Peaks in the Hartle–Hawking wavefunction from sums over topologies
Open accessAbstract
Recent developments in ‘Einstein Dehn filling’ allow the construction of infinitely many Einstein manifolds that have different topologies but are geometrically close to each other. Using these results, we show that for many spatial topologies, the Hartle–Hawking wavefunction for a spacetime with a negative cosmological constant develops sharp peaks at certain calculable geometries. The peaks we find are all centred on spatial metrics of constant negative curvature, suggesting a new mechanism for obtaining local homogeneity in quantum cosmology.
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Similar 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 [19]
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Research works printed but not linked: 5
- [1][1] S. W. Hawking, in General Relativity: An Einstein Centenary Survey, S. W. Hawking and W. Israel, editors (Cambridge University Press, 1979).
- [14][14] M. T. Anderson, math.dg/0303260. · arXiv
- [17][17] P. Petersen, Riemannian Geometry (Springer, 1998).
- [19][19] M. Burger, T. Gelander, A. Lubotzky, and S. Mozes, Geom. Funct. Anal. 12 (2002) 1161. 14 http://arxiv.org/abs/math/0303260 · arXiv
- [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).
Cited by
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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
- Anderson, M., Carlip, S., Ratcliffe, J. G., Surya, S., & Tschantz, S. T.
- Affiliations
- Stony Brook University (US)
- University of California, Davis (US)
- Vanderbilt University (US)
- Raman Research Institute (IN)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2003-12-23
- Volume
- 21
- Issue
- 2
- Pages
- 729-741
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2076853091
- Cited by
- 28
- References
- 0
- Citations by year
- 2024: 1 · 2023: 1 · 2022: 1 · 2014: 1 · 2013: 3 · 2012: 2
- FWCI
- 1.78
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.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 (0305865)
- U.S. Department of Energy
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- negative cosmological constant, Einstein manifolds, constant negative curvature, local homogeneity, quantum cosmology, spatial topology, Euclidean quantum gravity
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