CoChat
Sign Up
Cited by 129Cosmology and Gravitation TheoriesGalaxies: Formation, Evolution, PhenomenaNoncommutative and Quantum Gravity Theories

Conserved nonlinear quantities in cosmology

Open access
Langlois, David, Vernizzi, Filippo·2005·Physical Review D
DOI 10.1103/physrevd.72.103501
Open this paper in CoChat — free accountOpen PDF

Abstract

We give a detailed and improved presentation of our recently proposed formalism for nonlinear perturbations in cosmology, based on a covariant and fully nonperturbative approach. We work, in particular, with a covector combining the gradients of the energy density and of the local number of e-folds to obtain a nonlinear generalization of the familiar linear uniform-density perturbation. We show that this covector obeys a remarkably simple conservation equation which is exact, fully nonlinear and valid at all scales. We relate explicitly our approach to the coordinate-based formalisms for linear perturbations and for second-order perturbations. We also consider other quantities, which are conserved on sufficiently large scales for adiabatic perturbations, and discuss the issue of gauge invariance.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physrevd.72.103501

Cites

1 of 1 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The paper's results agree with the previous discussion of non-Gaussianity in a double quadratic potential by Alabidi and Lyth [23].

    “Our results agree with a previous discussion of non-Gaussianity in a double quadratic potential by Alabidi and Lyth [23], based on an estimate of δN given in [1] using the integral (42).”

    From Non-Gaussianities in two-field inflation (2006) · cites this paper as [23]

    The agreement with Alabidi and Lyth is attributed to [23] in the citing sentence, not to this source, [1]. Our copy discusses a local number of e-folds (Abstract, p. 1), but its discussion of equation (42) concerns a linear perturbation equation (Section 4, p. 10); the passages found do not establish an estimate of δN using an integral (42). (LLM, conf=0.76)

    Experimental — accuracy not yet measured

  • The results for double inflation coincide with the estimate of Ref. [23].

    “These results coincide with the estimate of Ref. [23].”

    From Non-Gaussianities in two-field inflation (2006) · cites this paper as [23]

    The Introduction (p. 2) and the discussion of second-order perturbations (p. 12) describe the paper’s cosmological-perturbation formalism, but do not report a double-inflation estimate or compare results with one. Searches for “double inflation” and “estimate coincide” found no passage addressing the claimed agreement; the identity of Ref. [23] in the citing paper is not established by this source’s reference list. (LLM, conf=0.74)

