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Self-consistent solutions for low-frequency gravitational background radiation

G. Dautcourt
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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 $T^{e}_{μν}$ is calculated in terms of the correlation functions of the process. We discuss in particular a situation where $T^{e}_{μν}$ 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 $p = -ρ$ as effective equation of state.

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G. Dautcourt. 1997-12-09. Self-consistent solutions for low-frequency gravitational background radiation. https://arxiv.org/abs/gr-qc/9712042

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