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

TL;DR

This paper explores how primordial non-Gaussianity affects the formation and characteristics of primordial black holes, especially focusing on type II fluctuations and their thresholds, with implications for black hole mass and formation conditions.

Contribution

It provides a detailed analysis of the influence of local type non-Gaussianity on the thresholds and types of primordial black holes formed, highlighting new behaviors for large positive and negative non-Gaussianity parameters.

Findings

Threshold for type B PBHs decreases with increasing non-Gaussianity parameter 3;

Large positive 3 values make type B thresholds approach type II fluctuation thresholds;

For 3 4, some fluctuations of type II do not form black holes.

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 $\zeta$ given by a function of a Gaussian random variable $\zeta_{\rm G}$ as $\beta\zeta=-\ln(1-\beta \zeta_{\rm G})$ with a parameter $\beta$. 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 $\beta>-2$, the threshold for distinguishing between type A and type B PBHs decreases with increasing $\beta$ similarly to the threshold for black hole formation. Additionally, for large positive values of $\beta$, the threshold for type B PBHs approaches that for type II fluctuations. We also find that, for a sufficiently large negative value of $\beta\lesssim-4.0$, the threshold value is in the type II region of $\mu$, i.e., there are fluctuations of type II that do not form black holes. Lastly, we calculate the PBH mass for several values of $\beta$. 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.