Exact Cosmological Solution and Modulus Stabilization in the Randall-Sundrum Model with Bulk Matter

TL;DR

This paper derives exact time-dependent cosmological solutions in the Randall-Sundrum model with bulk matter, explaining how the extra dimension remains stabilized despite a flat classical potential.

Contribution

It provides the first exact dynamic solutions connecting to static RS metrics and offers a novel explanation for modulus stabilization without a potential.

Findings

Exact time-dependent solutions in RS model with bulk matter

Reduction to Friedmann equations in static limit

Proposed mechanism for modulus stabilization

Abstract

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.