Existence and bounds of nonlinear singularity-free cosmological solutions in a string-inspired gravity

TL;DR

This paper rigorously proves the existence of globally singularity-free, homogeneous, isotropic cosmological solutions in Einstein-dilaton-Gauss-Bonnet gravity with exponential coupling, confirming numerical findings and establishing a solid mathematical foundation.

Contribution

It introduces a novel power identity method to prove the existence of singularity-free solutions in a nonlinear string-inspired gravity model, overcoming previous analytical challenges.

Findings

Existence of solutions valid for all time with positive, asymptotically vanishing Hubble parameter.

Scalar field evolves monotonically in these solutions.

Results align with numerical simulations, providing a rigorous mathematical foundation.

Abstract

We provide a rigorous proof for the existence of homogeneous, isotropic and globally singularity-free cosmological solutions in Einstein-dilaton-Gauss-Bonnet (EdGB) gravity with exponential coupling. While numerical studies suggested such solutions exist, a formal proof remained elusive. By employing a novel ``power identity method'' and overcoming significant challenges posed by the strong nonlinearities of the exponential coupling, which are not present in the quadratic coupling analyzed in our companion paper \cite{he2025proofssingularityfreesolutionsscalarization}, we establish a FLRW solution valid for all time $t\in(-\infty,+\infty)$, where the Hubble parameter remains positive and vanishes asymptotically, while the scalar field evolves monotonically. This result align with numerical simulations and offer a firm mathematical foundation for singularity-free cosmology in a string-inspired setting.