Can backreaction prevent eternal inflation?
Open accessAbstract
We study the effects exerted by the backreaction of long-wavelength fluctuations on stochastic inflation. In the cases of power-law and Starobinsky inflation, these effects are too weak to terminate the stochastic growth of the inflaton field. However, in the case of the cyclic ekpyrotic scenario, the backreaction effects prevent the unlimited growth of the scalar field.
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The backreaction of fluctuations that have exited the Hubble radius leads to a decrease in effective energy density strong enough to prevent eternal expansion in the late-time dark-energy phase of ekpyrotic cosmology.
“However, as Brandenberger et al. [119] show, the backreaction of fluctuations that have already exited the Hubble radius will lead to a decrease in the effective energy density, which is strong enough to prevent eternal expansion in the late-time dark-energy phase of ekpyrotic cosmology.”
From Weyl Curvature Hypothesis in Light of Quantum Backreaction at Cosmological Singularities or Bounces (2021) · cites this paper as [119]
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Cites
Inflationary universe: A possible solution to the horizon and flatness problems
Guth, A. H. (1981) · Physical Review D · doi:10.1103/physrevd.23.347 · Cited by 9,983 · see citing works
A new type of isotropic cosmological models without singularity
Starobinsky, A. A. (1980) · Physics Letters B · doi:10.1016/0370-2693(80)90670-x · Cited by 7,677 · see citing works
Theory of cosmological perturbations
Mukhanov, V (1992) · Physics Reports · doi:10.1016/0370-1573(92)90044-z · Cited by 3,608 · see citing works
Linde, A. D. (1983) · Physics Letters B · doi:10.1016/0370-2693(83)90837-7 · Cited by 3,299 · see citing works
Gauge-invariant cosmological perturbations
Bardeen, J. M. (1980) · Physical Review D · doi:10.1103/physrevd.22.1882 · Cited by 2,393 · see citing works
First-order phase transition of a vacuum and the expansion of the Universe
Sato, K. (1981) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/195.3.467 · Cited by 1,792 · cited 2× · see citing works
“Inflationary cosmology [1–4] is the current paradigm of early universe cosmology.”
BackgroundEleven-dimensional supergravity on a manifold with boundary
Hořava, P., & Witten, E. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(96)00308-2 · Cited by 1,626 · see citing works
Ekpyrotic universe: Colliding branes and the origin of the hot big bang
Khoury, J., Ovrut, B. A., Steinhardt, P. J., & Turok, N. (2001) · Physical Review D · doi:10.1103/physrevd.64.123522 · Cited by 1,549 · see citing works
Martin, J. (2012) · Comptes Rendus Physique · doi:10.1016/j.crhy.2012.04.008 · Cited by 918 · see citing works
Monodromy in the CMB: Gravity waves and string inflation
Silverstein, E. M., & Westphal, A. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.106003 · Cited by 896 · see citing works
Li, M., Li, X.-D., Wang, S., & Wang, Y. (2011) · Communications in Theoretical Physics · doi:10.1088/0253-6102/56/3/24 · Cited by 838 · see citing works
Cosmic evolution in a cyclic universe
Steinhardt, P. J., & Turok, N. (2002) · Physical Review D · doi:10.1103/physrevd.65.126003 · Cited by 813 · see citing works
Spectrum of relict gravitational radiation and the early state of the universe
Старобинский, А. А. (1996) · World Scientific series in 20th century physics · doi:10.1142/9789814317344_0078 · Cited by 698 · see citing works
Large Scale Quantum Fluctuations in the Inflationary Universe
Sasaki, M. (1986) · Progress of Theoretical Physics · doi:10.1143/ptp.76.1036 · Cited by 646 · see citing works
The creation of the universe as a quantum phenomenon
Brout, R., Englert, F., & Gunzig, E. (1978) · Annals of Physics · doi:10.1016/0003-4916(78)90176-8 · Cited by 435 · see citing works
Eternal inflation and its implications
Guth, A. H. (2007) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/40/25/s25 · Cited by 366 · see citing works
Buchbinder, E. I., Khoury, J., & Ovrut, B. A. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.123503 · Cited by 344 · see citing works
Backreaction Problem for Cosmological Perturbations
Mukhanov, V., Abramo, L. R., & Brandenberger, R. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.1624 · Cited by 309 · see citing works
Self-citationQuantum gravity slows inflation
Tsamis, N. C., & Woodard, R. P. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(96)00246-5 · Cited by 307 · see citing works
Energy-momentum tensor for cosmological perturbations
Abramo, L. R., Brandenberger, R., & Mukhanov, V. (1997) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.56.3248 · Cited by 300 · see citing works
Self-citationField Theory, Quantum Gravity and Strings
de Vega, H. J., & Sanchez, N. G. (1986) · Lecture notes in physics · doi:10.1007/3-540-16452-9 · Cited by 299 · see citing works
