Initial conditions of pre-inflation with Hilltop potential in loop quantum cosmology

TL;DR

This paper explores how initial conditions in loop quantum cosmology with Hilltop potential influence pre-inflation dynamics, identifying conditions that lead to successful slow-roll inflation and sufficient e-folds, with detailed numerical and phase space analysis.

Contribution

It provides a numerical and phase space analysis of initial conditions in loop quantum cosmology with Hilltop potential, highlighting conditions for successful inflation.

Findings

Physically viable initial conditions at the bounce generate sufficient e-folds.

Kinetic energy dominated initial conditions show three distinct phases before inflation.

Potential energy dominated initial conditions can still lead to slow-roll inflation under certain parameters.

Abstract

In this paper, we investigate the dynamics of pre-inflation with Hilltop potential in the framework of loop quantum cosmology. The initial conditions of inflaton field at the quantum bounce is categorized into two classes, first one is dominated by kinetic energy and second one by potential energy. In both cases, the physically viable initial values of inflaton field at the bounce are obtained numerically that generate the desired slow-roll inflation and also sufficient number of $e$-folds. To be consistent with observations at least 60 $e$-folds are required. In case of kinetic energy dominated initial conditions of inflaton field at the bounce, the numerical evolution of the background prior to preheating is divided into three different regions: {\it bouncing, transition and slow-roll inflation} whereas bouncing and transition phases disappear in the potential energy dominated case but still slow-roll inflation is achieved. This is true in case of $p=4$ and $v=1 M_{Pl}$ of Hilltop potential. However for other cases, slow-roll inflation can not be obtained. Moreover, we study the phase space analysis for Hilltop potential and discuss the phase space trajectories under the chosen parameters.