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Cited by 33Cosmology and Gravitation TheoriesNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical Physics

Canonical measure and the flatness of a FRW universe

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Coule, D H·1995·Classical and Quantum Gravity
DOI 10.1088/0264-9381/12/2/015
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Abstract

We consider the claim of Hawking and Page that the canonical measure applied to Friedmann--Robertson--Walker models with a massive scalar field can solve the flatness problem, i.e. , regardless of inflation occurring or not. We point out a number of ways in which this prediction, which relies predominantly on post-Planckian regions of the classical phase space, could break down. By considering a general potential we are able to understand how the ambiguity for found by Page in the -theory is present, in general, for scalar field models when the potential is bounded from above. We suggest reasons why such potentials are more realistic, which then results in the value of being arbitrary. Although the canonical measure gives an ambiguity (due to the infinite measure over arbitrary scale factors) for the possibility of inflation, the inclusion of an input from quantum cosmology could resolve this ambiguity. This could simply be that due to a `quantum event' the Universe started small, and provided a suitable scalar potential is present an inflationary period could then be `near certain' to proceed in order to set infinitesimally close to unity. We contrast the measure obtained in this way with the more usual ones obtained in quantum cosmology: the Hartle--Hawking and tunnelling ones.

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Crossref · 10.1088/0264-9381/12/2/015

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  • Later works [65, 66, 67] correctly described the divergence as arising from nearly-flat universes.

    “Later works [65, 66, 67] correctly described the divergence as arising from nearly-flat universes.”

    From In What Sense Is the Early Universe Fine-Tuned? (2014) · cites this paper as [66]

  • Larger black holes which maximize the entropy have lower temperatures.

    “For example, larger Black holes which maximize the entropy have lower temperatures [14].”

    From Entropic Issues in Contemporary Cosmology (2003) · cites this paper as [14]

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Authors
Coule, D. H.
Affiliations
University of Cape Town (ZA)
Corresponding author
Coule, D H
Venue
Classical and Quantum Gravity
Publisher
IOP Publishing
Published
1995-02-01
Volume
12
Issue
2
Pages
455-469
ISSN
  • 0264-9381 (ISSN-L)
  • 1361-6382
DOI
10.1088/0264-9381/12/2/015
OpenAlex
W2062292546
Cited by
33
References
26
Citations by year
2026: 1 · 2023: 1 · 2021: 2 · 2020: 4 · 2019: 1 · 2017: 2 · 2016: 2 · 2015: 1 · 2014: 1 · 2013: 1 · 2012: 2
FWCI
0.40
Type
journal article
Language
en
Open access
Locations
  • Classical and Quantum Gravity (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
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 › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
Keywords
canonical measure, flatness problem, FRW universe, massive scalar field, inflation (cosmology), quantum cosmology, initial singularity

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