Probability of primordial black hole formation and its dependence on the radial profile of initial configurations

TL;DR

This paper develops a probabilistic model for primordial black hole formation that accounts for the initial radial profile of inhomogeneities, improving estimates of their abundance in the early universe.

Contribution

It introduces a new method to incorporate the radial profile of curvature inhomogeneities into PBH formation probability calculations, enhancing previous models.

Findings

Probability depends strongly on the radial profile parameters.

Derived joint probability distribution for initial inhomogeneity parameters.

Extended analysis to include curvature inhomogeneity profiles.

Abstract

In this paper we derive the probability of the radial profiles of spherically symmetric inhomogeneities in order to provide an improved estimation of the number density of primordial black holes (PBHs). We demonstrate that the probability of PBH formation depends sensitively on the radial profile of the initial configuration. We do this by characterising this profile with two parameters chosen heuristically: the amplitude of the inhomogeneity and the second radial derivative, both evaluated at the centre of the configuration. We calculate the joint probability of initial cosmological inhomogeneities as a function of these two parameters and then find a correspondence between these parameters and those used in numerical computations of PBH formation. Finally, we extend our heuristic study to evaluate the probability of PBH formation taking into account for the first time the radial profile of curvature inhomogeneities.