The dynamics of scalar-tensor cosmology from RS two-brane model

TL;DR

This paper analyzes a scalar-tensor cosmological model derived from the Randall-Sundrum two-brane setup, providing exact solutions for the universe's expansion under various matter contents and studying radion stabilization and observational constraints.

Contribution

It offers exact solutions for the A-brane scale factor in a scalar-tensor framework and examines radion dynamics and stability within the RS two-brane model.

Findings

Exact solutions for different matter types on the A-brane.

Radion stabilization at finite values under certain conditions.

Convergence towards general relativity in the model.

Abstract

We consider a Randall-Sundrum two-brane cosmological model in the low energy gradient expansion approximation by Kanno and Soda. It is a scalar-tensor theory with a specific coupling function and a specific potential. Upon introducing the FLRW metric and perfect fluid matter on both branes in the Jordan frame, the effective dynamical equation for the the A-brane (our Universe) scale factor decouples from the scalar field and B-brane matter leaving only a non-vanishing integration constant (the dark radiation term). We find exact solutions for the A-brane scale factor for four types of matter: cosmological constant, radiation, dust, and cosmological constant plus radiation. We perform a complementary analysis of the dynamics of the scalar field (radion) using phase space methods and examine convergence towards the limit of general relativity. In particular, we find that radion stabilizes at a certain finite value for suitable negative matter densities on the B-brane. Observational constraints from Solar system experiments (PPN) and primordial nucleosynthesis (BBN) are also briefly discussed.