  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 universal
scaling relation between black hole mass and initial perturbation found for a
variety of collapsing space-times also applies to PBH formation, indicating the
possibility of the formation of PBHs with masses much smaller than one horizon
mass. 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. This result suggests
that the constraints on the primordial fluctuation spectrum based on the
abundance of PBHs at different mass scales may have to be revisited.
