Effects of Critical Collapse on Primordial Black-Hole Mass Spectra
  Certain inflationary models as well as realisations of phase transitions in
the early Universe predict the formation of primordial black holes. For most
mass ranges, the fraction of matter in the form of primordial black holes is
limited by many different observations on various scales. Primordial black
holes are assumed to be formed when overdensities that cross the horizon have
Schwarzschild radii larger than the horizon. Traditionally it was therefore
assumed that primordial black-hole masses were equal to the horizon mass at
their time of formation. However, detailed calculations of their collapse show
that primordial black holes formed at each point in time should rather form a
spectrum of different masses, obeying critical scaling. Though this has been
known for more than fifteen years, the effect of this scaling behaviour is
largely ignored when considering predictions for primordial black hole mass
spectra. In this paper we consider the critical collapse scaling for a variety
of models which produce primordial black holes, and find that it generally
leads to a shift, broadening and an overall decrease of the mass contained in
primordial black holes. This effect is model and parameter dependent and cannot
be contained by a constant rescaling of the spectrum; it can become important
and should be taken into account when comparing to observational constraints.
