A probability measure for FLRW models
Abstract
We use Jaynes' principle to find new probability measures for ensembles of open and closed dust-FLRW models and generalize the results to a γ-equation of state. For big-bang solutions the measures are non-integrable at Ω 0 = 1 and Ω 0 = ∞. Together with additional restrictions on the possible values of the cosmological constant Λ, these measures can solve the flatness problem.
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The relevant integrals may diverge, making assignment of mean values or averages for physical quantities in an ensemble problematic.
“Finally, the relevant integrals may diverge.In that case, assigning mean values or averages for physical quantities in an ensemble of universes is problematic”
From Multiverses and physical cosmology (2004) · cites this paper as Kirchner & Ellis 2003
If the domain is all positive real numbers, the minimum-information measure gives a non-normalizable a priori probability distribution proportional to 1/ρ.
“If, on the other hand, the domain is given by all positive real numbers then the minimum-information measure gives an (non-normalizable) a priori probability distribution proportional to 1/ρ (Kirchner & Ellis 2003).”
From Multiverses and physical cosmology (2004) · cites this paper as Kirchner & Ellis 2003
Cites
A natural measure on the set of all universes
Gibbons, G. W., Hawking, S. W., & Stewart, J. M. (1987) · Nuclear Physics B · doi:10.1016/0550-3213(87)90425-1 · Cited by 156 · see citing works
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Multiverses and physical cosmology
Ellis, G. F. R., Kirchner, U., & Stoeger, W. R. (2004) · Monthly Notices of the Royal Astronomical Society · doi:10.1111/j.1365-2966.2004.07261.x · Cited by 82 · see citing works
“This life-allowing region is indicated schematically. equation of state has been discussed in Kirchner & Ellis (2003).”
BackgroundInfluentialSelf-citation
- Authors
- Kirchner, U., & Ellis, G. F. R.
- Affiliations
- University of Cape Town (ZA)
- ORCID
- Ellis, G F R
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2003-03-03
- Volume
- 20
- Issue
- 6
- Pages
- 1199-1213
- ISSN
- 0264-9381 (ISSN-L)
- OpenAlex
- W2053676352
- Cited by
- 15
- References
- 1
- Citations by year
- 2021: 1 · 2020: 1 · 2018: 1 · 2017: 1 · 2014: 1
- FWCI
- 0.77
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Classical and Quantum Gravity (publishedVersion)
- Funders
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- University of Cape Town
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Keywords
- FLRW models, probability measures, open universe, closed universe, dust cosmology, initial singularity, flatness problem, cosmological constant
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