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A natural measure on the set of all universes
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“Gibbons, Hawking and Stewart (GHS, [63]) showed that there is nevertheless a unique measure satisfying a small number of reasonable constraints: it is positive, independent of coordinate choices, respects the symmetries of the theory, and does not require the introduction of any additional structures.”
From In What Sense Is the Early Universe Fine-Tuned? (2014) · cites this paper as [63]
Citations
Cites
Mathematical Methods of Classical Mechanics
Arnol'd, V. I. (1978) · Graduate texts in mathematics · doi:10.1007/978-1-4757-1693-1 · Cited by 5,169
Linde, A. D. (1983) · Physics Letters B · doi:10.1016/0370-2693(83)90837-7 · Cited by 3,299
Bulmer, M. G. (1965) · Cited by 678
Inflationary stages in cosmological models with a scalar field
Belinsky, V., Грищук, Л. П., Khalatnikov, I. M., & Zel’dovich, Y. B. (1985) · Physics Letters B · doi:10.1016/0370-2693(85)90644-6 · Cited by 248
A fractal set of perpetually bouncing universe?
Page, D. N. (1984) · Classical and Quantum Gravity · doi:10.1088/0264-9381/1/4/015 · Cited by 116
Beaumont, G. P., & Bulmer, M. G. (1966) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2343516 · Cited by 100
Willmore, T. J., & Hitchin, N. J. (1984) · Medical Entomology and Zoology · Cited by 85
Inflation in universes with a massive scalar field
Piran, T., & Williams, R. M. (1985) · Physics Letters B · doi:10.1016/0370-2693(85)90291-6 · Cited by 75
Research works printed but not linked: 1
- Hartle, 1983, Phys. Rev., D28, 2960
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Sorted by citations
Items 101–155 of 155
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Li, M., & Wang, Y. (2007) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2007/06/012 · Cited by 11
Partouche, H., Toumbas, N., & de Vaulchier, B. (2021) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2021.115600 · Cited by 10
Measure on a subspace of FRW solutions and ‘‘the flatness problem’’ of standard cosmology
Cho, H. T., & Kantowski, R. (1994) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.50.6144 · Cited by 9
Initial conditions of inflation in a Bianchi I Universe
Finn, K. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.101.063512 · Cited by 8
Spacetime averaging of exotic singularity universes
Da̧browski, M. P. (2011) · Physics Letters B · doi:10.1016/j.physletb.2011.07.043 · Cited by 8
Can Typicality Arguments Dissolve Cosmology’s Flatness Problem?
McCoy, C. D. (2017) · Philosophy of Science · doi:10.1086/694109 · Cited by 8
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Page, D. N. (2011) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2011/06/038 · Cited by 7
Quantum creation and inflationary universes: A critical appraisal
Coule, D. H. (2000) · Physical Review D · doi:10.1103/physrevd.62.124010 · Cited by 9
Early universe thermostatistics in curved momentum spaces
Gorji, M. A., Hosseinzadeh, V., Nozari, K., & Vakili, B. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.93.064029 · Cited by 5
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Reichert, P. (2024) · Fundamental theories of physics · doi:10.1007/978-3-031-45434-9_20 · Cited by 5
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Coule, D. H., & Madsen, M. S. (1989) · Physics Letters B · doi:10.1016/0370-2693(89)90283-9 · Cited by 5
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Roukema, B. F., & Blanlœil, V. (2009) · HAL · Cited by 5
