General Gauss-Bonnet brane cosmology

TL;DR

The paper addresses 5D Gauss-Bonnet brane cosmology with a negative bulk cosmological constant by solving for bulk spacetimes of constant 3-space curvature. It finds two bulk solution classes: Class I exists only under the fine-tuning $8\alpha k^2=1$ and allows time- and space-dependent metrics, while Class II is static and generalizes AdS-Schwarzschild black holes with a potential $V(r)=\kappa+{r^2\over 4\alpha}\left[1\pm\sqrt{1-8\alpha k^2+8\alpha \mu/r^4}\right]$, where $\mu$ is a mass parameter. On the brane, the Gauss-Bonnet term yields a generalized Friedmann equation, a cubic in $X=H^2+V(R)/R^2$, given by $(\rho/(16\alpha))^2=X^3\mp C X^2+(C^2/4) X$ with $C=\frac{3}{4\alpha}\sqrt{1-8\alpha k^2+8\alpha \mu/R^4}$, modifying early- and late-time cosmology. The work shows how GB corrections alter the relation between 5D and 4D gravity and can reproduce standard 4D cosmology under appropriate limits, while connecting to string-inspired quantum gravity corrections and altering the effective 5D Planck scale.

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.