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

Abstract

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 $g_{\mathrm{NL}}$ and ${\tau }_{\mathrm{NL}}$ parameters of the trispectrum, we find that non-Gaussianity parameters for various types of the bispectrum are linearly combined to give an effective parameter, $f_{\mathrm{NL}}^{\mathrm{eff}}$, that determines the PBH mass fraction in the narrow spectral shape limit.

19 pages, 8 figures, Matches with the published version

References in corpus (11)

• Primordial Black Holes as Dark Matter: Recent Developments
• Primordial black hole formation in the radiative era: investigation of the critical nature of the collapse
• Calculating the mass spectrum of primordial black holes
• Non-Gaussianity in the modulated reheating scenario
• The Threshold for Primordial Black Hole Formation: a Simple Analytic Prescription
• Primordial trispectrum from inflation
• Primordial Black Holes as Dark Matter Candidates
• Primordial black holes as biased tracers
• Peaks and primordial black holes: the effect of non-Gaussianity
• Solving peak theory in the presence of local non-gaussianities
• Non-Gaussian corrections to the probability distribution of the curvature perturbation from inflation

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• Sudden braking and turning with a two-field potential bump: primordial black hole formation
• Extended $\delta N$ formalism: Nonspatially Flat Separate Universe Approach
• Primordial black hole isocurvature modes from non-Gaussianity
• Non-Gaussianities and Primordial Black Holes
• $\delta n$ formalism: A new formulation for the probability density of the curvature perturbation