Separate universe approach and the evolution of nonlinear superhorizon cosmological perturbations
Open accessAbstract
In this paper we review the separate universe approach for cosmological perturbations and point out that it is essentially the lowest order approximation to a gradient expansion. Using this approach, one can study the nonlinear evolution of inhomogeneous spacetimes and find the conditions under which the long wavelength curvature perturbation can vary with time. When there is one degree of freedom or a well-defined equation of state the nonlinear long wavelength curvature perturbation remains constant. With more degrees of freedom it can vary and this variation is determined by the nonadiabatic pressure perturbation, exactly as in linear theory. We identify combinations of spatial vectors characterizing the curvature perturbation which are invariant under a change of time hypersurfaces.
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The definition of N as the volume expansion rate of the t=const hypersurface holds also at second or higher order in cosmological perturbations.
“This definition is not restricted to linear theory but holds also at second or higher order in the cosmological perturbations [32, 33, 18, 21].”
From Non-Gaussianities in two-field inflation (2006) · cites this paper as [18]
Section II (p. 4) defines a local scale factor from the spatial-metric determinant, and Section III (p. 6) uses that determinant to construct a nonlinear curvature perturbation. This supports a nonlinear volume-expansion interpretation in the paper’s long-wavelength approximation, but not an unrestricted claim about perturbations at all scales. The paper also calls its symbol N the lapse function, not the volume expansion rate (Section II, p. 2). (LLM, conf=0.83)
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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
- Authors
- Rigopoulos, G. I., & Shellard, E. P. S.
- Affiliations
- University of Cambridge (GB)
- ORCID
- Rigopoulos, G. I.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2003-12-17
- Volume
- 68
- Issue
- 12
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W1980133080
- Cited by
- 199
- References
- 0
- Citations by year
- 2026: 9 · 2025: 13 · 2024: 4 · 2023: 3 · 2022: 5 · 2021: 5 · 2020: 5 · 2019: 8 · 2018: 5 · 2017: 4 · 2016: 5 · 2015: 10 · 2014: 6 · 2013: 18 · 2012: 15
- FWCI
- 6.17
- 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)
- 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
- superhorizon perturbations, curvature perturbations, gradient expansion, inhomogeneous spacetime, long-wavelength perturbations
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