Inflation without a beginning: A null boundary proposal
Open accessAbstract
We develop our recent suggestion that inflation may be made past eternal, so that there is no initial cosmological singularity or ``beginning of time.'' Inflation with multiple vacua generically approaches a steady-state statistical distribution of regions at these vacua, and our model follows directly from making this distribution hold at all times. We find that this corresponds (at the semiclassical level) to particularly simple cosmological boundary conditions on an infinite null surface near which the spacetime looks de Sitter. The model admits an interesting arrow of time that is well defined and consistent for all physical observers that can communicate, even while the statistical description of the entire universe admits a symmetry that includes time reversal. Our model suggests, but does not require, the identification of antipodal points on the manifold. The resulting ``elliptic'' de Sitter spacetime has interesting classical and quantum properties. The proposal may be generalized to other inflationary potentials, or to boundary conditions that give semieternal but nonsingular cosmologies.
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Each of the other cosmological scenarios (pre-Big-Bang, ekpyrotic/cyclic, Aguirre-Gratton, and Bojowald loop quantum gravity) invokes special low-entropy conditions on some Cauchy surface, either asymptotically in the far past or at some moment of minimum size for the universe.
“To the best of our understanding, each of these proposals invokes special low-entropy conditions on some Cauchy surface, either asymptotically in the far past or at some moment of minimum size for the universe.”
From Spontaneous inflation and the origin of the arrow of time (2004) · cites this paper as [99]
The section on (semi-)classical boundary conditions specifies a particularly simple state on an infinite null hypersurface, and the Summary and Conclusions says time flows away from it. But the paper explicitly distinguishes its null boundary from a spacelike initial-value surface; it does not place the conditions on a Cauchy surface. The cited paper also cannot establish the sentence’s claim about the other named proposals. (LLM, conf=0.88)
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Cites
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 · see citing works
Inflationary Spacetimes Are Incomplete in Past Directions
Borde, A., Guth, A. H., & Vilenkin, A. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.151301 · Cited by 582 · see citing works
Could the universe have recovered from a slow first-order phase transition?
Guth, A. H., & Weinberg, E. J. (1983) · Nuclear Physics B · doi:10.1016/0550-3213(83)90307-3 · Cited by 576 · see citing works
Garriga, J., & Vilenkin, A. (1998) · Physical Review D · doi:10.1103/physrevd.57.2230 · Cited by 154 · see citing works
Decay of the true vacuum in curved space-time
Lee, K., & Weinberg, E. J. (1987) · Physical Review D · doi:10.1103/physrevd.36.1088 · Cited by 150 · see citing works
Causality and cosmic inflation
Vachaspati, T., & Trodden, M. (1999) · Physical Review D · doi:10.1103/physrevd.61.023502 · Cited by 141 · see citing works
Parikh, M., Savonije, I., & Verlinde, E. (2003) · Physical Review D · doi:10.1103/physrevd.67.064005 · Cited by 111 · see citing works
Flagged first, then by citations
Research works printed but not linked: 49
- A. Linde, D. Linde and A. Mezhlumian, Phys. Rev. D 54, 2504 (1996);
- A. Vilenkin, Phys. Rev. D 46, 2355 (1992).
- See, for example, A.H. Guth, Phys. Rept. 333, 555 (2000) and references therein;
- A.D. Linde in The Very Early Universe, edited by G.W. Gibbons, S.W. Hawking and S.T.C. Sik- los (Cambridge University Press, Cambridge, England, 1983);
- For a review, see A. Borde and A. Vilenkin, Int. J. Mod. Phys. D5 (1996) 813-824.
- A. Borde, A.H. Guth and A. Vilenkin, gr-qc/0110012. · arXiv
- A.H. Guth, Phys. Rev. D 23, 347 (1981).
- M. Bucher, A.S. Goldhaber and N. Turok, Phys. Rev. D 52, 3314 (1995).
- J.R. Gott, Nature (London) 295, 304 (1982);
- K. Ya- mamoto, M. Sasaki, and T. Tanaka, Astrophys. J. 455, 412 (1995);
- A. Linde and A. Mezhlumian, Phys. Rev. D 52, 6789 (1995)
- A. Vilenkin, Phys. Rev. D 46, 2355 (1992).
- M. Spradlin, A. Strominger, and A. Volovich, hep-th/0110007. · arXiv
- S. Coleman and F. De Luccia, Phys. Rev. D 21, 3305 (1980).
- P.J. Steinhardt and N. Turok, hep-th/0111030. · arXiv
- R. Courant, Methods of Mathematical Physics: Vol. II, Partial Differential Equations (New York: Interscience Publishers, John Wiley & Sons, 1962).
- R. Penrose, Gen. Rel. and Grav. 12, 225 (1980).
- V.A.Rubakov and S.M.Sibiryakov Theor. Math. Phys. 120, 1194 (1999).
- See, e.g., H.D. Zeh, "The physical basis of the direction of time", (Berlin: Springer-Verlag, 1999).
- R. Penrose, in "Quantum Gravity 2: A Second Oxford Symposium", ed. C.J. Isham, et al. (Oxford: Clarenden Press), 1981.
