Cosmology and Modulus Stabilization in the Randall-Sundrum Setup with Bulk Matter

We provide the exact time-dependent cosmological solutions in the Randall-Sundrum (RS) setup with bulk matter, which may be smoothly connected to the static RS metric. In the static limit of the extra dimension, the solutions are reduced to the standard Friedmann equations. In view of our solutions, we also propose an explanation for how the extra dimension is stabilized in spite of a flat modulus potential at the classical level.