Role of quantum cosmology in the chaotic dynamics of inflation

Abstract

The dynamics of LFRW universes with a massive scalar field is examined where a potential term derived from quantum cosmology is introduced in the equations of motion of the system. This potential term is connected to a repulsive force arising from the equations of Bohmian trajectories in the framework of the de Broglie--Bohm interpretation of quantum cosmology. For a nonzero mass, the dynamics is nonintegrable and chaotic and the quantum potential term creates metastable configurations confined between KAM tori. For certain domains of the parameter space labeled by the scalar field mass and the conserved Hamiltonian, we have nonlinear resonance phenomena that may induce the destruction of KAM tori. This leads to a rapid growth of the scale factor and the scalar field, with the disruption of metastable states and consequent escape of the Universe into inflation. A semianalytical approach to these phenomena is made and possible consequences to structure formation discussed. Also the dynamics connected with the breaking and crossing of homoclinic cylinders present in the phase space of the models is examined, as they induce effective mechanisms of a chaotic exit to inflation for other sets of initial conditions, but with a milder oscillatory behavior of the degrees of freedom.