- R. Penrose, in "Fourteenth Texas Symposium on Rel- ativistic Astrophysics, Dallas, Tex., 1988" (New York: Annals of the New York Academy of Sciences, 1989);
- S. Hollands and R. Wald; gr-qc/0205058; · arXiv
- N. Turok, Class. Quantum Grav. 19, 3449 (2002).
- T. Vachaspati and M. Trodden, Phys. Rev. D 61, 023502 (2000).
- R. Penrose and W. Rindler, "Spinors and Space-Time, Vol. I", (Cambridge: Cambridge University Press, 1984).
- T. Heinzl, Lect. Notes Phys. 572, 55 (2001), hep-th/0008096. · arXiv
- S. Gratton and N. Turok, Phys. Rev. D 63, 123514 (2001).
- S.W. Hawking and T. Hertog, Phys. Rev. D 66, 123509 (2002).
- S.W. Hawking and R. Penrose, The Nature of Space and Time (Princeton University Press, Princeton, New Jer- sey, USA, 1996).
- A. Vilenkin, Phys. Rev. D 27, 2848 (1983).
- A. D. Sakharov, JETP Lett. 5, 24 (1967).
- A. D. Sakharov, Sov. Phys. JETP 52, 349 (1980).
- A. D. Sakharov, Sov. Phys. JETP 56, 705 (1982).
- A. D. Sakharov, Sov. Phys. JETP 60, 214 (1984).
- A. H. Guth, Phys. Rev. D 23, 347 (1981).
- W. de Sitter, M.N.R.A.S 78,3 (1917).
- E. Schrödinger, Expanding Universes (Cambridge Uni- versity Press, Cambridge, England, 1956).
- H. Schmidt, Fortschr. Phys. 41, 179 (1993).
- J.L. Fried- man and A. Higuchi, Phys. Rev. D 52, 5687 (1995).
- M. Parikh, I. Savonije and E. Verlinde, hep-th/0209120. · arXiv
- S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time (Cambridge University Press, Cambridge, England, 1973).
- F. Leblond, D. Marolf and R. C. Myers, JHEP 0206, 052 (2002).
- E. Mottola, Phys. Rev. D 31, 754 (1985);
- B. Allen, Phys. Rev. D 32, 3136 (1985).
- K. Lee and E.J. Weinberg, Phys. Rev. D 36, 1088 (1987).
- J. Garriga and A. Vilenkin 1998, Phys. Rev. D 57, 2230 (1998).
- A. Linde, D. Linde and A. Mezhlumian, Phys. Rev. D 49, 1783 (1994).
- R. Bousso, Rev. Mod. Phys. 74, 825 (2002).
- M. Sasaki, T. Tanaka and K. Yamamoto, Phys. Rev. D 51, 2979 (1995).
Cited by
Sorted by citations
Spontaneous inflation and the origin of the arrow of time
Carroll, S. M., & Chen, J. (2004) · arXiv · doi:10.48550/arxiv.hep-th/0410270 · Cited by 135 · see citing works
Does inflation provide natural initial conditions for the universe
Carroll, S. M., & Chen, J. (2005) · General Relativity and Gravitation · doi:10.1007/s10714-005-0148-2 · Cited by 41 · see citing works
DOES INFLATION PROVIDE NATURAL INITIAL CONDITIONS FOR THE UNIVERSE?
CARROLL, S. M., & CHEN, J. (2005) · International Journal of Modern Physics D · doi:10.1142/s0218271805008054 · Cited by 25 · see citing works
State-to-State Cosmology: A New View on the Cosmological Arrow of Time and the Past Hypothesis
Deutsch, J. M., & Aguirre, A. (2022) · Foundations of Physics · doi:10.1007/s10701-022-00597-3 · Cited by 3 · see citing works
“8 Nonetheless, it seems plausible that if our result applies to fields and self-gravitating particles, it could underlie just the sort of “time reversal” inflationary cosmology proposed in [4].”
BackgroundInfluentialSelf-citationA Casimir turning point as the beginning of a small flat universe
Zhang, A. (2026) · arXiv · doi:10.48550/arxiv.2610.24905
“…own expansion, inflation and reheating, with an arrow of time pointing away from the turn, as in time-symmetric cosmologies with two arrows [133, 134] and in past-eternal inflation, whose arrows point away from a null boundary surface [135, 136]; here they point away from a regular turning point.”
- Authors
- Aguirre, A., & Gratton, S.
- Affiliations
- Institute for Advanced Study (US)
- Princeton University (US)
- ORCID
- Aguirre, Anthony
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2003-04-29
- Volume
- 67
- Issue
- 8
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2036255656
- Cited by
- 73
- References
- 7
- Citations by year
- 2026: 2 · 2025: 4 · 2024: 5 · 2023: 4 · 2022: 3 · 2021: 2 · 2020: 6 · 2019: 2 · 2018: 2 · 2017: 2 · 2016: 3 · 2015: 2 · 2013: 2 · 2012: 3
- FWCI
- 2.45
- 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)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy (FG0291ER40671)
- W. M. Keck Foundation
- 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
- eternal inflation, origin of time, de Sitter space, arrow of time, time-reversal symmetry, multiple vacua, semiclassical cosmology, cosmological boundary conditions
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