String-inspired cosmology: Late time transition from scaling matter era to dark energy universe caused by a Gauss-Bonnet coupling

TL;DR

This paper investigates how a Gauss-Bonnet coupling to a scalar field can cause a transition from a matter-dominated universe to accelerated expansion, providing insights into late-time cosmic evolution and dark energy.

Contribution

It derives conditions for cosmological scaling solutions with Gauss-Bonnet coupling and identifies models that enable a transition to late-time acceleration.

Findings

Gauss-Bonnet coupling can induce late-time acceleration after a matter era.

Scaling solutions exist for specific exponential forms of the coupling and Lagrangian.

Models with exponential potentials and tachyon fields can realize this cosmological evolution.

Abstract

The Gauss-Bonnet (GB) curvature invariant coupled to a scalar field $\phi$ can lead to an exit from a scaling matter-dominated epoch to a late-time accelerated expansion, which is attractive to alleviate the coincident problem of dark energy. We derive the condition for the existence of cosmological scaling solutions in the presence of the GB coupling for a general scalar-field Lagrangian density $p(\phi, X)$, where $X=-(1/2)(\nabla \phi)^2$ is a kinematic term of the scalar field. The GB coupling and the Lagrangian density are restricted to be in the form $f(\phi) \propto e^{\lambda \phi}$ and $p=Xg (Xe^{\lambda \phi})$, respectively, where $\lambda$ is a constant and $g$ is an arbitrary function. We also derive fixed points for such a scaling Lagrangian with a GB coupling $f(\phi) \propto e^{\mu \phi}$ and clarify the conditions under which the scaling matter era is followed by a de-Sitter solution which can appear in the presence of the GB coupling. Among scaling models proposed in the current literature, we find that the models which allow such a cosmological evolution are an ordinary scalar field with an exponential potential and a tachyon field with an inverse square potential, although the latter requires a coupling between dark energy and dark matter.