PRIMORDIAL BLACK HOLE FORMATION IN THE MATTER-DOMINATED PHASE OF THE UNIVERSE

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 beta(0) of primordial black holes. The numerical result obtained is applicable even if the density fluctuation sigma at horizon entry is of the order of unity. For sigma << 1, we find a semi-analytic formula beta(0) similar or equal to 0.05556 sigma(5), 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 sigma greater than or similar to 0.05, while they are comparable with each other for sigma greater than or similar to 0.05. We also discuss how s can be written in terms of primordial curvature perturbations.