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

TL;DR

This paper investigates how a finite-width upward step in the inflaton potential during inflation creates a highly asymmetric probability distribution of curvature perturbations, affecting primordial black hole estimates and large-scale structure signatures.

Contribution

It introduces a detailed calculation of the curvature perturbation PDF considering finite step width, revealing significant asymmetries and exponential tails not previously characterized.

Findings

The PDF exhibits an exponential tail for positive curvature perturbations influenced by step width.

The asymmetry in the PDF is prominent on scales before the step, correlating with dips in the power spectrum.

The asymmetric PDF could produce observable effects in large-scale structures like voids.

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