On the Isotropization of a 3-Brane in an Extra-Dimensional Tolman–Bondi Universe

Abstract

We report here on the results of Brax et al. (Phys. Rev. D 85:123516, 2012) where we consider the dynamics of a 3-brane embedded in an extra-dimensional Tolman–Bondi Universe where the origin of space plays a special role. We study the mirage cosmology on the probe brane, resulting in an inhomogeneous and anisotropic four dimensional cosmology where the origin of space is also special. We show that the induced geometry, which is initially inhomogeneous and anisotropic, converges to an isotropic and homogeneous Friedmann–Lemaitre 4d space-time around the origin of the spatial geometry. For example, 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 analyse this isotropisation process and show that it is a late time attractor.