Singularity-free cosmological solutions in quadratic gravity

TL;DR

This paper demonstrates that quadratic Gauss-Bonnet coupling in scalar gravity models can produce singularity-free cosmological solutions, contrasting with the singular solutions typical in standard models.

Contribution

It introduces a class of scalar-Gauss-Bonnet gravity models with specific coupling functions that admit non-singular cosmological solutions, supported by analytical and numerical analysis.

Findings

Singularity-free solutions exist for even n in the coupling function.

Singular solutions are confined to a specific phase space region.

Non-singular solutions occupy the remaining phase space.

Abstract

We study a general field theory of a scalar field coupled to gravity through a quadratic Gauss-Bonnet term $\xi(\phi) R^2_{GB}$. The coupling function has the form $\xi(\phi)=\phi^n$, where $n$ is a positive integer. In the absence of the Gauss-Bonnet term, the cosmological solutions for an empty universe and a universe dominated by the energy-momentum tensor of a scalar field are always characterized by the occurrence of a true cosmological singularity. By employing analytical and numerical methods, we show that, in the presence of the quadratic Gauss-Bonnet term, for the dual case of even $n$, the set of solutions of the classical equations of motion in a curved FRW background includes singularity-free cosmological solutions. The singular solutions are shown to be confined in a part of the phase space of the theory allowing the non-singular solutions to fill the rest of the space. We conjecture that the same theory with a general coupling function that satisfies certain criteria may lead to non-singular cosmological solutions.