Global dynamics in Einstein-Gauss-Bonnet scalar field cosmology with matter

Abstract

We study the dynamics of the field equations in a four-dimensional isotropic and homogeneous spatially flat Friedmann--Lema\^ıtre--Robertson--Walker geometry in the context of Einstein-Gauss-Bonnet theory with a matter source and a scalar field coupled to the Gauss-Bonnet scalar. In this theory, the Gauss-Bonnet term contributes to the field equations. The mass of the scalar field depends on the potential function and the Gauss-Bonnet term. For the scalar field potential, we consider the exponential function and the coupling function between the scalar field and the Gauss-Bonnet scalar is considered to be the linear function. Moreover, the scalar field can have a phantom behaviour. We consider a set of dimensionless variables and write the field equations into a system or algebraic-differential equations. For the latter, we investigate the equilibrium points and their stability properties. In order to perform a global analysis of the asymptotic dynamics, we use compactified variables. This gravitational theory can explain the Universe's recent and past acceleration phases. Therefore, it can be used as a toy model for studying inflation or as a dark energy candidate.

arXiv comment33 pages, 11 compound figures

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• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• Dynamical system analysis of scalar field cosmology in coincident $f(Q)$ gravity
• Fractional Einstein-Gauss-Bonnet scalar field cosmology
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