Homogeneity, flatness, and "large" extra dimensions

We consider a model in which the Universe is the direct product of an ordinary (3 + 1)-dimensional space-a brane where all the standard model fields are confined-and a compact hyperbolic manifold. The decay of massive Kaluza-Klein modes leads to the injection of bulk entropy into the observable Universe. The large statistical averaging inherent in the collapse of the initial entropy onto the brane smoothes out any initial inhomogeneities in the distribution of matter and of three-curvature.