Cosmological evolution in compactified Horava-Witten theory induced by matter on the branes

Abstract.

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 $\varphi$ with potentials in the 5-d bulk and on the 3-branes, and allow for an arbitrary coupling of the additional matter to $\varphi$ 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 $\varphi$ 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 $\varphi$ 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.