMB, which has an average temperature of minus 455 degrees Fahrenheit. It is also a point where the gravitational forces of the Sun and Earth and the orbital motion of a spacecraft are balanced, so that WMAP orbited the Sun approximately in line with Earth and required minimal station keeping. The James Webb Space Telescope is currently orbiting at L2.

Data from WMAP’s first year in operation was a revelation, revealing that the first stars in the Universe formed much earlier than scientists had thought, just 200 million years after the Big Bang. These first stars, scientists now believe, were hundreds of times larger than our Sun, burning much brighter before rapidly becoming supernovae.

Diagram of the gravitational potential (white lines) associated with the Sun-Earth system. Lagrange Points, designated by L1 to L3 (dynamically unstable) and L4 and L5 (stabilize by Coriolis effect), are positions in space where the gravitational forces produce enhanced regions of attraction (red arrows) and repulsion (blue arrows). Note: Image is not to scale. Credit: NASA / WMAP Science Team

One key question the WMAP was designed to examine was how stars, galaxies and large-scale structures formed in the early Universe. Cosmologists at the time believed that the galaxies grew from the gravitational pull of small fluctuations in the nearly-uniform density of the early Universe, according to the WMAP website . “These fluctuations leave an imprint in the cosmic microwave background radiation in the form of temperature fluctuations from point to point across the sky. The WMAP satellite measures these small fluctuations in the temperature of the cosmic microwave background radiation and in turn probes the early stages of structure formation,” the site reads.

WMAP’s first year of data suggested the Universe was 13.77 billion years old and supported the theories of the Big Bang and Cosmic Inflation. The data indicated that the Universe was composed of just 4 percent ordinary matter (atoms). Most of the Universe, WMAP’s data indicated, was dark energy—73 percent, with dark matter accounting for 23 percent. (Current estimates place dark matter at 27 percent of the Universe, with dark energy at 68 percent, and ordinary matter at 5 percent.)

“This is a beginning of a new stage in our study of the early Universe,” said David N. Spergel, a professor at Princeton University, and a member of the WMAP team, quoted in a NASA press release . “We can use this portrait not only to predict the properties of the nearby universe, but [also] to understand the first moments of the Big Bang.”

WMAP operated for nine years, collecting data for the last time on August 20, 2010. On 29 December 2012, NASA released the final WMAP data and images. By that time, the team had refined the age of the Universe to 13.77 billion years old, with a degree of error of one percent. The data pointed to curious patterns in the CMB that later missions would examine.

A representation of the evolution of the universe over 13.77 billion years. The far left depicts the earliest moment we can now probe, when a period of “inflation” produced a burst of exponential growth in the universe. (Size is depicted by the vertical extent of the grid in this graphic.) For the next several billion years, the expansion of the universe gradually slowed down as the matter in the universe pulled on itself via gravity. More recently, the expansion has begun to speed up again as the repulsive effects of dark energy have come to dominate the expansion of the universe. The afterglow light seen by WMAP was emitted about 375,000 years after inflation and has traversed the universe largely unimpeded since then. The conditions of earlier times are imprinted on this light; it also forms a backlight for later developments of the universe. Credit: NASA / WMAP Science Team

The final data also supported the theory that the Universe expanded exponentially in the first trillionths of a second, ruling out some theories of how that happened, while supporting others.

“It never ceases to amaze me that we can make a measurement that can distinguish between what may or may not have happened in the first trillionth of a second of the universe,” said Bennett in a 2010 NASA press release about the end of the mission.

WMAP data provided precise measurements of the fundamental parameters of the universe, which scientists continue to use. In 2018, the WMAP team was awarded The Breakthrough Prize in Fundamental Physics for their work on the mission. WMAP research papers were among the most widely cited scientific papers in the world across all scientific disciplines for a decade.

“Every astronomer will remember the moment he heard the results from WMAP,” said John Bahcall (1934–2005), then a Professor of Astrophysics in the School of Natural Sciences at the Institute for Advanced Study. “Before the WMAP results, astronomers and physicists had put together a very implausible picture of our universe. It had a tiny amount of ordinary matter. It had a modest amount of dark matter, whatever that is. It had an overwhelming amount of dark energy, which is a strange beast. I have to confess I was very skeptical of this picture. But the WMAP results have convinced me,” Bahcall added.

