New approach to the evolution of cosmological perturbations on large scales
Open accessAbstract
We discuss the evolution of linear perturbations about a Friedmann-Robertson-Walker background metric, using only the local conservation of energy momentum. We show that on sufficiently large scales the curvature perturbation on spatial hypersurfaces of uniform density is conserved when the non-adiabatic pressure perturbation is negligible. This is the first time that this result has been demonstrated independently of the gravitational field equations. A physical picture of long-wavelength perturbations as being composed of separate Robertson-Walker universes gives a simple understanding of the possible evolution of the curvature perturbation, in particular clarifying the conditions under which super-horizon curvature perturbations may vary.
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According to the δN-formalism, ζ evaluated at some time tc is equivalent, on large scales, to the perturbation of the number of e-foldings N from an initial flat hypersurface at t* to a final comoving or uniform density hypersurface at tc.
“According to the so called δN -formalism [30, 31, 32], ζ , evaluated at some time t = t c , is equivalent, on large scales , to the perturbation of the number of e -foldings N ( t c , t ∗ , x ) from an initial fl at hypersurface at t = t ∗ , to a final comoving - or, equivalently, uniform density - hypersurface at t = t c .”
From Non-Gaussianities in two-field inflation (2006) · cites this paper as [32]
The Separate Universe Approach (p. 4) relates the large-scale curvature perturbation to differences in integrated expansion between hypersurfaces, supporting the δN part of the claim. But the paper says comoving and uniform-density hypersurfaces coincide for adiabatic perturbations (p. 6) and need not coincide when non-adiabatic pressure perturbations are present (p. 7). The citing sentence omits that qualification when calling the final hypersurfaces equivalent. (LLM, conf=0.88)
Experimental — accuracy not yet measuredThe 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 [32]
The rate-of-change discussion (p. 3) defines an expansion rate with respect to coordinate time for constant-time hypersurfaces, and the separate-universe discussion (p. 4) defines the integrated expansion N. But the paper frames its treatment in linear perturbation theory and says in the Conclusions (p. 8) that the separate-universe description applies as long as linear perturbation theory is valid. It does not establish that this definition holds at second or higher order. (LLM, conf=0.86)
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Cites
Heterotic and Type I string dynamics from eleven dimensions
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Flagged first, then by citations
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Cited by
Sorted by citations
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-citationBojowald, M. (2015) · Reports on Progress in Physics · doi:10.1088/0034-4885/78/2/023901 · Cited by 174 · see citing works
Possibility of Observable Amount of Gravitational Waves from Inflation
Pilo, L., Riotto, A., & Zaffaroni, A. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.201303 · Cited by 19 · see citing works
- Authors
- Wands, D., Malik, K. A., Lyth, D. H., & Liddle, A. R.
- Affiliations
- University of Portsmouth (GB)
- Lancaster University (GB)
- University of Sussex (GB)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2000-07-27
- Volume
- 62
- Issue
- 4
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2086160589
- Cited by
- 862
- References
- 1
- Citations by year
- 2026: 42 · 2025: 38 · 2024: 33 · 2023: 39 · 2022: 34 · 2021: 33 · 2020: 26 · 2019: 24 · 2018: 32 · 2017: 19 · 2016: 46 · 2015: 42 · 2014: 36 · 2013: 60 · 2012: 42
- FWCI
- 13.12
- 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
- Royal Society
- 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
- cosmological perturbations, curvature perturbations, large-scale structure, Friedmann-Robertson-Walker metric, long-wavelength perturbations, Robertson-Walker universe, linear perturbations
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