Cosmological Challenges in Theories with Extra Dimensions and Remarks on the Horizon Problem

If our observable universe is a 3-brane located at the $Z_2$ symmetry fixed plane of a $Z_2$ symmetric five-dimensional spacetime as in the Horava-Witten model compactified on a Calabi-Yau, we find generically that substantial modifications to the standard Friedmann Robertson Walker cosmology result such that a large class of such models is observationally inconsistent. We find that the existence of the bulk and the boundary conditions on the orbifold fixed plane tend to make cosmological constraints coming from Big Bang Nucleosynthesis, structure formation, and the age of the universe difficult to satisfy. For a broad class of models, we also find a somewhat surprising result that the stabilization of the radius of the extra dimension and hence the four dimensional Planck mass requires unrealistic fine tuning of the equation of state on our 3-brane. In the last third of the paper, we make remarks about causality and the horizon problem that apply to {\it any} theory in which the volume of the extra dimension determines the four-dimensional gravitational coupling. We point out that some of the assumptions that lead to the usual inflationary requirements are modified.