Power spectrum in stochastic inflation

Abstract We compute the power spectrum of curvature perturbations in stochastic inflation. This combines distribution first crossing times through end-of-inflation surface, which has been previously studied, with fields value at time when a given scale crosses out Hubble radius during inflation, we show how to compute. allows stochastic-? N formalism make concrete contact observations. As an application, study quantum diffusion small scales (arising e.g. models leading primordial black holes) affects large-scale observed cosmic microwave background. find that even if those sets are well separated, large effects can arise from distortion classical relationship between field values and wavenumbers brought about by near end shows background measurements set explicit constraints on entire inflationary potential down