Classical back reaction of low-frequency cosmic gravitational radiation

TL;DR

This paper investigates how low-frequency gravitational waves influence the overall gravitational field in an Einstein-deSitter universe, considering both subhorizon and superhorizon modes with stochastic wave amplitudes.

Contribution

It provides a detailed calculation of the effective stress-energy tensor for stochastic gravitational waves, including superhorizon modes, and explores solutions with pure gravitational radiation universes.

Findings

Superhorizon modes can contribute negatively to energy density and pressure.

The effective stress-energy tensor is expressed in terms of correlation functions.

Solutions include universes dominated by pure gravitational radiation.

Abstract

We study in a Brill-Hartle type of approximation the back reaction of a superposition of linear gravitational waves on the mean gravitational field up to second order in the wave amplitudes. The background field is taken as an Einstein-deSitter geometry. In order to follow inflationary scenarios, the wavelengths are allowed to exceed the temporary Hubble distance. As in optical coherence theory, the wave amplitudes are considered as random variables, which form a homogeneous and isotropic stochastic process, sharing the symmetries of the background metric. The effective stress-energy tensor for the random waves is calculated in terms of correlation functions and covers subhorizon as well as superhorizon modes, the latter give in many cases negative contributions to energy density and pressure. We discuss solutions of the second-order equations including pure gravitational radiation universes.