Abstract
The dynamics of closed LFRW universes with a massive inflaton field is examined where Friedmann equations are corrected by the introduction of a potential term arising from quantum gravity corrections to cosmological scenarios near the singularity. This extra term implements nonsingular bounces in the early evolution of the universe. For certain windows in the parameter space (labeled by the scalar field mass and the conserved Hamiltonian), phenomena of nonlinear resonance take place. Nonlinear resonance may induce the destruction of KAM tori that trap the inflaton, leading to a rapid growth of the scale factor and consequent escape of the universe into inflation. We make a complete analysis of the nonlinear resonance phenomena and show that windows of parametric resonance, characterized by an integer n > 2, are the ones that strongly favour inflation in the system. We discuss how generic is this behaviour for inflationary models.
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