The Threshold for Primordial Black Hole Formation: a Simple Analytic Prescription

TL;DR

This paper presents a simple analytical method, based on numerical simulations, to determine the threshold for primordial black hole formation, accounting for non-linear effects at horizon crossing that significantly influence the threshold value.

Contribution

It introduces a novel prescription that incorporates non-linearities at horizon crossing, improving the accuracy of primordial black hole formation predictions.

Findings

Non-linear effects at horizon crossing increase the threshold by about a factor of two.

The method provides a straightforward way to compute the formation threshold from the power spectrum.

The prescription aligns with numerical simulation results for better modeling of early universe phenomena.

Abstract

Primordial black holes could have been formed in the early universe from non linear cosmological perturbations re-entering the cosmological horizon when the Universe was still radiation dominated. Starting from the shape of the power spectrum on superhorizon scales, we provide a simple prescription, based on the results of numerical simulations, to compute the threshold $\delta_c$ for primordial black hole formation. Our procedure takes into account both the non linearities between the Gaussian curvature perturbation and the density contrast and, for the first time in the literature, the non linear effects arising at horizon crossing, which increase the value of the threshold by about a factor two with respect to the one computed on superhorizon scales.