Equivalence between the Covariant and Bardeen Perturbation Formalisms

Дата и время публикации : 2013-11-26T16:34:02Z

Авторы публикации и институты :
S. D. P. Vitenti
F. T. Falciano
N. Pinto-Neto

Ссылка на журнал-издание: Ссылка на журнал-издание не найдена
Коментарии к cтатье: 12 pages, no figures, revtex4-1, submitted to PRD, typos fixed
Первичная категория: astro-ph.CO

Все категории : astro-ph.CO, gr-qc

Краткий обзор статьи: 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 the 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 that yields an adequate language to treat both perturbative approaches in a common framework. Additionally, we define full non-linear tensors that at first order correspond to the three known gauge invariant variables $Phi$, $Psi$ and $Xi$. We also stress that in the referred covariant approach one necessarily introduces an additional hyper-surface choice to the problem, and the same tensor combinations above at first order are also hyper-surface invariant making the gauge invariant variables $Phi$, $Psi$ and $Xi$ both gauge and hyper-surface invariant.

Category: Physics