The Stochastic Gravitational–wave Background Produced by Non–linear Cosmological Perturbations

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 gaugedependent. 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.