The stochastic gravitational-wave background produced by non-linear cosmological perturbations

TL;DR

This paper investigates the stochastic gravitational-wave background generated by non-linear density fluctuations in the universe, using relativistic perturbation theory up to second order within an Einstein-de Sitter cosmology.

Contribution

It provides a detailed analysis of the gauge dependence and physical interpretation of gravitational waves produced by cosmological density perturbations.

Findings

The gravitational-wave background contains gauge-dependent components.

In the Poisson gauge, the background includes a constant term and an oscillating component.

The oscillating component's amplitude diminishes inside the Hubble radius.

Abstract

The cosmological stochastic gravitational-wave background produced by the mildly non-linear evolution of density fluctuations is analyzed, in the frame of an Einstein-de Sitter model, by means of a fully relativistic perturbation expansion up to second order. The form of these gravitational-instability-induced gravitational waves is gauge-dependent. In the synchronous gauge, where the second-order expansion is most easily carried out, the transverse and traceless tensor modes which are produced also contain a Newtonian and post-Newtonian piece, whose interpretation as gravitational waves is non-trivial. A more direct physical understanding of this background is obtained in the so-called Poisson gauge, where it is seen to consist of a constant term plus an oscillating piece whose amplitude decays inside the Hubble radius.