Dynamics of a higher-dimensional Einstein–Scalar–Gauss–Bonnet cosmology

Abstract

We study the dynamics of the field equations in a five-dimensional spatially flat Friedmann–Lemaître–Robertson–Walker metric in the context of a Gauss–Bonnet–Scalar field theory where the quintessence scalar field is coupled to the Gauss–Bonnet scalar. Contrary to the four-dimensional Gauss–Bonnet theory, where the Gauss–Bonnet term does not contribute to the field equations, in this five-dimensional Einstein–Scalar–Gauss–Bonnet model, the Gauss–Bonnet term contributes to the field equations even when the coupling function is a constant. Additionally, we consider a more general coupling described by a power-law function. For the scalar field potential, we consider the exponential function. For each choice of the coupling function, we define a set of dimensionless variables and write the field equations into a system of ordinary differential equations. We perform a detailed analysis of the dynamics for both systems and classify the stability of the equilibrium points. We determine the presence of scaling and super-collapsing solutions using the cosmological deceleration parameter. This means that our models can explain the Universe’s early and late-time acceleration phases. Consequently, this model can be used to study inflation or as a dark energy candidate.