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 primordial black holes (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 the 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(NL) similar to -1.