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
NL and τ
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
NL
eff, that determines the PBH mass
fraction in the narrow spectral shape limit.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.