Abstract
We study a single-field inflation model in which the inflaton potential has an upward step
between two slow-roll regimes by taking into account the finite width of the step. We calculate
the probability distribution function (PDF) of the curvature perturbation P[
] using the
δN formalism. The PDF has an exponential-tail only for positive whose slope
depends on the step width. We find that the tail may have a significant impact on the estimation
of the primordial black hole abundance. We also show that the PDF P[] becomes highly
asymmetric on a particular scale exiting the horizon before the step, at which the curvature power
spectrum has a dip. This asymmetric PDF may leave an interesting signature in the large scale
structure such as voids.
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