Brane dynamics in the Randall-Sundrum model, inflation and graceful exit

We study the averaged action of the Randall-Sundrum model with a time-dependent metric ansatz. It can be reformulated in terms of a Brans-Dicke action with time-dependent Newton's constant. We show that the physics of the early universe, particularly inflation, is governed by the Brans-Dicke theory. The Brans-Dicke scalar, however, quickly settles to its equilibrium value and decouples from the post-inflationary cosmology. The deceleration parameter is negative to start with but changes sign before the Brans-Dicke scalar settles to its equilibrium value. Consequently, the brane metric smoothly exits inflation. We have also studied the slow-roll inflation in our model and investigated the spectra of the density perturbation generated by the radion field and find them consistent with the current observations