Highly asymmetric probability distribution from a finite-width upward step during inflation

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 $P[\mathcal{R}]$ using the $\delta N$ formalism. The PDF has an exponential-tail only for positive $\mathcal{R}$ 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 $P[\mathcal{R}]$ 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.

20 pages, 7 figures

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