To learn more about the Wilkinson Microwave Anisotropy Probe, visit the mission page here .

About the Author

Kevin Wilcox is a technical writer for APPEL Knowledge Services.

Share With Your Colleagues

Recommended.

First results from DESI make the most precise measurement of our expanding universe

Researchers have used the Dark Energy Spectroscopic Instrument to make the largest 3D map of our universe and world-leading measurements of dark energy, the mysterious force behind its accelerating expansion.

Understanding how our universe has evolved is tied to one of the biggest mysteries in physics: dark energy, the unknown ingredient causing our universe to expand faster and faster.

To study dark energy’s effects over the past 11 billion years, DESI has created the largest 3D map of our cosmos ever constructed, with the most precise measurements to date. This is the first time scientists have measured the expansion history of the young universe with a precision better than 1%, giving us our best view yet of how the universe evolved. Researchers shared the analysis of their first year of collected data in multiple papers posted today on the arXiv and in talks at the American Physical Society meeting in the United States and the Rencontres de Moriond in Italy.

“We’re incredibly proud of the data, which have produced world-leading cosmology results and are the first to come out of new generation of dark energy experiments,” said Michael Levi, DESI director and a scientist at the Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab), which manages the project. “So far, we’re seeing basic agreement with our best model of the universe, but we’re also seeing some potentially interesting differences that could indicate that dark energy is evolving with time. Those may or may not go away with more data, so we’re excited to start analyzing our three-year dataset soon.”

DESI is an international collaboration that analyzes the spectra, or colors, of light from galaxies and extremely distant objects called quasars – giant black holes that give off bright light as material spirals into their. By the end of the survey, DESI plans to map 3 million quasars and 37 million galaxies.

“No spectroscopic experiment has had this much data before, and we’re continuing to gather data from more than a million galaxies every month,” said Nathalie Palanque-Delabrouille, a Berkeley Lab scientist and co-spokesperson for the experiment. “It’s astonishing that with only our first year of data, we can already measure the expansion history of our universe at seven different slices of cosmic time, each with a precision of 1 to 3%. The team put in a tremendous amount of work to account for instrumental and theoretical modeling intricacies, which gives us confidence in the robustness of our first results.”

Researchers at DOE's SLAC National Accelerator Laboratory played a key role in building sophisticated survey simulations that were used to test the various techniques that went into DESI's first round of results, said Sandy Yuan, a postdoctoral fellow at the Kavli Institute for Particle Astrophysics and Cosmology. 

"I am excited about DESI shedding light on important open questions in cosmology," Yuan said, such as tensions between different measurements of the Hubble constant, which expresses how fast the universe is expanding. "The accuracy and purity of DESI data will cast a strong vote in these tensions, and DESI will also push hard on questions regarding the primordial universe, neutrinos, and dark energy."

Emmanuel Schaan, a staff scientist at SLAC who works on DESI and the Atacama Cosmology Telescope (ACT), said that he is looking forward to collaborations made possible by the amount of data coming in and the large area of the sky DESI covers. "DESI and ACT both observe large parts of the sky, resulting in a large overlap. We can therefore look for correlations between the galaxy catalogs of DESI and the microwave maps of ACT," Schaan said. "These correlations reveal a wealth of new information that wouldn't be seen in either DESI or ACT alone: the whole is greater than the sum of its parts."

DESI’s data will similarly be used to complement future sky surveys such as the Vera C. Rubin Observatory and Nancy Grace Roman Space Telescope, and to prepare for a potential upgrade to DESI (DESI-II) that was recommended in a recent  report by the U.S. Particle Physics Project Prioritization Panel.

"I am very excited to see the most precise measurements of spectroscopic galaxy clustering ever made, and what they tell us about cosmology," Schaan said "In particular, as hints of mild tensions have emerged between different cosmological observables, the DESI first-year measurements will be helpful in assessing consistency of different cosmological methods.

