Evolution of Nonlinear Cosmological Perturbations
Open accessAbstract
We define fully nonperturbative generalizations of the uniform density and comoving curvature perturbations, which are known, in the linear theory, to be conserved on sufficiently large scales for adiabatic perturbations. Our nonlinear generalizations are defined geometrically, independently of any coordinate system. We give the equations governing their evolution on all scales. Also, in order to make contact with previous works on first- and second-order perturbations, we introduce a coordinate system and show that previous results can be recovered, on large scales, in a remarkably simple way, after restricting our definitions to first and second orders in a perturbative expansion.
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Rigopoulos et al. used numerical simulations of the stochastic dynamics on large scales and found significant non-Gaussianity even in simple two-field models.
“Rigopoulos et al. [22] have used numerical simulations of the stochastic dynamics on large scales and found significant non-Gaussianity even in simple two-field models.”
From Non-Gaussianities in two-field inflation (2006) · cites this paper as [22]
The discussion on p. 4 says only that non-Gaussianity can evolve on large scales when more than one field is present. The references on p. 4 name Rigopoulos and Shellard, but our copy does not say they ran numerical simulations of stochastic dynamics or found significant non-Gaussianity in two-field models (searched: numerical, stochastic, two-field). (LLM, conf=0.76)
Experimental — accuracy not yet measuredThe paper's results disagree with those of Rigopoulos et al. [22], who found that double quadratic inflation, in particular the model studied in Sec. 5.2, can generate large non-Gaussianity.
“Our results disagree with those of Rigopoulos et al. [22] who found that double quadratic inflation, in particular the model studied in Sec. 5.2, can generate large non-Gaussianity.”
From Non-Gaussianities in two-field inflation (2006) · cites this paper as [22]
The discussion on p. 4 says that non-Gaussianity can evolve on large scales when more than one field is present, but it does not discuss double quadratic inflation or a large non-Gaussianity result for that model. The references on p. 4 list Rigopoulos and Shellard, without reporting the finding attributed to them. Searches for the model and the alleged disagreement found no passage addressing either point. (LLM, conf=0.73)
Experimental — accuracy not yet measuredThe paper's conclusion that f_NL is small for the specific double quadratic inflation model investigated in Sec. 5 is in qualitative agreement with an improved numerical calculation by the authors of [22].
“Note added: After completing this work we have learnt [50] that our conclusion that f NL is small for the specific double quadratic inflation model investigated in Sec. 5 is in qualitative agreement with an improved numerical calculation by the authors of [22].”
From Non-Gaussianities in two-field inflation (2006) · cites this paper as [22]
The Conclusion (p. 4) discusses the evolution of non-Gaussianity during inflation, but gives no result for f_NL in a double quadratic model. Searches for the model, Sec. 5, and the improved numerical calculation found no passage addressing the claimed agreement. (LLM, conf=0.76)
Experimental — accuracy not yet measuredThe formalism used by Rigopoulos et al. differs from the δN-formalism in that it takes into account the sub-Hubble evolution of field perturbations via stochastic terms and integrates explicitly the coupled evolution of the adiabatic and entropy super-Hubble perturbations.
“The formalism used by Rigopoulos et al. differs from the δN -formalism in two aspects: First, it takes into account the sub-Hubble evolution of the field perturbations via stochastic terms. Second, it integrates explicitly the coupled evolution of the adiabatic and entropy super-Hubble perturbations.”
From Non-Gaussianities in two-field inflation (2006) · cites this paper as [22]
The paper identifies Rigopoulos and Shellard in its references (p. 4) and notes a related long-wavelength result (p. 2), but does not describe their formalism as using stochastic terms or explicitly integrating coupled adiabatic and entropy perturbations. Its discussion of evolution at all scales concerns the authors’ own formulation (p. 4). Searches for those distinctive features did not find support for the claimed comparison with δN. (LLM, conf=0.76)
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Research works printed but not linked: 2
- [8]G. I. Rigopoulos and E. P. S. Shellard, Phys. Rev. D 68 123518 (2003); G. I. Rigopoulos and E. P. S. Shellard, arXiv:astro-ph/0405185. · arXiv
- [14]G. F. R. Ellis, Relativistic Cosmology, in General Relativity and Cosmology , proceedings of the XLVII Enrico Fermi Summer School, edited by R. K. Sachs (Academic, New York, 1971). [15]
Cited by
Sorted by citations
Towards a nonsingular bouncing cosmology
Cai, Y.-F., Easson, D. A., & Brandenberger, R. (2012) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2012/08/020 · Cited by 439 · see citing works
Non-Gaussianities in two-field inflation
Vernizzi, F., & Wands, D. (2006) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2006/05/019 · Cited by 274 · see citing works
Self-citation
- Authors
- Langlois, D., & Vernizzi, F.
- Affiliations
- Centre National de la Recherche Scientifique (FR)
- University of Helsinki (FI)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2005-08-26
- Volume
- 95
- Issue
- 9
- Pages
- 091303-091303
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2024509936
- Cited by
- 131
- References
- 0
- Citations by year
- 2026: 2 · 2025: 4 · 2024: 2 · 2023: 2 · 2022: 2 · 2021: 2 · 2020: 3 · 2018: 6 · 2017: 5 · 2016: 5 · 2015: 6 · 2014: 8 · 2013: 9 · 2012: 6
- FWCI
- 8.33
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- PubMed (publishedVersion)
- HAL (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- curvature perturbations, adiabatic perturbations, comoving curvature perturbation, second-order perturbation theory, large-scale structure, perturbation expansion
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