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

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.

Version 2 with corrections from referees included, changes mostly improve the presentation

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• The long-short wavelength mode coupling tightens primordial black hole constraints
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• Effect of accretion on primordial black holes in Brans-Dicke theory
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• Constraining Hybrid Natural Inflation with recent CMB data
• Evolution of Primordial Black Hole Mass Spectrum in Brans-Dicke Theory
• Extended primordial black hole mass functions with a spike
• Vacuum energy and Primordial Black Holes in Brans-Dicke Theory