A phase-space representation of Friedmann-Lemaitre universes containing both dust and radiation and the inevitability of a big bang
Open accessAbstract
We classify all non-static Friedmann–Lemaître universes containing dust and radiation (or, as limiting cases, vacuum), and exhibit their histories as orbits in a three-dimensional (phase-) space ℘, which faithfully reflects the topology of the set of states. As coordinates in ℘ we take the dimensionless parameters Ω, ω and λ representing, respectively, the energy density of the dust, the radiation and the vacuum (corresponding to the cosmological constant). Three open subspaces of ℘ contain, respectively, the orbits representing oscillating, inflectional and bouncing universes; their boundaries and edges contain the orbits of all the other universes. The classification proceeds from initial values |$(\Omega_0, \omega_0)$| in terms of (a, λ0) diagrams (a = R/R0). An alternative set of ‘invariant’ parameters is also introduced, characterizing whole models rather than states of models. Finally we show that present-day redshift and density data exclude all models not having a big bang, without using assumptions about the origin of the microwave background radiation and without a priori assumptions about the value of the cosmological constant.
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Ehlers & Rindler (1989) developed a parametrization in terms of observable density parameters and the Hubble parameter.
“Ehlers & Rindler (1989) developed a parametrization in terms of the observable density parameters (they also include a radiation component) and the Hubble parameter.”
From Multiverses and physical cosmology (2004) · cites this paper as Ehlers & Rindler 1989
The Introduction (pp. 2–3) parametrizes expanding states using dust and radiation density parameters and the Hubble parameter. But the authors generally also use λ, representing the cosmological constant, and explicitly say its present value is not observable in principle; the claim therefore overstates the parametrization as being in terms of observable parameters. (LLM, conf=0.86)
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Research works printed but not linked: 3
- Hawking, SD. & Israel, W., 1988. 300 Years of Gravitation, Cambridge University Press.
- Rindler, W., 1977. Essential Relativity, 2nd edn, Springer-Verlag, New York.
- Wolf, J. A., 1972. Spaces of Constant Curvature, 2nd edn, Berkeley University Press.
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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
“Ehlers & Rindler (1989) developed a parametrization in terms of the observable density parameters (they also include a radiation component) and the Hubble parameter.”
BackgroundMethodInfluential
- Authors
- Ehlers, J., & Rindler, W.
- Affiliations
- Max Planck Society (DE)
- ORCID
- Ehlers, J.
- Venue
- Monthly Notices of the Royal Astronomical Society
- Publisher
- Oxford University Press (OUP)
- Published
- 1989-05-01
- Volume
- 238
- Issue
- 2
- Pages
- 503-521
- ISSN
- 0035-8711 (ISSN-L)
- 1365-2966
- OpenAlex
- W2029899471
- Cited by
- 43
- References
- 0
- Citations by year
- 2021: 1 · 2020: 2 · 2018: 2 · 2015: 2 · 2014: 3 · 2012: 1
- FWCI
- 2.05
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Monthly Notices of the Royal Astronomical Society (publishedVersion)
- Max Planck Institute for Plasma Physics (submittedVersion)
- Max Planck Digital Library (submittedVersion, other-oa)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Stellar, planetary, and galactic studies
- Keywords
- cosmological constant, Big Bang, cyclic cosmology, bouncing universe, cosmological models, invariant parameters
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