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

Sabino Matarrese*, Silvia Mollerach, Marco Bruni

*Corresponding author for this work

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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 nonlinear regime to the analysis of secondary anisotropies of the cosmic microwave background.

Original languageEnglish
Article number043504
Number of pages22
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number4
Publication statusPublished - 15 Aug 1998


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