Primordial Black Hole Formation from Type II Fluctuations with Primordial Non-Gaussianity

Abstract

This study investigates the formation of primordial black holes (PBHs) resulting from the collapse of adiabatic fluctuations with large amplitudes and non-Gaussianity. Ref. \cite{Uehara:2024yyp} showed that fluctuations with large amplitudes lead to the formation of type B PBHs, characterized by the existence of the bifurcating trapping horizons, distinct from the more common type A PBHs without a bifurcating trapping horizon. We focus on the local type non-Gaussianity characterized by the curvature perturbation $ζ$ given by a function of a Gaussian random variable $ζ_{\rm G}$ as $βζ=-\ln(1-βζ_{\rm G})$ with a parameter $β$. Then we examine how the non-Gaussianity influences the dynamics and the type of PBH formed, particularly focusing on type II fluctuations, where the areal radius varies non-monotonically with the coordinate radius. Our findings indicate that, for $β>-2$, the threshold for distinguishing between type A and type B PBHs decreases with increasing $β$ similarly to the threshold for black hole formation. Additionally, for large positive values of $β$, the threshold for type B PBHs approaches that for type II fluctuations. We also find that, for a sufficiently large negative value of $β\lesssim-4.0$, the threshold value is in the type II region of $μ$, i.e., there are fluctuations of type II that do not form black holes. Lastly, we calculate the PBH mass for several values of $β$. Then we observe that the final mass monotonically increases with the initial amplitude within the parameter region of type A PBHs, which differs from previous analytical expectations.