Effect of nonlinearity between density and curvature perturbations on
  the primordial black hole formation
  We study the effect of the nonlinear relation between density and curvature
perturbations on the formation of PBHs. By calculating the variance and
skewness of the density perturbation we derive the non-Gaussian property. As a
criterion for PBH formation, the compaction function is used and it is found
that larger curvature perturbations are required due to the nonlinear effect.
We estimate the PBH abundance based on the Press-Schechter formalism with
non-Gaussian probability density function during Radiation dominated era. It is
found that the nonlinear effect slightly suppresses the PBH formation and the
suppression is comparable to that expected if the primordial curvature
perturbation would have the local form of non-Gaussianity with nonlinear
parameter $f_\text{NL} \sim -1$.