The Quantum Gravitational Back-Reaction on Inflation
Tsamis, N. C., & Woodard, R. P. (1997) · Annals of Physics · doi:10.1006/aphy.1997.5613 · Cited by 294 · see citing works
Eternal inflation and its implicationsPreprint
Guth, A. H. (2007) · Cited by 245 · see citing works
Relaxing the cosmological constant
Tsamis, N. C., & Woodard, R. P. (1993) · Physics Letters B · doi:10.1016/0370-2693(93)91162-g · Cited by 210 · see citing works
Generating ekpyrotic curvature perturbations before the big bang
Lehners, J.-L., McFadden, P. L., Turok, N., & Steinhardt, P. J. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.103501 · Cited by 207 · see citing works
Lectures on the Theory of Cosmological Perturbations
Brandenberger, R. (2004) · Lecture notes in physics · doi:10.1007/978-3-540-40918-2_5 · Cited by 205 · see citing works
Self-citationA smooth bouncing cosmology with scale invariant spectrum
Creminelli, P., & Senatore, L. (2007) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2007/11/010 · Cited by 199 · see citing works
A smooth bouncing cosmology with scale invariant spectrum
Creminelli, P., & Senatore, L. (2007) · CERN Document Server (European Organization for Nuclear Research) · Cited by 197 · see citing works
Back reaction and the local cosmological expansion rate
Geshnizjani, G., & Brandenberger, R. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.66.123507 · Cited by 184 · see citing works
Self-citationChaotic inflation in supergravity
Goncharov, A. S., & Linde, A. D. (1984) · Physics Letters B · doi:10.1016/0370-2693(84)90027-3 · Cited by 179 · see citing works
Quantum Theory of Gauge Invariant Cosmological Perturbations
Mukhanov, V. (1988) · Journal of Experimental and Theoretical Physics · Cited by 176 · see citing works
Isocurvature perturbations in the Ekpyrotic Universe
Notari, A., & Riotto, A. (2002) · Nuclear Physics B · doi:10.1016/s0550-3213(02)00765-4 · Cited by 106 · see citing works
Back-reaction of perturbations in two scalar field inflationary models
Geshnizjani, G., & Brandenberger, R. (2005) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2005/04/006 · Cited by 103 · see citing works
Self-citationNo one loop back reaction in chaotic inflation
Abramo, L. R., & Woodard, R. P. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.65.063515 · Cited by 88 · see citing works
Back Reaction Of Perturbations In Two Scalar Field Inflationary Models
Geshnizjani, G., & Brandenberger, R. (2003) · CERN Document Server (European Organization for Nuclear Research) · Cited by 86 · see citing works
Self-citationThe Early Universe and Observational Cosmology
Cervantes–Cota, J. L., Salgado, M., & Bretón, N. (2004) · Lecture notes in physics · doi:10.1007/b97189 · Cited by 71 · see citing works
Cosmological long wavelength perturbationsPreprint
Unruh, W. G. (1998) · arXiv (Cornell University) · doi:10.48550/arxiv.astro-ph/9802323 · Cited by 67 · see citing works
Isocurvature Perturbations in the Ekpyrotic Universe
Notari, A., & Riotto, A. (2002) · CERN Document Server (European Organization for Nuclear Research) · Cited by 65 · see citing works
Back Reaction of Cosmological Perturbations and the Cosmological Constant ProblemPreprint
Brandenberger, R. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0210165 · Cited by 53 · see citing works
Self-citationEffects of gravitational backreaction on cosmological perturbations
Martineau, P., & Brandenberger, R. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.72.023507 · Cited by 48 · see citing works
Self-citationCosmological backreaction for a test field observer in a chaotic inflationary model
Marozzi, G., Vacca, G. P., & Brandenberger, A. R. H. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/02/027 · Cited by 38 · see citing works
Perreault-Levasseur, L. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.88.083537 · Cited by 32 · see citing works
Cosmological Backreaction for a Test Field Observer in a Chaotic Inflationary ModelPreprint
Marozzi, G., Vacca, G. P., & Brandenberger, R. (2016) · Cited by 30 · see citing works
Self-citationTransfer of metric fluctuations when extra dimensions bounce or stabilize
Battefeld, T. J., Patil, S. P., & Brandenberger, R. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.73.086002 · Cited by 28 · see citing works
Self-citationLectures on the Theory of Cosmological PerturbationsPreprint
Brandenberger, R. (2003) · doi:10.48550/arxiv.hep-th/0306071 · Cited by 5 · see citing works
Self-citationQuantum Gravity Slows InflationPreprint
Tsamis, N. C., & Woodard, R. P. (1996) · doi:10.48550/arxiv.hep-ph/9602315
Flagged first, then by citations
Research works printed but not linked: 6
- [5]5. V. Mukhanov and G. Chibisov, "Quantum Fluctuation And Nonsingular Universe. (In Russian)," JETP Lett. 33, 532 (1981) [Pisma Zh. Eksp. Teor. Fiz. 33, 549 (1981)].
