Towards Stochastic Inflation in Higher-Curvature Gravity

We study stochastic inflation in the presence of higher-curvature terms non-minimally coupled to the inflaton. Focusing on quadratic curvature invariants, we single out the Gauss-Bonnet term which is known to avoid ghosts, while having non-trivial effects on the background and scalar mode evolution when coupled to the scalar field. Stochastic Klein-Gordon and Langevin equations are derived in the presence of the Gauss-Bonnet coupling, and their slow-roll and ultra-slow-roll limits are studied. By using first-passage time method, scalar power spectrum and PBH mass fraction are estimated in these limits. Stochastic evolution of a Gauss-Bonnet-coupled spectator field in de Sitter vacuum is also discussed.