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

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<jats:title>Abstract</jats:title> <jats:p>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 <jats:italic>δ𝒩</jats:italic>  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 <jats:italic>ζ</jats:italic>, which we find to decay faster than exp(-3<jats:italic>ζ</jats:italic>).</jats:p>

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