Stability analysis of cosmological models through Liapunov's method

TL;DR

This paper applies Liapunov's method to analyze the stability and basin of attraction of various cosmological models, providing insights into their asymptotic behavior and the reheating mechanism of the inflaton field.

Contribution

It introduces Liapunov's method as a novel approach for stability analysis in cosmological models, surpassing traditional linear and perturbation techniques.

Findings

Liapunov's method effectively determines stability and attraction basins.

The approach offers insights into the reheating process of the inflaton field.

It applies to both autonomous and non-autonomous cosmological systems.

Abstract

We investigate the general asymptotic behaviour of Friedman-Robertson-Walker (FRW) models with an inflaton field, scalar-tensor FRW cosmological models and diagonal Bianchi-IX models by means of Liapunov's method. This method provides information not only about the asymptotic stability of a given equilibrium point but also about its basin of attraction. This cannot be obtained by the usual methods found in the literature, such as linear stability analysis or first order perturbation techniques. Moreover, Liapunov's method is also applicable to non-autonomous systems. We use this advantadge to investigate the mechanism of reheating for the inflaton field in FRW models.