Qualitative Approach to Semi-Classical Loop Quantum Cosmology

TL;DR

This paper provides a qualitative analysis of semi-classical Loop Quantum Cosmology, confirming singularity avoidance and exploring initial conditions for inflation in different scalar field models.

Contribution

It offers a novel qualitative dynamical system analysis of Loop Quantum Cosmology, extending understanding of singularity avoidance and inflation conditions.

Findings

Singularity avoidance confirmed in positively curved models.

Initial conditions for inflation can be generated with scalar field self-interaction.

Bounce behavior discussed in flat and negatively curved models.

Abstract

Recently the mechanism was found which allows avoidance of the cosmological singularity within the semi-classical formulation of Loop Quantum Gravity. Numerical studies show that the presence of self-interaction potential of the scalar field allows generation of initial conditions for successful slow-roll inflation. In this paper qualitative analysis of dynamical system, corresponding to cosmological equations of Loop Quantum Gravity is performed. The conclusion on singularity avoidance in positively curved cosmological models is confirmed. Two cases are considered, the massless (with flat potential) and massive scalar field. Explanation of initial conditions generation for inflation in models with massive scalar field is given. The bounce is discussed in models with zero spatial curvature and negative potentials.