Brane-World Cosmology of Modulus Stabilization with a Bulk Scalar Field

TL;DR

The paper revisits radion stabilization in the RS brane-world with a bulk scalar in a simplified Goldberger–Wise framework, showing the potential has a metastable minimum at infinite brane separation and that generic cosmological evolution tends to bypass stabilization unless thermal or inflationary effects are considered. It provides an exact form for the radion potential and analyzes both zero-temperature minima and finite-temperature phase transitions to the true vacuum, including a detailed computation of the Euclidean bounce and the nucleation rate with a fluctuation determinant. The results demonstrate that finite brane potentials can significantly modify the nucleation rate and the radion mass, and that, for a broad range of parameters, a thermally assisted transition to the true minimum can complete, thereby achieving stabilization without requiring unrealistic inflationary dynamics. The work highlights cosmological viability and constraints for radion stabilization in brane-world scenarios and points to further refinements such as backreaction, time-dependent stabilization dynamics, and more realistic reheating.

Abstract

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.