Non-linear resonance in bouncing braneworld universes and initial conditions for inflation

We examine the phase space dynamics of closed Friedmann-Robertson-Walker universes with a massive inflaton field, where the Friedmann equations contain additional terms arising from high energy corrections to cosmological scenarios. The model is based upon a Randall-Sundrum type of action, with an extra timelike dimension, and the corrections implement non-singular bounces in the early evolution of the universe. In narrow windows of the parameter space of the models non-linear resonance phenomena of Kolmogorov Arnold-Moser tori are shown to occur, leading to the destruction of tori that trap the inflaton. As a consequence the escape into inflation takes place. These resonance windows are labeled with an integer n >= 2, where n is related to the ratio of the frequencies in the scale factor to those in the scalar field degrees of freedom. We examine the constraints imposed by non-linear resonance in the physical domain of parameters of the model so that inflation may be realized. The larger the order n of the resonance, the stronger the gravitational interaction in the braneworld universe inflated from initial conditions connected with the resonance considered. We also discuss the structural stability of the resonance pattern, the complex dynamics arising in this pre-infationary phase and some of its possible imprints in the physics of inflation.