Qualitative study in Loop Quantum Cosmology

TL;DR

This paper provides a qualitative analysis of scalar field dynamics in Loop Quantum Cosmology and General Relativity, focusing on the stability of solutions mimicking perfect fluid behavior with different equations of state.

Contribution

It offers a detailed phase space analysis of scalar field solutions in Loop Quantum Cosmology, highlighting stability properties depending on the EoS parameter, which is a novel approach.

Findings

Analytic solutions replicate perfect fluid dynamics.

Stability of solutions varies with EoS parameter.

Convergence or divergence of orbits analyzed at early and late times.

Abstract

This work contains a detailed qualitative analysis, in General Relativity and in Loop Quantum Cosmology, of the dynamics in the associated phase space of a scalar field minimally coupled with gravity, whose potential mimics the dynamics of a perfect fluid with a linear Equation of State (EoS). Dealing with the orbits (solutions) of the system, we will see that there are analytic ones, which lead to the same dynamics as the perfect fluid, and our goal is to check their stability, depending on the value of the EoS parameter, i.e., to show whether the other orbits converge or diverge to these analytic solutions at early and late times.