Abundance of primordial black holes with local non-Gaussianity in peak theory

Abstract

We discuss the effect of local type non-Gaussianity on the abundance of\nprimordial black holes (PBH) based on the peak theory. We provide the PBH\nformation criterion based on the so-called compaction function and use the peak\ntheory statistics associated with the curvature perturbation with the local\ntype non-Gaussianity. Providing a method to estimate the PBH abundance, we\ndemonstrate the effects of non-Gaussianity. It is explicitly shown that the\nvalue of non-linear parameter $|f_{\\rm NL}| \\sim 1$ induces a similar effect to\na few factors of difference in the amplitude of the power spectrum.\n