Dynamics of a higher-dimension Einstein-Scalar-Gauss-Bonnet cosmology

TL;DR

This paper investigates the dynamics of a five-dimensional Einstein-Scalar-Gauss-Bonnet cosmological model, revealing how the Gauss-Bonnet term influences the evolution and stability of the universe's acceleration phases.

Contribution

It introduces a five-dimensional Gauss-Bonnet-Scalar field model with novel contributions of the Gauss-Bonnet term and analyzes its dynamical behavior and stability.

Findings

Gauss-Bonnet term affects field equations in 5D, unlike 4D.

Identifies stable scaling and super-collapsing solutions.

Model can describe early and late-time cosmic acceleration.

Abstract

We study the dynamics of the field equations in a five-dimensional spatially flat Friedmann-Lema\^itre-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.