Phase-Space Analysis of an Einstein-Gauss-Bonnet Scalar Field Cosmology

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-Lemaitre-Robertson-Walker spacetime. For the scalar field potential, we consider the exponential function. In contrast, we assume two cases for the coupling function of the scalar field with the Gauss-Bonnet term: the exponential function and the power-law function. We write the field equations in dimensionless variables and study the equilibrium points using normalized and compactified variables. We recover previous results, but also find new asymptotic solutions not previously studied. Finally, these couplings provide a rich cosmological phenomenology.

Automated summary

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-Lemaitre-Robertson-Walker spacetime. We consider the exponential function for the scalar field potential and assume two cases for the coupling function of the scalar field with the Gauss-Bonnet term: the exponential function and the power-law function. By writing the field equations in dimensionless variables and studying the equilibrium points using normalized and compactified variables, we recover previous results and discover new asymptotic solutions. These couplings provide a rich cosmological phenomenology.