Non-gaussianities for primordial black hole formation

Abstract

We analyze primordial non-gaussianities in presence of an ultra-slow phase during the inflationary dynamics, focusing on scenarios relevant for the production of primordial black holes. We compute the three-point correlation function of comoving curvature perturbations finding that non-gaussianities are sizable, and predominantly local. In the context of threshold statistics, we analyze their impact for the abundance of primordial black holes, and their interplay with the non-gaussianities arising from the non-linear relation between density and curvature perturbations. We find that non-gaussianities significantly modify the estimate of the primordial black holes abundance obtained with the gaussian approximation. However, we show that this effect can be compensated by a small change, of a factor 2÷3 at most, of the amplitude of the primordial power spectrum of curvature perturbations. This is obtained with a small tuning of the parameters of the inflationary model.

PBH Formation from Spherically Symmetric Hydrodynamical Perturbations: A Review

“…Although it goes beyond the scope of the review, we should mention that one could also consider the effect of the inclusion of non-Gaussianities in Equation ( 81), which can have important consequences for the PBH abundance estimation. There are vast and extensive works that consider its impact on the thresholds and PBH abundances [103,107,108,[180][181][182][183][184][185][186][187][188][189][190][191][192][193][194][195], including some of them that have used numerical simulations following the basics shown in this review [196,197].…”

Solving peak theory in the presence of local non-gaussianities

“…Refs. [18,19] indeed find that during an ultra slow-roll phase sizable non-gaussianities of local type are generated. In the rest of this paper we will dub these non-gaussianities "primordial" to distinguish them from non-gaussianities that arise from the non-linear relation between curvature and density perturbations.…”

Constant-rate inflation: primordial black holes from conformal weight transitions

“…In section 2 and 3 we consider a three-stage single-field inflation with sharp transitions to different phases at η = η * and η = η * * , as given by figure 1, where δ ≡ φ/(H φ) is the rate-ofrolling of inflaton φ, and ∆ ≡ 3/2−ν is the scaling dimension of the curvature perturbation R in the late-time limit 2 fixed by the dilatation symmetry of the four-dimensional de Sitter background [49,53,54]. Such a piecewise simplification of the inflationary dynamics can also be found in [19,21,42]. ν is the dimensionless mass parameter of the mode functions of R. The first slow-roll parameters in Phase 2 and 3 are set to zero for simplicity (namely,…”

“…That enhanced primordial density fluctuations from inflationary models with large curvature perturbations on small scales is the mainstream scenario for PBH formation. PBHs from models of inflation, with targeting masses spanning in the range of 10 −17 -10 9 M , can be realized either in the single-field [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] or multi-field [22][23][24][25][26][27][28][29][30][31][32][33][34][35] framework.…”