Pre-inflationary dynamics in loop quantum cosmology: Power-law potentials

Abstract: In this paper, we study the pre-inflationary dynamics for the power-law potential $(V(\phi) \propto \phi^n)$ with $n<2$ in the framework of loop quantum cosmology. In the case where the kinetic energy of the inflaton dominates at the initial, the evolution of the universe can always be divided into three different phases prior to preheating: {\em bouncing, transition and slow-roll inflation}. During the bouncing phase, the evolution of the expansion factor is independent not only on the initial conditions but also the inflationary potentials, and is given explicitly by an analytical solution. In contrast, for the potential energy dominated initial conditions, this universality is lost. We also obtain total number of e-folds during the slow-roll inflation, whereby physically viable models are identified. In addition, we present phase space analysis for the inflationary potentials under consideration and compare our results with the ones obtained previously for different potentials.