Preinflationary dynamics of power-law potential in loop quantum cosmology

TL;DR

This paper studies the early universe dynamics with a power-law potential in loop quantum cosmology, showing how a quantum bounce leads to inflation and analyzing the evolution phases and initial conditions.

Contribution

It introduces a detailed analysis of pre-inflationary dynamics with a specific power-law potential in loop quantum cosmology, including phase portraits and initial condition effects.

Findings

Quantum bounce resolves big bang singularity.

The scale factor evolution is insensitive to initial conditions.

Number of e-folds is calculated for slow-roll inflation.

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.