Brane cosmology with an anisotropic bulk

In the context of brane cosmology, a scenario where our universe is a 3 + 1dimensional surface (the “brane”) embedded in a five-dimensional spacetime (the “bulk”), we study geometries for which the brane is anisotropic — more specifically Bianchi I — though still homogeneous. We first obtain explicit vacuum bulk solutions with anisotropic three-dimensional spatial slices. The bulk is assumed to be empty but endowed with a negative cosmological constant. We then embed Z2symmetric branes in the anisotropic spacetimes and discuss the constraints on the brane energy-momentum tensor due to the five-dimensional anisotropic geometry. We show that if the bulk is static, an anisotropic brane cannot support a perfect fluid. However, we find that for some of our bulk solutions it is possible to embed a brane with a perfect fluid though its energy density and pressure are completely determined by the bulk geometry. [email protected] [email protected] [email protected] [email protected] Unité Mixte de Recherche du CNRS (UMR 8627). 1