Primordial black holes from metric preheating: mass fraction in the
  excursion-set approach
  We calculate the mass distribution of Primordial Black Holes (PBHs) produced
during metric preheating. After inflation, the oscillations of the inflaton at
the bottom of its potential source a parametric resonant instability for
small-scale scalar perturbations, that may collapse into black holes. After
reviewing in a pedagogical way different techniques that have been developed in
the literature to compute mass distributions of PBHs, we focus on the
excursion-set approach. We derive a Volterra integral equation that is free of
a singularity sometimes encountered, and apply it to the case of metric
preheating. We find that if the energy density at which the instability stops,
$\rho_\Gamma$, is sufficiently smaller than the one at which inflation ends,
$\rho_\mathrm{end}$, namely if $\rho_\Gamma^{1/4}/\rho_\mathrm{end}^{1/4}<
10^{-5}(\rho_\mathrm{end}^{1/4}/10^{16}\mathrm{GeV})^{3/2}$, then PBHs dominate
the universe content at the end of the oscillatory phase. This confirms the
previous analysis of arXiv:1907.04236 . By properly accounting for the
"cloud-in-cloud" mechanism, we find that the mass distribution is more
suppressed at low masses than previously thought, and peaks several orders of
magnitude above the Hubble mass at the end of inflation. The peak mass ranges
from $10$ g to stellar masses, giving rise to different possible cosmological
effects that we discuss.
