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arXiv · 2507.15304

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

Chihang He·Chao Liu·Jinhua Wang
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Abstract

The search for singularity-free cosmological solutions has become a highly active topic in the physics community in recent years, yet existing results are largely numerical or based on asymptotic analysis. To place these developments on a firm mathematical footing, we rigorously establish the global existence and estimates of a class of singularity-free cosmological solutions to the fully nonlinear Einstein--scalar system in Einstein-scalar-Gauss-Bonnet gravity with quadratic coupling, providing proofs of previous numerical results in mathematical perspective. We further prove nonlinear scalarization triggered by a Gauss-Bonnet-induced tachyonic instability. Our analysis relies on a novel structural identity, the power identity, which yields decoupled differential inequalities for the Hubble parameter. This framework provides a new method for converting numerical evidence into a mathmatical proof for nonlinear systems.

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Chihang He, Chao Liu, Jinhua Wang. 2025-07-21. Proofs on singularity-free solutions and scalarization in nonlinear Einstein-scalar-Gauss-Bonnet cosmology. https://doi.org/10.1088/1361-6382%2Fae7795

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