Brane isotropization in an extra-dimensional Tolman-Bondi universe

Abstract

We consider the dynamics of a 3-brane embedded in an extra-dimensional Tolman-Bondi Universe where the origin of space plays a special rôle. The embedding is chosen such that the induced matter distribution on the brane respects the spherical symmetry of matter in the extra-dimensional space. The mirage cosmology on the probe brane is studied, resulting in an inhomogeneous and anisotropic fourdimensional cosmology where the origin of space is also special. We then focus on the spatial geometry around the origin and show that the induced geometry, which is initially inhomogeneous and anisotropic, converges to an isotropic and homogeneous Friedmann-Lemaitre 4d space-time. For instance, when a 3-brane is embedded in a 5d matter-dominated model, the 4d dynamics around the origin converge to a Friedmann-Lemaitre Universe in a radiation-dominated epoch. We analyze this isotropization process and show that it is a late-time attractor.