Non-Gaussianity effects on the primordial black hole abundance for sharply-peaked primordial spectrum

Understand

We perturbatively study the effect of non-Gaussianities on the mass fraction of primordial black holes (PBHs) at the time of formation by systematically taking its effect into account in the one-point probability distribution function of the primordial curvature perturbation.

• We focus on the bispectrum and trispectrum and derive formulas that describe their effects on the skewness and kurtosis of the distribution function.
• Then considering the case of narrowly peaked spectra, we obtain simple formulas that concisely express the effect of the bi- and trispectra.
• In particular, together with the $g_{\rm NL}$ and $\tau_{\rm NL}$ parameters of the trispectrum, we find that non-Gaussianity parameters for various types of the bispectrum are linearly combined to give an effective parameter, $f_{\rm NL}^{\rm eff}$, that determines the PBH mass fraction in the narrow spectral shape limit.