Bouncing braneworld cosmologies and initial conditions to inflation

Abstract

We examine the full nonlinear dynamics of closed Friedmann-Robertson-Walker universes in the framework of $D$-branes formalism. Friedmann equations contain additional terms arising from the bulk-brane interaction that provide a concrete model for nonsingular bounces in the early phase of the Universe. We construct nonsingular cosmological scenarios sourced with perfect fluids and a massive inflaton field, which are past eternal, oscillatory, and may emerge into an inflationary phase due to nonlinear resonance mechanisms. Oscillatory behavior becomes metastable when the system is driven into a resonance window of the parameter space of the models, with consequent breakup of KAM tori that trap the inflaton, leading the Universe to the inflationary regime. A construction of the resonance chart of the models is made. Resonance windows are labeled by an integer $n\ensuremath{\ge}2$, where $n$ is related to the ratio of the frequencies in the scale factor/scalar field degrees of freedom. They are typically small compared to the volume of the whole parameter space, and we examine the constraints imposed by nonlinear resonance in the physical domain of initial configurations so that inflation may be realized. We discuss the complex dynamics arising in this preinflationary stage, the structural stability of the resonance pattern and some of its possible imprints in the physics of inflation. We also approach the issue of initial configurations that are connected to a chaotic exit to inflation. Pure scalar field bouncing cosmologies are constructed. Contrary to models with perfect fluid components, the structure of the bouncing dynamics is highly sensitive to the initial amplitude and to the mass of the inflaton; dynamical potential barriers allowing for bounces appear as a new feature of the dynamics. We argue that if our actual Universe is a brane inflated by a parametric resonance mechanism triggered by the inflaton, some observable cosmological parameters should then have a signature of the particular resonance from which the brane inflated.