Quantum diffusion in sharp transition to non-slow-roll phase

Abstract Transitions between different inflationary slow-roll scenarios are known to provide short non-slow-roll periods with non-trivial consequences. We consider the effect of quantum diffusion on the inflationary dynamics in a transition process. Using the stochastic δ𝒩 formalism, we follow the detailed evolution of noises through a sharp transition modeled by the Starobinsky potential, although some of our results apply to any sharp transition. We find how the stochastic noise induced by the transition affects the coarse-grained fields. We then consider the special case that the potential is flat after the transition. It is found that, during a particular phase of evolution, the noise we obtain cannot drive the inflaton past the classically unreachable field values; so the boundary crossing is delayed. By deriving the characteristic function, we also study the tail behavior for the distribution of curvature perturbations ζ , which we find to decay faster than exp(-3 ζ ).