100 years of mathematical cosmology: Models, theories and problems, Part B
Cotsakis, S., & Yefremov, A. P. (2022) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2021.0171 · Cited by 7
Uniform probability in cosmology
Wenmackers, S. (2023) · Studies in History and Philosophy of Science Part A · doi:10.1016/j.shpsa.2023.08.009 · Cited by 4
A measure on the set of compact Friedmann–Lemaître–Robertson–Walker models
Roukema, B. F., & Blanlœil, V. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/24/245001 · Cited by 4
Comments on the canonical measure in cosmology
Kaya, A. (2012) · Physics Letters B · doi:10.1016/j.physletb.2012.05.035 · Cited by 4
Arguments against the flatness problem in classical cosmology: a review
Helbig, P. (2021) · The European Physical Journal H · doi:10.1140/epjh/s13129-021-00006-9 · Cited by 4
Khalfin, L. A. (1989) · International Journal of Theoretical Physics · doi:10.1007/bf00670352 · Cited by 4
QUANTUM COSMOLOGIES AND THE “BEGINNING”
Drees, W. B. (1991) · Zygon® · doi:10.1111/j.1467-9744.1991.tb00825.x · Cited by 4
On the Locality of the No Hair Conjecture and the Measure of the Universe
Pacher, T., & Stein‐Schabes, J. A. (1991) · Annalen der Physik · doi:10.1002/andp.19915030803 · Cited by 3
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CPHT, C., Partouche, H., Toumbas, N., de Vaulchier, B., & CPHT, C. (2021) · International Conference on Beyond Standard Model: From Theory to Experiment (BSM) · doi:10.31526/acp.bsm-2021.34 · Cited by 4
Legendre scalarization in gravity and cosmology
Cotsakis, S., Mimoso, J. P., & Miritzis, J. (2023) · The European Physical Journal C · doi:10.1140/epjc/s10052-023-11628-2 · Cited by 3
Stability in Cosmology, from Einstein to Inflation
McCoy, C. D. (2020) · Einstein studies · doi:10.1007/978-3-030-47782-0_4 · Cited by 3
Effective field theories as a novel probe of fine-tuning of cosmic inflation
Azhar, F. (2020) · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics · doi:10.1016/j.shpsb.2020.05.001 · Cited by 4
Solution space of Bianchi type I spacetime in loop quantum cosmology
Fujio, K., & Futamase, T. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.064013 · Cited by 3
Sloan, D. (2016) · The Open Journal of Astrophysics · doi:10.21105/astro.1602.02113 · Cited by 3
Stephen William Hawking CH CBE. 8 January 1942—14 March 2018
Carr, B. J., Ellis, G. F. R., Gibbons, G. W., Hartle, J. B., Hertog, T., Penrose, R., Perry, M. J., & Thorne, K. S. (2019) · Biographical Memoirs of Fellows of the Royal Society · doi:10.1098/rsbm.2019.0001 · Cited by 3
Self-citationWavefunction of the universe: Diffeomeorphism invariance and field redefinitions
Partouche, H., Toumbas, N., & de Vaulchier, B. (2022) · Corfu Summer Institute School and Workshops on Elementary Particle Physics and Gravity (CORFU) · doi:10.22323/1.406.0159 · Cited by 2
A formalism for the ambiguities of the Wheeler-DeWitt equation
Kaimakkamis, E., & Sil, K. (2024) · Corfu Summer Institute School and Workshops on Elementary Particle Physics and Gravity (CORFU) · doi:10.22323/1.463.0227 · Cited by 5
Remarks on inhomogeneous anisotropic cosmology
Kaya, A. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.043509 · Cited by 2
Physics of the Early Universe and Inflation
Kofman, L. A. (2007) · Les Houches/Les Houches · doi:10.1016/s0924-8099(07)80030-8 · Cited by 2
Toy model studies of tuning and typicality with an eye toward cosmology
Hernley, A., Albrecht, A., & Dray, T. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.123515 · Cited by 2
