Spacetime Foam and the Cosmological Constant
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In the saddle point approximation, the Euclidean path integral for quantum gravity closely resembles a thermodynamic partition function, with the cosmological constant $\ensuremath{\Lambda}$ playing the role of temperature and the ``density of topologies'' acting as an effective density of states. For $\ensuremath{\Lambda}<0$, the density of topologies grows superexponentially, and the sum over topologies diverges. In thermodynamics, such a divergence can signal the existence of a maximum temperature. The same may be true in quantum gravity: the effective cosmological constant may be driven to zero by a rapid rise in the density of topologies.
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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 [79]
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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 [79]
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Cites
The cosmological constant problem
Weinberg, S. (1989) · Reviews of Modern Physics · doi:10.1103/revmodphys.61.1 · Cited by 7,341 · see citing works
Besse, A. L. (1987) · doi:10.1007/978-3-540-74311-8 · Cited by 2,164 · see citing works
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Research works printed but not linked: 3
- [4][4] S. W. Hawking, in General Relativity, an Einstein Centenary Survey , edited by S. W. Hawking and W. Israel (Cambridge University Press, 1979). -
- [21][21] See, for example, the articles by D. J. Gross, V. Kazakov, and M.R. Douglas in Strings 90 , edited by R. Arnowitt et al. (World Scientific, 1991). -
- [22][22] K. Kuchaˇ r, in General Relativity and Relativistic Astrophysics, Proceedings of the 4th Canadian Conference , edited by G. Kunstatter, D. E. Vincent, and J. G. Williams (World Scientific, 1992). -
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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
Self-citationHolographic principle and topology change in string theory
Rey, S.-J. (1999) · Classical and Quantum Gravity · doi:10.1088/0264-9381/16/7/102 · Cited by 23 · see citing works
- Authors
- Carlip, S.
- Affiliations
- University of California, Davis (US)
- Corresponding author
- Carlip, S.
- ORCID
- Carlip, S.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1997-11-24
- Volume
- 79
- Issue
- 21
- Pages
- 4071-4074
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2079585986
- Cited by
- 40
- References
- 2
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 1 · 2023: 2 · 2019: 1 · 2018: 1 · 2017: 1 · 2015: 2 · 2014: 1 · 2013: 4 · 2012: 1
- FWCI
- 2.47
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- PIRSA
- Bulletin of the American Physical Society
- Funders
- National Science Foundation
- 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 › Cosmology and Gravitation Theories
- Keywords
- spacetime foam, cosmological constant, quantum gravity, saddlepoint approximation, Euclidean path integral, partition function, effective density of states, maximum temperature, vacuum energy
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