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

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.

arXiv comment9 pages, 4 figures; references and discussion added; further minor revision, accepted to PRD

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• Inflation driven by Einstein-Gauss-Bonnet gravity
• Viable Inflationary Models in a Ghost-free Gauss-Bonnet Theory of Gravity
• Gauss-Bonnet term corrections in scalar field cosmology
• Primordial perturbations with pre-inflationary bounce
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• Gauss-Bonnet Gravity in $D=4$ Without Gauss-Bonnet Coupling to Matter - Cosmological Implications