报告题目：Nonlinear singularity-free cosmological solutions and scalarization in ESGB theories

报告人：刘超 副研究员（华中科技大学）

邀请人：张华丽

时间地点：2025年12月12日 周五 下午15:00-16:00 数财神捕鱼官网 425教室

摘要：This talk presents rigorous proofs for two classes of singularity-free cosmological models: one in Einstein–scalar–Gauss–Bonnet (EsGB) gravity with quadratic coupling and the other in Einstein–dilaton–Gauss–Bonnet (EdGB) gravity with exponential coupling. Although the existence of such solutions has been anticipated for many years by physicists, supported by numerical simulations and linear analyses, formal mathematical proofs have been lacking. For both theories, we establish the global existence of homogeneous and isotropic FLRW solutions that remain free of big bang singularities for all time, in full agreement with previous numerical findings. By introducing a new “power identity method,” we achieve precise control over the Hubble parameter and scalar field even in strongly nonlinear regimes, providing the first rigorous foundation for singularity-free cosmology and nonlinear spontaneous scalarization. The method also offers a flexible framework applicable to a wide range of nonlinear gravitational systems. This talk is partially based on joint work with Chihang He and Jinhua Wang.

个人简介：刘超副研究员于 2018 年在 Monash 大学获得博士学位，现为华中科技大学数学中心副研究员。其研究方向包括非线性双曲方程与波方程、数学广义相对论、Einstein 方程及其与流体、Yang–Mills 场的耦合系统，以及 Euler–Poisson 方程等。相关成果已发表于 Journal of the European Mathematical Society、Mathematische Annalen、Communications in Mathematical Physics、SIAM Journal on Mathematical Analysis、Physical Review D、Annales Henri Poincaré 等国际知名期刊。