Scalar field cosmology in phase space

TL;DR

This paper analyzes the evolution of a scalar field in a flat universe using dynamical systems, identifying equilibrium points and their stability to understand inflation and dark energy scenarios.

Contribution

It provides a geometric phase space analysis of scalar field cosmology, independent of specific potentials or high-energy models.

Findings

Identification of equilibrium points corresponding to de Sitter solutions

Stability analysis of these points using perturbation and Lyapunov methods

Insights into late-time behavior of scalar field cosmologies

Abstract

Using dynamical systems methods, we describe the evolution of a minimally coupled scalar field and a Friedmann-Lemaitre-Robertson-Walker universe in the context of general relativity, which is relevant for inflation and late-time quintessence eras. Focussing on the spatially flat case, we examine the geometrical structure of the phase space, locate the equilibrium points of the system (de Sitter spaces with a constant scalar field), study their stability through both a third-order perturbation analysis and Lyapunov functions, and discuss the late-time asymptotics. As we do not specify the scalar field's origin or its potential, the results are independent of the high-energy model.