Primordial black holes in peak theory with a non-Gaussian tail

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