    Experimental — accuracy not yet measured

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 26

  1. [5][5] R. Durrer, Fundamental of Cosmic Physics, 1994, Vol.15., No. 3, pp 209-339. -
  2. [6][6] N. Bartolo, E. Komatsu, S. Matarrese and A. Riotto, Phys. Rept. 402 , 103 (2004) [arXiv:astro-ph/0406398]. - · arXiv
  3. [7][7] N. Bartolo, S. Matarrese and A. Riotto, Phys. Rev. Lett. 93 , 231301 (2004) [arXiv:astro-ph/0407505]. - · arXiv
  4. [8][8] N. Bartolo, S. Matarrese and A. Riotto, JCAP 0508 , 010 (2005) [arXiv:astro-ph/0506410]. - · arXiv
  5. [9][9] M. Bruni, S. Matarrese, S. Mollerach and S. Sonego, Class. Quant. Grav. 14 , 2585 (1997) [arXiv:gr-qc/9609040]. - · arXiv
  6. [10][10] M. Bruni, S. Matarrese, S. Mollerach and S. Sonego, arXiv:gr-qc/9611048. - · arXiv
  7. [11][11] V. Acquaviva, N. Bartolo, S. Matarrese and A. Riotto, Nucl. Phys. B 667 , 119 (2003) [arXiv:astro-ph/0209156]. - · arXiv
  8. [12][12] K. A. Malik and D. Wands, Class. Quant. Grav. 21 , L65 (2004) [arXiv:astro-ph/0307055]. - · arXiv
  9. [14][14] F. Vernizzi, Phys. Rev. D 71 , 061301 (2005) [arXiv:astro-ph/0411463]. - · arXiv
  10. [15][15] [K. A. Malik, arXiv:astro-ph/0506532.](http://arxiv.org/abs/astro-ph/0506532) - · arXiv
  11. [16][16] G. I. Rigopoulos and E. P. S. Shellard, Phys. Rev. D 68 (2003) 123518 [arXiv:astro-ph/0306620]; - · arXiv
  12. [17][17] E. W. Kolb, S. Matarrese, A. Notari and A. Riotto, arXiv:astro-ph/0410541. - · arXiv
  13. [18][18] D. H. Lyth, K. A. Malik and M. Sasaki, JCAP 0505 , 004 (2005) [arXiv:astro-ph/0411220]. - · arXiv
  14. [19][19] N. Afshordi and R. H. Brandenberger, Phys. Rev. D 63 , 123505 (2001) [arXiv:gr-qc/0011075]. - · arXiv
  15. [22][22] N. Deruelle and D. Langlois, Phys. Rev. D 52 , 2007 (1995) [arXiv:gr-qc/9411040]. - · arXiv
  16. [23][23] A. A. Starobinsky, JET Lett. 42 , 152 (1985) [Pis ma Hz. ESP. Tor. Fizz. 42, 124 (1985)]. -
  17. [24][24] M. Sasaki and E. D. Stewart, Prog. Theor. Phys. 95 , 71 (1996) [arXiv:astro-ph/9507001]; M. Sasaki and T. Tanaka, Prog. Theor. Phys. 99 , 763 (1998) [arXiv:gr-qc/9801017]. - · arXiv
  18. [25][25] D. Langlois and F. Vernizzi, Phys. Rev. Lett. 95, 091303 (2005) [arXiv:astro-ph/0503416]. - · arXiv
  19. [27][27] C. A. Clarkson, Phys. Rev. D 70 , 103524 (2004) [Erratum-ibid. D 70 , 129902 (2004)] [arXiv:astro-ph/0311505]. - · arXiv
  20. [31][31] 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). -
  21. [32][32] D. Wands, K. A. Malik, D. H. Lyth and A. R. Liddle, Phys. Rev. D 62 (2000) 043527 [arXiv:astro-ph/0003278]. - · arXiv
  22. [33][33] A. Lewis, PhD Thesis; C. Gordon and A. Lewis, Phys. Rev. D 67 , 123513 (2003) [arXiv:astro-ph/0212248]. - · arXiv
  23. [36][36] A. R. Liddle and D. H. Lyth, Cosmological inflation and large-scale structure (Cambridge University Press, Cambridge, England, 2000). -
  24. [37][37] D. Langlois, lectures given at the Cargese School Of Particle Physics And Cosmology: The Interface, edited by D. Kazakov, G. Smadja. Dordrecht, Springer, 2005. [arXiv:hep-th/0405053] - · arXiv
  25. [38][38] D. H. Lyth and Y. Rodriguez, Phys. Rev. D 71 , 123508 (2005) [arXiv:astro-ph/0502578]. - · arXiv
  26. [40][40] D. H. Lyth and D. Wands, Phys. Rev. D 68 , 103515 (2003) [arXiv:astro-ph/0306498]. · arXiv

Cited by

Sorted by citations

Authors
Langlois, D., & Vernizzi, F.
Affiliations
  • Centre National de la Recherche Scientifique (FR)
  • University of Helsinki (FI)
ORCID
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
2005-11-02
Volume
72
Issue
10
Pages
103501
ISSN
  • 0556-2821 (ISSN-L)
  • 1550-7998
  • 1550-2368
DOI
10.1103/physrevd.72.103501
OpenAlex
W2072918761
Cited by
129
References
1
Citations by year
2026: 5 · 2025: 1 · 2024: 3 · 2022: 1 · 2020: 2 · 2019: 3 · 2018: 4 · 2017: 4 · 2016: 9 · 2015: 4 · 2014: 9 · 2013: 16 · 2012: 5
FWCI
7.94
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • HAL (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
covariant formalism, non-perturbative methods, energy-density gradients, number of e-folds, conservation equations, second-order perturbation theory, adiabatic perturbations, gauge invariance, large-scale structure

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review