Early-time cosmological solutions in Einstein-scalar-Gauss-Bonnet theory

TL;DR

This paper explores early-universe solutions in Einstein-scalar-Gauss-Bonnet theory, revealing new analytical solutions with potential implications for inflation and singularity avoidance based on specific coupling functions.

Contribution

It introduces a class of analytical solutions in Einstein-scalar-Gauss-Bonnet theory with particular coupling functions, highlighting their unique cosmological features.

Findings

Negative coupling yields inflationary and de Sitter solutions.

Positive coupling produces singularity-free, non-Big Bang solutions.

Ricci scalar's role is negligible at early times in these models.

Abstract

In this work, we consider a generalised gravitational theory that contains the Einstein term, a scalar field and the quadratic Gauss-Bonnet term. We focus on the early-universe dynamics, and demonstrate that a simple choice of the coupling function between the scalar field and the Gauss-Bonnet term and a simplifying assumption regarding the role of the Ricci scalar can lead to new, analytical, elegant solutions with interesting characteristics. We first argue, and demonstrate in the context of two different models, that the presence of the Ricci scalar in the theory at early times, when the curvature is strong, does not affect the actual cosmological solutions. By considering therefore a pure scalar-GB theory with a quadratic coupling function we derive a plethora of interesting, analytic solutions: for a negative coupling parameter, we obtain inflationary, de Sitter-type solutions or expanding solutions with a de Sitter phase in their past and a natural exit mechanism at later times; for a positive coupling function, we find instead singularity-free solutions with no Big-Bang singularity. We show that the aforementioned solutions arise only for this particular choice of coupling function, a result that may hint to some fundamental role that this coupling function may hold in the context of an ultimate theory.