Dominant topologies in Euclidean quantum gravity
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The dominant topologies in the Euclidean path integral for quantum gravity differ sharply according to the sign of the cosmological constant. For , saddle points can occur only for topologies with vanishing first Betti number and finite fundamental group. For , on the other hand, the path integral is dominated by topologies with extremely complicated fundamental groups; while the contribution of each individual manifold is strongly suppressed, the `density of topologies' grows fast enough to overwhelm this suppression. The value is thus a sort of boundary between phases in the sum over topologies. I discuss some implications for the cosmological constant problem and the Hartle-Hawking wavefunction.
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The discovery that the sum over topologies can lead to a divergent partition function has been extended to 3+1 dimensions, at least for Λ < 0, and it has been argued that this behavior might signal a phase transition that could prohibit a conventional cosmology with a negative cosmological constant.
“Second, the discovery that the sum over topologies can lead to a divergent partition function has been extended to 3 + 1 dimensions, at least for Λ < 0, and it has been argued that this behavior might signal a phase transition that could prohibit a conventional cosmology with a negative cosmological constant [79, 80].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [80]
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Experimental — accuracy not yet measuredSimilar results for sums over topologies have been found in four dimensions.
“It is only quite recently that similar results for sums over topologies have been found in four dimensions [79, 80, 229, 19].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [80]
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Research works printed but not linked: 9
- See, for example, Polchinski J 1993 Recent Directions in Particle Theory: from Superstrings and Black Holes to the Standard Model (TASI 92) ed J Harvey and J Polchinski (Singapore: World Scientific)
- Hawking S W 1979 General Relativity, an Einstein Centenary Survey ed S W Hawking and W Israel (Cambridge: Cambridge University Press)
- Besse A L 1987 Einstein Manifolds (Berlin: Springer)
- Bishop R L and Goldberg S I 1964 Trans. Am. Math. Soc. 112 508
- Ratcliffe J G 1994 Foundations of Hyperbolic Manifolds (Berlin: Springer)
- See, for example, Gardiner F P 1987 Teichmüller Theory and Quadratic Differentials (New York: Wiley)
- See, for example, the articles by Gross D J, Kazakov V and Douglas M R 1991 Strings 90 ed R Arnowitt et al (Singapore: World Scientific)
- Kuchař K 1992 General Relativity and Relativistic Astrophysics, Proc. 4th Canadian Conf. ed G Kunstatter, D E Vincent and J G Williams (Singapore: World Scientific)
- Hartle J B 1995 Gravitation and Quantizations ed B Julia and J Zinn-Justin (Amsterdam: Elsevier)
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Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
Self-citationCarlip, S. (2023) · Reports on Progress in Physics · doi:10.1088/1361-6633/acceb4 · Cited by 41 · see citing works
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- Authors
- Carlip, S.
- Affiliations
- University of California, Davis (US)
- Corresponding author
- Carlip, S
- ORCID
- Carlip, S
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1998-09-01
- Volume
- 15
- Issue
- 9
- Pages
- 2629-2638
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2054988941
- Cited by
- 41
- References
- 0
- Citations by year
- 2025: 1 · 2023: 1 · 2021: 1 · 2020: 2 · 2015: 4 · 2014: 2 · 2013: 2 · 2012: 1
- FWCI
- 3.71
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (9357203)
- U.S. Department of Energy (FG0391ER40674)
- Topics
- 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
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- Euclidean quantum gravity, path integral, cosmological constant, saddle points, first Betti number, fundamental group, cosmological constant problem
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