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Euclidean vacuum mode functions for a scalar field on open de Sitter space
Open accessAbstract
Motivated by recent studies of the one-bubble inflationary universe scenario that predicts a low density, negative curvature universe, we investigate the Euclidean vacuum mode functions of a scalar field in a spatially open chart of de Sitter space which is foliated by hyperbolic time slices. When we consider the possibility of an open inflationary universe, we are faced with the problem of the initial condition for the quantum fluctuations of the inflaton field, because the inflationary era should not last too long to lose all information of the initial condition. In the one-bubble scenario, in which an open universe is created in an exponentially expanding false vacuum universe triggered by quantum decay of a false vacuum, it seems natural that the initial state is the de Sitter--invariant Euclidean vacuum. Here we present explicit expressions for the Euclidean vacuum mode functions in the open chart for a scalar field with arbitrary mass and curvature coupling.
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In the present case, all three measures mentioned (comoving probability, causal patch, and scale-factor cutoff) give similar predictions.
“however in the present case it turns out that all three measures mentioned above give similar predictions [66,67,68,69].”
From Observable effects of anisotropic bubble nucleation (2010) · cites this paper as [66]
Section II discusses scalar-field mode functions, and Section IV discusses the Euclidean vacuum power spectrum; neither compares cosmological probability measures. Searches for comoving probability, causal patch, scale-factor cutoff, and similar predictions found no passage addressing the claim in our copy. (LLM, conf=0.75)
Experimental — accuracy not yet measuredThe prior distribution from [66] suggests the landscape might strongly prefer fewer e-folds of slow-roll inflation, with dP(N) ∝ N^-4 dN.
“The prior distribution is addressed in [66], where an (admittedly crude) argument is given to suggest that the landscape might strongly prefer fewer e-folds of slow-roll inflation, with the distribution dP (N ) ∝ N -4 dN .”
From Observable effects of anisotropic bubble nucleation (2010) · cites this paper as [66]
The Introduction discusses open-universe inflation and the duration of secondary inflation, but gives no landscape prior. Searches for the e-fold distribution and N^-4 found only unrelated mode-function equations; no passage in our copy addresses the claimed probability distribution. (LLM, conf=0.76)
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Gravitational effects on and of vacuum decay
Coleman, S., & De Luccia, F. (1980) · Physical Review D · doi:10.1103/physrevd.21.3305 · Cited by 1,537
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Research works printed but not linked: 22
- S.D.M. White, 1992, Clusters and Superclusters of Galaxies
- G. Smoot, 1992, Astrophys. J., 396, L1, 10.1086/186504 · DOI
- D.H. Lyth, 1990, Phys. Lett. B, 252, 336, 10.1016/0370-2693(90)90548-K · DOI
- B. Ratra, 1994, Astrophys. J. Lett., 432, L5, 10.1086/187498 · DOI
- N. Sugiyama, 1992, Prog. Theor. Phys., 88, 803, 10.1143/ptp/88.5.803 · DOI
- W. Hu, 1994, Phys. Rev. D, 50, 627, 10.1103/PhysRevD.50.627 · DOI
- A. Kashlinsky, 1994, Phys. Rev. Lett., 73, 1582, 10.1103/PhysRevLett.73.1582 · DOI
- M. Sasaki, 1993, Phys. Lett. B, 317, 510, 10.1016/0370-2693(93)91364-S · DOI
- J.R. Gott, 1982, Nature (London), 295, 304, 10.1038/295304a0 · DOI
- S. Coleman, 1977, Phys. Rev. D, 15, 2929, 10.1103/PhysRevD.15.2929 · DOI · Paper page
- C. Callan, 1977, Phys. Rev. D, 16, 1763, 10.1103/PhysRevB.16.1763 · DOI
- V.A. Rubakov, 1984, Nucl. Phys., B245, 481, 10.1016/0550-3213(84)90443-7 · DOI
- T. Vachaspati, 1991, Phys. Rev. D, 43, 3846, 10.1103/PhysRevD.43.3846 · DOI
- T. Tanaka, 1994, Phys. Rev. D, 49, 1039, 10.1103/PhysRevD.49.1039 · DOI
- M. Sasaki, 1993, Prog. Theor. Phys., 90, 1019, 10.1143/ptp/90.5.1019 · DOI
- T. Tanaka, 1994, Phys. Rev. D, 50, 6444, 10.1103/PhysRevD.50.6444 · DOI
- K. Yamamoto, 1995, Phys. Rev. D, 51, 2968, 10.1103/PhysRevD.51.2968 · DOI
- E.A. Tagirov, 1973, Ann. Phys. (N.Y.), 76, 561, 10.1016/0003-4916(73)90047-X · DOI
- T.S. Bunch and P.C. Davies, 1978, Ser. A, 360, 117, 10.1098/rspa.1978.0060 · DOI
- B. Allen, 1988, Phys. Rev. D, 37, 2078, 10.1103/PhysRevD.37.2078 · DOI
- J.D. Pfautsch, 1982, Phys. Lett., 117B, 283, 10.1016/0370-2693(82)90719-5 · DOI
- D. Gromes, 1973, Nucl. Phys., B75, 313
Cited by
Sorted by citations
ANNINOS, D. (2012) · International Journal of Modern Physics A · doi:10.1142/s0217751x1230013x · Cited by 174
Holographic framework for eternal inflation
Freivogel, B., Sekino, Y., Susskind, L., & Yeh, C.-P. (2006) · Physical Review D · doi:10.1103/physrevd.74.086003 · Cited by 117
Observable effects of anisotropic bubble nucleation
Blanco-Pillado, J. J., & Salem, M. P. (2010) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2010/07/007 · Cited by 44
Quantized gravitational waves in the Milne universe
Tanaka, T., & Sasaki, M. (1997) · Physical Review D · doi:10.1103/physrevd.55.6061 · Cited by 25
Self-citation
Metadata
- Authors
- Sasaki, M., Tanaka, T., & Yamamoto, K.
- Affiliations
- Kyoto University (JP)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1995-03-15
- Volume
- 51
- Issue
- 6
- Pages
- 2979-2995
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2086053586
- Cited by
- 133
- References
- 1
- Citations by year
- 2026: 7 · 2025: 7 · 2024: 1 · 2023: 4 · 2022: 6 · 2021: 5 · 2020: 8 · 2019: 7 · 2018: 4 · 2017: 2 · 2016: 4 · 2015: 5 · 2014: 9 · 2013: 10 · 2012: 7
- FWCI
- 12.69
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- University of Cambridge
- Ministry of Education, Culture, Sports, Science and Technology (05640342)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- Euclidean vacuum, mode functions, scalar field, initial conditions, quantum fluctuations, inflaton, false vacuum decay, curvature coupling, negative curvature
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