Primordial black holes in peak theory with a non-Gaussian tail
  In this paper, we update the peak theory for the estimation of the primordial
black hole (PBH) abundance, particularly by implementing the critical behavior
in the estimation of the PBH mass and employing the averaged compaction
function for the PBH formation criterion to relax the profile dependence. We
apply our peak theory to a specific non-Gaussian feature called the exponential
tail, which is characteristic in ultra slow-roll models of inflation. With this
type of non-Gaussianity, the probability of a large perturbation is not
suppressed by the Gaussian factor but decays only exponentially, so the PBH
abundance is expected to be much enhanced. Not only do we confirm this
enhancement even compared to the case of the corresponding nonlinearity
parameter $f_\mathrm{NL}=5/2$, but also we find that the resultant PBH mass
spectrum has a characteristic maximal mass which is not seen in the simple
Press--Schechter approach.
