Dynamics of scalar-tensor cosmology from a Randall-Sundrum two-brane model

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 Friedmann-Lemaitre-Robertson-WalkerFLRW metric and perfect fluid matter on both branes in the Jordan frame, the effective dynamical equation for the A-brane ( our Universe) scale factor decouples from the scalar field and B-brane matter leaving only a nonvanishing 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.