Preinflationary dynamics of power-law potential in loop quantum cosmology

Abstract

In this article, I mainly discuss the dynamics of the pre-inflationary Universe for the potential $V(\phi) \propto \phi^n$ with $n=5/3$ in the context of loop quantum cosmology, in which the big bang singularity is resolved by a non-singular quantum bounce. In the case of the kinetic energy-dominated initial conditions of the scalar field at the bounce, the numerical evolution of the Universe can be split up into three regimes: {\em bouncing, transition,} and {\em slow-roll inflation}. In the bouncing regime, the~numerical evolution of the scale factor does not depend on a wide range of initial values, {or on}~the inflationary potentials. I calculate the number of $e$-folds in the slow-roll regime, by which observationally identified initial conditions are obtained. Additionally, I display the phase portrait for the model under consideration.