On Bouncing and Nonsingular Solutions in Einstein-scalar-Gauss-Bonnet Cosmology

TL;DR

This paper investigates Einstein-scalar-Gauss-Bonnet gravity and finds that it generally does not support bouncing solutions in flat and open universes, with any such solutions being unstable, thus challenging its effectiveness in curing singularities.

Contribution

The study demonstrates the non-existence of stable bouncing solutions in Einstein-scalar-Gauss-Bonnet cosmology for flat and open universes and provides explicit unstable bouncing solutions for closed universes.

Findings

No stable bouncing solutions in flat and open universes.

Explicit unstable bouncing solution in closed universe.

Early-time singularity-free cosmologies are unstable.

Abstract

It is generically believed that higher-order curvature corrections to the Einstein-Hilbert action might cure the curvature singularities that plague general relativity. Here we consider Einstein-scalar-Gauss-Bonnet gravity, the only four-dimensional, ghost-free theory with quadratic curvature terms. For any choice of the coupling function and of the scalar potential, we show that the theory does not allow for bouncing solutions in the flat and open Friedmann universe. For the case of a closed universe, using a reverse-engineering method, we explicitly provide a bouncing solution which is nevertheless linearly unstable in the scalar gravitational sector. Moreover, we show that the expanding, singularity-free, early-time cosmologies allowed in the theory are unstable. These results rely only on analyticity and finiteness of cosmological variables at early times.