Brane cosmology with an anisotropic bulk

In the context of brane cosmology, a scenario where our universe is a 3 + 1-dimensional surface (the “brane”) embedded in a five-dimensional spacetime (the “bulk”), we study geometries for which the brane is anisotropic — more specifi-cally 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 Z 2 symmetric 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