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

Kavli Affiliate: Misao Sasaki

| First 5 Authors: Takahiko Matsubara, Misao Sasaki, , ,

| Summary:

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.

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