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 primordial black holes based on the peak theory. It is explicitly shown that the value of non-linear parameter |f NL | ∼ 1 induces a similar effect to a few factors of difference in the amplitude of the power spectrum.Primordial black holes (PBHs) repeatedly come up as a hot topic in cosmology and astrophysics since the pioneering works of Zel'dovich and Novikov [1] and Hawking [2]. For instance, PBHs are still fascinating candidate for dark matter (e.g., see [3][4][5][6][7][8][9][10][11][12][13][14] and references therein), and observational constraints are frequently updated (see e.g. [10,15]). Number of interesting scenarios which produce substantial number of PBHs are proposed (see e.g. a recent review [16] and references therein).One of inevitable issues is the estimation of PBH abundance. Simplest conventional way to estimate PBH abundance is the Press-Schechter (PS) formalism [17], where the Gaussian distribution of a perturbation variable and its threshold for PBH formation are assumed. The validity of these assumptions has been under discussion for a long time (see e.g. [4,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]). Recently, a more plausible procedure for PBH formation in a radiation dominated era is proposed [33], where an enhanced feature is assumed in the primordial power spectrum around some specific scale which enters the horizon in a radiation dominated era. Another important assumption is the random Gaussian distribution of the curvature perturbation. Then, a reliable procedure for the estimation of PBH abundance is derived based on the peak theory [34,35] of the curvature perturbation, by taking the non-linear effect between the curvature perturbation and the density perturbation into account (see e.g. [36][37][38] for the significance of the non-linearity).The purpose of this article is to show the impact of the local type non-Gaussianity of the curvature perturbation extending the procedure given in [33]. The effect of non-Gaussianity on the PBH abundance and the spatial distribution of PBHs have been discussed in [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. However, since a new plausible procedure is proposed, it is important to check how the previously reported effect of the non-Gaussianity works in the new procedure. Providing a method to estimate PBH abundance including the local type non-Gaussianity, we demonstrate the effect of the non-Gaussianity of the curvature perturbation.This article is organized as follows. In Section 2, the typical profile of the curvature perturbation is derived for a given scale and amplitude of the peak with the non-linear parameter f NL . The general implicit expression for the PBH fraction is derived in Section 3. Two specific primordial power spectra are shown as examples to present the impact of non-Gaussianity in Section 4. Section 5 is devoted to a short summary. Some technical detail is given in the appendices. Throughout this arti...

Initial clustering and the primordial black hole merger rate

“…Full consideration of this will require consideration of the the shape of the small-scale power spectrum, typical profile shapes and the shape of the bispectrum, amongst other factors, and goes beyond the scope of this paper. However, much work has been completed on this topic in the past [15,[19][20][21][22][23][24][25]27], and a more complete analysis using the methods presented in this paper would yield qualitatively similar results. We have also only considered an expansion to second order in local-type non-Gaussianity, although it has been shown that higher-order terms can also be important [21].…”

Scalar Induced Gravitational Waves Review

“…Precise estimations of the fraction of PBH is an active and ongoing research field, e.g., see Refs. [202,[214][215][216][217][218][219][220][221] and references therein. For our purposes, it is enough to know that only large induced GWs have a large associated fraction of PBH and, inversely, the absence of large induced GWs rules out PBHs from large primordial fluctuations.…”

“…For the details see the recent discussions in Refs. [217,[219][220][221]256,[281][282][283][284]. Then, ideally one may use the two observations, the PBH mass function and the induced GW counterpart, to perhaps disentangle the primordial non-gaussianity from the primordial spectrum.…”

PBH Formation from Spherically Symmetric Hydrodynamical Perturbations: A Review

“…In this review, we do not focus on the statistical estimation of PBH abundances, for which there are extensive works in this direction, with different approaches and methods. If the reader is interested, we suggest checking these references and the ones therein [60,[95][96][97][98][99][100][101][101][102][103][104][105][106][107][108][109][110][111][112][113][114]. However, to show this topic at the basic level, we basically describe the Press-Schechter [115] and the peak theory [116] procedures.…”