Title: Stochastic inflation: numerics and constraints
Abstract: Stochastic inflation is a method to solve inflationary perturbations in a non-linear way. It can describe even the strong and rare perturbations responsible for producing primordial black holes and resolve the perturbation probability distribution deep into its non-Gaussian tail.
In the stochastic equations, the coarse-grained long-wavelength inflaton field is affected by quantum noise from short-wavelength perturbations.
I discuss recent progress in solving these equations numerically in a setup where the short-wavelength noise is computed beyond the de Sitter approximation. I show that the squeezing and freezing of the short-wavelength modes constrain the problem to one dimension in a typical primordial black hole model. I solve the system numerically but efficiently using importance sampling around the “most probable paths,” which I solve semi-analytically.
