The Ineludible non-Gaussianity of the Primordial Black Hole Abundance
  We study the formation of primordial black holes when they are generated by
the collapse of large overdensities in the early universe. Since the density
contrast is related to the comoving curvature perturbation by a nonlinear
relation, the overdensity statistics is unavoidably non-Gaussian. We show that
the abundance of primordial black holes at formation may not be captured by a
perturbative approach which retains the first few cumulants of the non-Gaussian
probability distribution. We provide two techniques to calculate the
non-Gaussian abundance of primordial black holes at formation, one based on
peak theory and the other on threshold statistics. Our results show that the
unavoidable non-Gaussian nature of the inhomogeneities in the energy density
makes it harder to generate PBHs. We provide simple (semi-)analytical
expressions to calculate the non-Gaussian abundances of the primordial black
holes and show that for both narrow and broad power spectra the gaussian case
from threshold statistics is reproduced by increasing the amplitude of the
power spectrum by a factor ${\cal O}(2\div 3)$.
