Phase-space analysis of an Einstein-Gauss-Bonnet scalar field cosmology

TL;DR

This paper analyzes the phase-space of Einstein-Gauss-Bonnet scalar field cosmology with exponential and power-law couplings, revealing new asymptotic solutions and diverse cosmological behaviors.

Contribution

It introduces a comprehensive phase-space analysis for different coupling functions, uncovering new asymptotic solutions and scaling behaviors in Einstein-Gauss-Bonnet cosmology.

Findings

Asymptotic solutions include de Sitter universes and Gauss-Bonnet dominated spacetimes.

New asymptotic solutions not previously studied were identified.

Power-law coupling yields a variety of cosmological phenomenologies.

Abstract

We perform a detailed study of the phase-space of the field equations of an Einstein-Gauss-Bonnet scalar field cosmology for a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime. For the scalar field potential, we consider the exponential function. In contrast, for the coupling function of the scalar field with the Gauss-Bonnet term, we assume two cases, the exponential function and the power-law function. We write the field equations in dimensionless variables and study the equilibrium points using Poincare variables. For the exponential coupling function, the asymptotic solutions describe de Sitter universes or spacetimes where the Gauss-Bonnet term dominates. We recovered previous results but found new asymptotic solutions not previously studied. For the power-law coupling function, equilibrium points which describe the scaling solution appear. Finally, the power-law coupling provides a rich cosmological phenomenology.