$\Lambda$CDM-like evolution in Einstein-scalar-Gauss-Bonnet gravity

TL;DR

This paper demonstrates that Einstein-scalar-Gauss-Bonnet gravity can produce cosmological evolution similar to the standard $ ext{Lambda}$CDM model, with solutions compatible with observations and maintaining regular scalar fields.

Contribution

It shows that EsGB gravity admits $ ext{Lambda}$CDM-like solutions with fixed points and phase space behavior similar to GR, extending the understanding of alternative gravity models.

Findings

EsGB cosmology has fixed points analogous to GR's radiation, matter, and accelerated phases.

Numerical solutions in EsGB match $ ext{Lambda}$CDM$ predictions and observational data.

Scalar field and coupling remain finite and regular during evolution.

Abstract

In this work, we analyze the Einstein-scalar-Gauss-Bonnet (EsGB) theory of gravity in a cosmological context using the formalism of dynamical systems. We obtain the equations of motion of the theory and introduce an appropriate set of dynamical variables to allow for a direct comparison with the results from General Relativity (GR). We observe that the cosmological phase space features the same set of fixed points as in standard GR, i.e., radiation-dominated, matter-dominated, curvature-dominated, and exponentially-accelerated solutions independently of the values of the coupling function and the scalar field. Furthermore, the radiation-dominated fixed points are repellers and the exponentially accelerated fixed points are attractors in the phase space, thus allowing for cosmological solutions behaving qualitatively similar to the $\Lambda$CDM model, i.e., transitioning from a radiation-dominated phase into a matter-dominated phase, and later into a late-time cosmic acceleration phase supported by the scalar field potential. Following a reconstruction method through which we produce the cosmological solutions in the GR limit of the theory and introduce them into the general EsGB dynamical system, a numerical integration of the dynamical system shows that the EsGB theory provides cosmological solutions indistinguishable from those of the standard $\Lambda$CDM model, compatible with the current observations from the Planck satellite and weak-field solar system dynamics, while maintaining the scalar field and the coupling function finite and regular throughout the entire time evolution.