General Gauss-Bonnet brane cosmology

TL;DR

This paper derives general solutions for 5D spacetimes with Gauss-Bonnet terms, explores their properties, and discusses implications for brane cosmology and modified Friedmann equations.

Contribution

It provides the first comprehensive solutions for Gauss-Bonnet corrected 5D spacetimes and extends Birkhoff's theorem within this context.

Findings

Two classes of bulk solutions identified.

Fine tuning condition between Gauss-Bonnet coupling and cosmological constant.

Modified Friedmann equations for brane cosmology derived.

Abstract

We consider 5-dimensional spacetimes of constant 3-dimensional spatial curvature in the presence of a bulk cosmological constant. We find the general solution of such a configuration in the presence of a Gauss-Bonnet term. Two classes of non-trivial bulk solutions are found. The first class is valid only under a fine tuning relation between the Gauss-Bonnet coupling constant and the cosmological constant of the bulk spacetime. The second class of solutions are static and are the extensions of the AdS-Schwarzchild black holes. Hence in the absence of a cosmological constant or if the fine tuning relation is not true, the generalised Birkhoff's staticity theorem holds even in the presence of Gauss-Bonnet curvature terms. We examine the consequences in brane world cosmology obtaining the generalised Friedmann equations for a perfect fluid 3-brane and discuss how this modifies the usual scenario.