Clough, K. (2018) · Springer theses · doi:10.1007/978-3-319-92672-8_4 · Cited by 2
Modeling the Past Hypothesis: A Mechanical Cosmology
Scharnhorst, J., & Aguirre, A. N. (2023) · Foundations of Physics · doi:10.1007/s10701-023-00745-3 · Cited by 2
On the probability of inflation in a higher-dimensional cosmological model
Ezawa, Y. (1989) · Classical and Quantum Gravity · doi:10.1088/0264-9381/6/9/011 · Cited by 2
Loop Quantum Cosmology and Probability of Inflation
VERESHCHAGIN, G. V., & Bedić, S. (2018) · Astronomy Reports · doi:10.1134/s1063772918120326 · Cited by 1
Zalel, S. (2024) · Springer eBooks · doi:10.1007/978-981-99-7681-2_82 · Cited by 1
Non-minimally coupled loop quantum inflation with inverse-volume corrections
Roy, R., Otalora, G., Saavedra, J., & Capozzıello, S. (2026) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2026.117530 · Cited by 4
Some Recent Advances in Loop Quantum Cosmology
Ashtekar, A. (2012) · Journal of Physics Conference Series · doi:10.1088/1742-6596/360/1/012001 · Cited by 1
Zalel, S. (2023) · Springer eBooks · doi:10.1007/978-981-19-3079-9_82-1 · Cited by 1
Rukpakawong, T., & Burikham, P. (2025) · Physics of the Dark Universe · doi:10.1016/j.dark.2025.101998 · Cited by 1
On Inflation and Creation of Matter
Kasper, U. (1990) · Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B · doi:10.1007/bf02742794 · Cited by 1
Koperski, J. (2014) · Wiley eBooks · doi:10.1002/9781118933800.ch2
Cosmology and Inductive Inference: A Bayesian FailurePreprint
Norton, J. D. (2009) · PhilSci-Archive (University of Pittsburgh)
Quasi‐de Sitter stage of the cosmic evolution, de Sitter space‐time, and creation of matter
Kasper, U. (1990) · Astronomische Nachrichten · doi:10.1002/asna.2113110304
Wu, Z. C. (2011) · Modern Physics Letters A · doi:10.1142/s0217732311036152
Holography as cutoff: A proposal for measure of inflationary universes
Novaes, F., & da Cunha, B. C. (2014) · International Journal of Modern Physics A · doi:10.1142/s0217751x14501024
Nash, P. L. (2013) · arXiv (Cornell University)
Comments on inhomogeneous anisotropic cosmologyPreprint
Kaya, A. (2016) · arXiv (Cornell University)
Calculation of the Hubble Parameter from GeometryPreprint
Nash, P. L. (2013) · viXra
Finn, K. (2021) · Springer theses · doi:10.1007/978-3-030-85269-6_6
Finn, K. (2021) · Springer theses · doi:10.1007/978-3-030-85269-6_8
Calzetta, E., & Hu, B. L. (2022) · Cambridge University Press eBooks · doi:10.1017/9781009291248.022
Rukpakawong, T., & Burikham, P. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5238473
Universe without a cause: a reply to David Lu
Linford, D. J. (2026) · International Journal for Philosophy of Religion · doi:10.1007/s11153-026-09992-6
Metadata
- Authors
- Gibbons, G. W., Hawking, S. W., & Stewart, J. M.
- Affiliations
- University of Cambridge (GB)
- Venue
- Nuclear Physics B
- Publisher
- Elsevier BV
- Published
- 1987-02
- Volume
- 281
- Issue
- 3-4
- Pages
- 736-751
- ISSN
- 0550-3213 (ISSN-L)
- OpenAlex
- W1993745521
- Cited by
- 156
- References
- 8
- Citations by year
- 2026: 2 · 2025: 3 · 2024: 3 · 2023: 6 · 2022: 5 · 2021: 8 · 2020: 6 · 2019: 4 · 2018: 3 · 2017: 3 · 2016: 5 · 2015: 5 · 2014: 9 · 2013: 9 · 2012: 5
- FWCI
- 14.58
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Nuclear Physics B (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Keywords
- Hamiltonian systems, Friedmann models, massive scalar field, cosmic inflation
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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