Non-linear resonance in bouncing braneworld universes and initial conditions forinflation

Abstract

We examine the phase space dynamics of closed Friedmann–Robertson–Walker universeswith a massive inflaton field, where the Friedmann equations contain additional termsarising from high energy corrections to cosmological scenarios. The model is basedupon a Randall–Sundrum type of action, with an extra timelike dimension, andthe corrections implement non-singular bounces in the early evolution of theuniverse. In narrow windows of the parameter space of the models non-linearresonance phenomena of Kolmogorov–Arnold–Moser tori are shown to occur, leadingto the destruction of tori that trap the inflaton. As a consequence the escapeinto inflation takes place. These resonance windows are labeled with an integern≥2,where n is related to the ratio of the frequencies in the scale factor to those in the scalar field degrees offreedom. We examine the constraints imposed by non-linear resonance in the physicaldomain of parameters of the model so that inflation may be realized. The larger the ordern of the resonance, the stronger the gravitational interaction in the braneworld universeinflated from initial conditions connected with the resonance considered. We also discussthe structural stability of the resonance pattern, the complex dynamics arising inthis pre-inflationary phase and some of its possible imprints in the physics ofinflation.