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

TL;DR

This paper investigates the cosmological evolution in a compactified Horava-Witten model with matter on branes, deriving exact solutions that include a dynamic or static extra dimension, without requiring radius stabilization.

Contribution

It provides exact solutions for the Einstein and scalar equations in the Horava-Witten scenario with matter on branes, considering arbitrary matter coupling and equations of state.

Findings

Solutions with a rolling radius and static 5D radius are obtained.

The solutions reproduce standard cosmological evolution.

No ad hoc stabilization of the extra dimension is needed.

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 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.