Self-consistent solutions for low-frequency gravitational background radiation

TL;DR

This paper investigates the back-reaction of stochastic gravitational waves on an Einstein-de Sitter universe, deriving effective stress-energy tensors and exploring solutions including de Sitter-like expansion.

Contribution

It provides a self-consistent analysis of gravitational wave back-reaction in a cosmological setting without wavelength restrictions, introducing new solutions with de Sitter characteristics.

Findings

Effective stress-energy tensor expressed via correlation functions.

Existence of solutions with de Sitter-like expansion.

Dominance of gravitational wave back-reaction in certain scenarios.

Abstract

We study in a Brill-Hartle type of approximation the back-reaction of a superposition of linear gravitational waves in an Einstein-de Sitter background up to the second order in the small wave amplitudes $h_{ik}$. The wave amplitudes are assumed to form a homogeneous and isotropic stochastic process. No restriction for the wavelengths is assumed. The effective stress-energy tensor $T^{e}_{\mu\nu}$ is calculated in terms of the correlation functions of the process. We discuss in particular a situation where $T^{e}_{\mu\nu}$ is the dominant excitation of the background metric. Apart from the Tolman radiation universe, a solution with the scale factor of the de Sitter universe exists with $p = -\rho$ as effective equation of state.