Аннотация
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 spectrums 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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