General Gauss–Bonnet brane cosmology

We consider five-dimensional spacetimes of constant three-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 generalized Birkhoff's staticity theorem holds even in the presence of Gauss–Bonnet curvature terms. We examine the consequences in braneworld cosmology obtaining the generalized Friedmann equations for a perfect fluid 3-brane and discuss how this modifies the usual scenario.