Brane-world cosmology of modulus stabilization with a bulk scalar field

We point out that the potential of Goldberger and Wise for stabilizing the distance between two 3-branes, separated from each other along an extra dimension with a warp factor, has a metastable minimum when the branes are infinitely separated. The classical evolution of the radion (brane separation) will place it in this false minimum for generic initial conditions. In particular, inflation could do this if the expansion rate is sufficiently large. We present a simplified version of the Goldberger-Wise mechanism in which the radion potential can be computed exactly, and we calculate the rate of thermal transitions to the true minimum, showing that model parameters can be chosen to ensure that the universe reaches the desired final state. Finiteness of bulk scalar field brane potentials can have an important impact on the nucleation rate; and it can also significantly increase the predicted mass of the radion.