insu-03645648
https://insu.hal.science/insu-03645648
https://insu.hal.science/insu-03645648/document
https://insu.hal.science/insu-03645648/file/PhysRevD.89.103538.pdf
arxiv:1311.6730
doi:10.1103/PhysRevD.89.103538
[INSU] INSU - Institut National des Sciences de l'Univers
[CNRS] CNRS - Centre national de la recherche scientifique
[IAP] Institut d'Astrophysique de Paris
[SORBONNE-UNIVERSITE] Sorbonne Université
[SU-INF-2018] SORBONNE université <2018
[SU-SCIENCES] Faculté des Sciences de Sorbonne Université
[SU-TI] Sorbonne Université - Texte Intégral
[ALLIANCE-SU] Alliance Sorbonne Université
Covariant Bardeen perturbation formalism
Vitenti, S. D. P.
Falciano, F. T.
Pinto-Neto, N.
[SDU] Sciences of the Universe [physics]
ART
98.80.-k
04.20.Cv
04.25.-g
98.80.Jk
Cosmology
Fundamental problems and general formalism
Approximation methods
equations of motion
Mathematical and relativistic aspects of cosmology
Astrophysics - Cosmology and Nongalactic Astrophysics
General Relativity and Quantum Cosmology
In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so-called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors, which yields an adequate language to treat both perturbative approaches in a common framework. We then stress that in the referred covariant approach, one necessarily introduces an additional hypersurface choice to the problem. Using our mixed and pure tensors approach, we are able to construct a one-to-one map relating the usual gauge dependence of the Bardeen formalism with the hypersurface dependence inherent to the covariant approach. Finally, through the use of this map, we define full nonlinear tensors that at first order correspond to the three known gauge invariant variables Φ, Ψ and Ξ, which are simultaneously foliation and gauge invariant. We then stress that the use of the proposed mixed tensors allows one to construct simultaneously gauge and hypersurface invariant variables at any order.
2014
2022-04-25
en
Physical Review D