Multiple Field Ultra Slow Roll Inflation: Primordial Black Holes From Straight Bulk And Distorted Boundary

TL;DR

This paper investigates a two-field ultra-slow-roll inflation model with a boundary in field space, showing how non-linear effects can significantly enhance primordial black hole production through boundary-induced inhomogeneities.

Contribution

It introduces a non-linear $ ext{delta}N$ formalism to analyze boundary effects in two-field USR inflation, revealing their impact on PBH abundance and the shape of the curvature perturbation PDF.

Findings

Non-linear effects can greatly increase PBH abundance.

The curvature perturbation PDF has a universal exponential tail.

Boundary geometry influences PBH formation rates.

Abstract

We study a model of two-field ultra-slow-roll (USR) inflation bounded by a curve in the field space. Curvature perturbations and non-Gaussianities can be enhanced both during the USR phase and from the inhomogeneities at the boundary. We employ the full non-linear $\delta N$ formalism to calculate the probability distribution function (PDF) for curvature perturbation non-perturbatively and show that the non-linear effects can significantly enhance the abundance of the primordial black holes (PBHs). For large curvature perturbations, the PDF has a universal exponential tail, but for the intermediate values, the PDF -- and, therefore, the abundance of the PBHs -- depend sensitively on the geometry of the boundary.