Beyond the cosmological parameter measurements, the unprecedentedly large galaxy catalogs themselves will be extremely valuable to the whole astrophysics community."

DESI is supported by the DOE Office of Science and by the National Energy Research Scientific Computing Center, a DOE Office of Science user facility. Additional support for DESI is provided by the U.S. National Science Foundation, the Science and Technology Facilities Council of the United Kingdom, the Gordon and Betty Moore Foundation, the Heising-Simons Foundation, the French Alternative Energies and Atomic Energy Commission (CEA), the National Council of Science and Technology of Mexico, the Ministry of Science and Innovation of Spain, and by the DESI member institutions.

The DESI collaboration is honored to be permitted to conduct scientific research on Iolkam Du’ag (Kitt Peak), a mountain with particular significance to the Tohono O’odham Nation.

This article is based on a press release from Berkeley Lab.

For questions or comments, contact the SLAC Office of Communications at  [email protected] .

SLAC is a vibrant multiprogram laboratory that explores how the universe works at the biggest, smallest and fastest scales and invents powerful tools used by scientists around the globe. With research spanning particle physics, astrophysics and cosmology, materials, chemistry, bio- and energy sciences and scientific computing, we help solve real-world problems and advance the interests of the nation.

SLAC is operated by Stanford University for the U.S. Department of Energy’s Office of Science . The Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time.

Related Topics

• Particle Astrophysics & Cosmology (PAC)
• Science news
• Astrophysics and cosmology
• Dark energy
• Particle physics

Related stories

Slac completes construction of the largest digital camera ever built for astronomy.

Once set in place atop a telescope in Chile, the 3,200-megapixel LSST Camera will help researchers better understand dark matter, dark energy and other...

Scientists propose a new way to search for dark matter

In a new study, SLAC researchers suggest a small-scale solution could be the key to solving a large-scale mystery.

Rubin Observatory will inspire a new era in space missions without ever leaving the ground

Vera C. Rubin Observatory’s detailed, big-picture view of our Solar System and ability to quickly detect and track moving objects will provide a gold...

Final supernova results from Dark Energy Survey offer unique insights into the expansion of the universe

The latest results put the strongest constraints on the expansion of the universe ever obtained with DES supernova data.

A day in the life of a mountaintop telescope builder

Margaux Lopez is helping prepare the Vera Rubin Observatory for the arrival of the largest digital camera ever built for astrophysics and cosmology.

Recommendations for U.S. government investments in particle physics include SLAC research priorities

A new report outlines suggestions for federal investments needed for the next generation of transformative discoveries in particle physics and cosmology, including priority projects...

Help | Advanced Search

General Relativity and Quantum Cosmology

Title: ultralight scalar dark matter versus non-adiabatic perfect fluid dark matter in pulsar timing.

Abstract: Recent evidence of direct detection of stochastic gravitational waves reported by pulsar timing array collaborations might open a new window for studying cosmology and astrophysical phenomena. In addition to signals from gravitational waves, there is motivation to explore residual signals from oscillating dark matter, which might partially comprise the galactic halo. We investigate fluctuations in pulsar timing originating from the coherent oscillation of scalar dark matter up to the subleading order of $\mathcal{O}(k/m)$, as well as from acoustic oscillations of non-adiabatic perfect fluid dark matter. Both types of dark matter can generate oscillating Newtonian potential perturbations and curvature perturbations, thereby affecting pulsar timing. Our results show distinctive signatures in pulsar timing residuals and angular correlations for these dark matters. Specifically, pulsar timing residuals from non-adiabatic perfect fluid dark matter exhibit different directional dependence and are shown to be more sensitive to the distance to a pulsar. We also study the angular correlation patterns from these dark matters in the NANOGrav 15-year data set. The best fit might suggest that the composition of non-adiabatic perfect fluid dark matter in our galaxy is much greater than that of ultralight scalar dark matter.

Submission history

Access paper:.

• HTML (experimental)
• Other Formats

References & Citations

• INSPIRE HEP
• Google Scholar
• Semantic Scholar

BibTeX formatted citation

Bibliographic and Citation Tools

Code, data and media associated with this article, recommenders and search tools.

• Institution

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .