Formation Thresholds for Primordial Black Holes Under a Maximum Density

Primordial black holes form, in the standard picture, when a rare large curvature perturbation re-enters the cosmological horizon during the radiation era and the overdense region collapses against radiation pressure. Whether collapse succeeds is decided by comparing the perturbation amplitude with a threshold. The headline computed values are: t min s = 6.431e-17; M min g = 2.596e+22; M min Msun = 1.306e-11; rho A g cm3 = 9.718e+54. The study is a computation from stated assumptions, not a measurement, and the deposited script reproduces every number quoted.