The Formation Probability of Primordial Black Holes

TL;DR

This paper calculates the precise formation probability of primordial black holes during inflation, revealing a transition from Gaussian to Cauchy distributions and indicating a potentially much higher abundance and larger masses than previously estimated.

Contribution

It provides an exact formulation of primordial black hole formation probability, highlighting a distribution transition and implications for black hole abundance and mass spectrum.

Findings

Formation probability interpolates between Gaussian and Cauchy distributions.

Primordial black hole abundance can be significantly higher than Gaussian estimates.

Mass function is shifted towards larger masses.

Abstract

We calculate the exact formation probability of primordial black holes generated during the collapse at horizon re-entry of large fluctuations produced during inflation, such as those ascribed to a period of ultra-slow-roll. We show that it interpolates between a Gaussian at small values of the average density contrast and a Cauchy probability distribution at large values. The corresponding abundance of primordial black holes may be larger than the Gaussian one by several orders of magnitude. The mass function is also shifted towards larger masses.