Self-consistent solutions for low-frequency gravitational background radiation

Details Self-consistent solutions for low-frequency gravitational background radiation Self-consistent solutions for low-frequency gravitational background radiation

1997-12-09

arxiv.org/abs/gr-qc/9712042v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

3 pages, Latex (requires mprocl.sty). To appear in the Proceedings of the Eighth Marcel Grossmann meeting (Jerusalem, June 22-

Scientific paper

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.

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