Proofs of singularity-free solutions and scalarization in nonlinear Einstein-scalar-Gauss-Bonnet cosmology

TL;DR

This paper rigorously proves the existence of singularity-free cosmological solutions and spontaneous scalarization in nonlinear Einstein-scalar-Gauss-Bonnet gravity, confirming and extending previous numerical findings.

Contribution

It provides the first rigorous mathematical proof of singularity-free solutions and scalarization phenomena in nonlinear ESGB cosmology with quadratic coupling.

Findings

Existence of singularity-free cosmological solutions

Proof of nonlinear spontaneous scalarization

Agreement with previous numerical results

Abstract

We establish the global existence and precise estimates of a class of singularity-free cosmological solutions in nonlinear Einstein-scalar-Gauss-Bonnet (ESGB) gravity with quadratic coupling, in close agreement with previous numerical results. Our analysis also yields a rigorous mathematical proof of nonlinear spontaneous scalarization, triggered by a tachyonic instability induced by the Gauss-Bonnet term. The proof is based on a set of decoupled differential inequalities for the Hubble parameter $H$, derived from a key structural identity that we refer to as the power identity.