- [11]11. M. Li, X. D. Li, S. Wang and Y. Wang, "Dark Energy," Commun. Theor. Phys. 56, 525 (2011) [arXiv:1103.5870 [astro-ph.CO]]; · arXiv
- [13]13. N. C. Tsamis and R. P. Woodard, "Relaxing the cosmo- logical constant," Phys. Lett. B 301, 351 (1993);
- [17]17. V. F. Mukhanov, L. R. W. Abramo and R. H. Bran- denberger, "On the Back reaction problem for gravita- tional perturbations," Phys. Rev. Lett. 78, 1624 (1997) [gr-qc/9609026]. · arXiv
- [22]22. P. Martineau and R. H. Brandenberger, "The Effects of gravitational back-reaction on cosmological pertur- bations," Phys. Rev. D 72, 023507 (2005) [astro-ph/ 0505236].
- [23]23. J. M. Bardeen, "Gauge Invariant Cosmological Pertur- bations," Phys. Rev. D 22, 1882 (1980).
Cited by
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Eternal inflation and the quantum birth of cosmic structure
León, G. (2017) · The European Physical Journal C · doi:10.1140/epjc/s10052-017-5288-5 · Cited by 12 · see citing works
Eternal inflation in a dissipative and radiation environment: Heated demise of eternity
Vicente, G. S., da Silva, L. A., & Ramos, R. O. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.93.063509 · Cited by 9 · see citing works
Varying fundamental constants: a full covariant approach and cosmological applicationsPreprint
Franzmann, G. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1704.07368 · Cited by 9 · see citing works
Self-citationWeyl Curvature Hypothesis in Light of Quantum Backreaction at Cosmological Singularities or Bounces
Hu, B.-L. (2021) · Universe · doi:10.3390/universe7110424 · Cited by 8 · see citing works
Eternal inflation and collapse theories
Lechuga, R.-L., & Sudarsky, D. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/01/038 · Cited by 6 · see citing works
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Blachier, B., & Ringeval, C. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/11/032 · Cited by 1 · see citing works
Inflationary quantum dynamics and backreaction using a classical-quantum correspondence
Bernardo, R. C. (2021) · The European Physical Journal C · doi:10.1140/epjc/s10052-021-09781-7 · Cited by 1 · see citing works
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Cheraghchi, S., & Shojai, F. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.100.103509 · Cited by 1 · see citing works
A note on trans-Planckian tail effects
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- Authors
- Brandenberger, R., Costa, R., & Franzmann, G.
- Affiliations
- McGill University (CA)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2015-08-25
- Volume
- 92
- Issue
- 4
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W1689867260
- Semantic Scholar
- 6fb0d8b4ab77cc4194b71c094b50f26a8f1f9a61
- Cited by
- 10
- References
- 44
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 1 · 2021: 2 · 2019: 1 · 2017: 2 · 2016: 1 · 2015: 1
- FWCI
- 0.76
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (publishedVersion, other-oa)
- arXiv (Cornell University) (submittedVersion)
- Americanae (AECID Library) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- Natural Sciences and Engineering Research Council of Canada
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (5149/2014-02)
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- 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
- backreaction, eternal inflation, stochastic inflation, long-wavelength fluctuations, power-law inflation, Starobinsky inflation, inflaton
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