  The cosmology in the Hubble expansion era of the Horava-Witten M-theory
compactified on a Calabi-Yau threefold is studied in the reduction to
five-dimensions where the effects of the Calabi-Yau manifold are summarized by
the volume modulus, and all perturbative potentials are included. Matter on the
branes are treated as first order perturbations of the static vacuum solution,
and all equations in the bulk and all boundary conditions on both end branes
are imposed. It is found that for a static volume modulus and a static fifth
dimension, y, one can recover the four dimensional Robertson Friedmann Walker
cosmology for relativistic matter on the branes, but not for non-relativistic
matter. In this case, the Hubble parameter H becomes independent of y to first
order in matter density. This result holds also when an arbitrary number of
5-branes are included in the bulk. The five dimensional Horava-Witten model is
compared with the Randall Sundrum phenomenology with a scalar field in the bulk
where a bulk and brane potential are used so that the vacuum solutions can be
rigorously obtained. (In the Appendix, the difficulty of obtaining approximate
vacuum solutions for other potentials is discussed.) In this case
non-relativistic matter is accommodated by allowing the distance between the
branes to vary. It is suggested that non-perturbative potentials for the vacuum
solution of Horava-Witten theory are needed to remove the inconsistency that
non-relativistic matter creates.
