Cosmological evolution in compactified Horava-Witten theory induced by   matter on the branes
  The combined Einstein equations and scalar equation of motion in the Horava-Witten scenario of the strongly coupled heterotic string compactified on a Calabi-Yau manifold are solved in the presence of additional matter densities on the branes. We take into account the universal Calabi-Yau modulus phi with potentials in the 5-d bulk and on the 3-branes, and allow for an arbitrary coupling of the additional matter to phi and an arbitrary equation of state. No ad hoc stabilization of the five dimensional radius is assumed. The matter densities are assumed to be small compared to the potential for phi on the branes; in this approximation we find solutions in the bulk which are exact in y and t. Depending on the coupling of the matter to phi and its equation of state, various solutions for the metric on the branes and in the 5-d bulk are obtained: Solutions corresponding to a ``rolling radius'', and solutions with a static 5-d radius, which reproduce the standard cosmological evolution. 
U. Ellwanger