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. [1] 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 G as β ζ=-ln(1- β ζ 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 ≲ -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.