Existence and bounds of nonlinear singularity-free cosmological solutions in a string-inspired gravity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914174693539840 |
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| author | He, Chihang Liu, Chao |
| author_facet | He, Chihang Liu, Chao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and bounds of nonlinear singularity-free cosmological solutions in a string-inspired gravity He, Chihang Liu, Chao Analysis of PDEs General Relativity and Quantum Cosmology 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. |
| title | Existence and bounds of nonlinear singularity-free cosmological solutions in a string-inspired gravity |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2512.00455 |