Near-Critical Gravitational Collapse and the Initial Mass Function of Primordial Black Holes

The recent discovery of critical phenomena arising in gravitational collapse near the threshold of black-hole formation is used to estimate the initial mass function of primordial black holes (PBHs). It is argued that the scaling relation between black-hole mass and initial perturbation found for a collapsing radiation fluid in an asymptotically flat space-time also applies to PBH formation in a Friedmann universe. Owing to the natural fine tuning of initial conditions by the exponential decline of the probability distribution for primordial density fluctuations, sub-horizon-mass PBHs are expected to form at all epochs. We derive a two-parameter mass function for PBHs.