2016ApJ...833...61H

We investigate primordial black hole formation in the matter-dominated phase of the universe, where nonspherical effects in gravitational collapse play a crucial role. This is in contrast to the black hole formation in a radiation-dominated era. We apply the Zel'dovich approximation, Thorne's hoop conjecture, and Doroshkevich's probability distribution and subsequently derive the production probability β₀ of primordial black holes. The numerical result obtained is applicable even if the density fluctuation σ at horizon entry is of the order of unity. For σ≪1, we find a semi-analytic formula β₀≃0.05556σ⁵, which is comparable to the Khlopov-Polnarev formula. We find that the production probability in the matter-dominated era is much larger than that in the radiation-dominated era for σ\lesssim0.05, while they are comparable with each other for σ>rsim0.05. We also discuss how σ can be written in terms of primordial curvature perturbations.