Relativistic second-order perturbations of the Einstein-de Sitter Universe

Details Relativistic second-order perturbations of the Einstein-de Sitter Universe Relativistic second-order perturbations of the Einstein-de Sitter Universe

1997-07-25

arxiv.org/abs/astro-ph/9707278v2

Phys.Rev. D58 (1998) 043504

Astronomy and Astrophysics

Astrophysics

Revised version with minor changes, accepted in The Physical Review D; LaTeX file using RevTeX macros, 28 pages

Scientific paper

10.1103/PhysRevD.58.043504

We consider the evolution of relativistic perturbations in the Einstein-de Sitter cosmological model, including second-order effects. The perturbations are considered in two different settings: the widely used synchronous gauge and the Poisson (generalized longitudinal) one. Since, in general, perturbations are gauge dependent, we start by considering gauge transformations at second order. Next, we give the evolution of perturbations in the synchronous gauge, taking into account both scalar and tensor modes in the initial conditions. Using the second-order gauge transformation previously defined, we are then able to transform these perturbations to the Poisson gauge. The most important feature of second-order perturbation theory is mode-mixing, which here also means, for instance, that primordial density perturbations act as a source for gravitational waves, while primordial gravitational waves give rise to second-order density fluctuations. Possible applications of our formalism range from the study of the evolution of perturbations in the mildly non-linear regime to the analysis of secondary anisotropies of the Cosmic Microwave Background.

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