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The statistics of primordial black holes in a radiation dominated Universe -- recent and new results
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We review the non-linear statistics of Primordial Black Holes that form from the collapse of over-densities in a radiation dominated Universe. We focus on the scenario in which large over-densities are generated by rare and Gaussian curvature perturbations during inflation. As new results, we show that the mass spectrum follows a power law determined by the critical exponent of the self-similar collapse up to a power spectrum dependent cut-off, and that the abundance related to very narrow power spectra is exponentially suppressed. Related to this, we discuss and explicitly show that the Press-Schechter approximation, as well as the statistics of mean profiles, lead to wrong conclusions for the abundance and mass spectrum. Finally, we clarify that the transfer function in the statistics of initial conditions for primordial black holes formation (the abundance) does not play a significant role.
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Cited by 3 Pith papers
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The statistics of curvature-profile dispersion in primordial black hole formation
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A broad power spectrum of primordial curvature perturbations produces a bimodal primordial black hole mass function whose dominant peak is near the infrared scale, not the ultraviolet scale.
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In one non-attractor inflation model, initially similar field fluctuations produce three distinct black-hole formation channels—trapped, overdense, void—with collapse thresholds determined by the full density profile,...
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