Double-peaked inflation model: Scalar induced gravitational waves and primordial-black-hole suppression from primordial non-Gaussianity

Abstract

A significant abundance of primordial black hole (PBH) dark matter can be produced by curvature perturbations with power spectrum ∆ζ(kpeak) ∼ O(10−2) at small scales, associated with the generation of observable scalar induced gravitational waves (SIGWs). However, the primordial non-Gaussianity may play a non-negligible role, which is not usually considered. We propose two inflation models that predict double peaks of order O(10−2) in the power spectrum and study the effects of primordial non-Gaussianity on PBHs and SIGWs. This model is driven by a power-law potential, and has a noncanonical kinetic term whose coupling function admits two peaks. By field-redefinition, it can be recast into a canonical inflation model with two quasi-inflection points in the potential. We find that the PBH abundance will be altered saliently if non-Gaussianity parameter satisfies |fNL(kpeak, kpeak, kpeak)| & ∆ζ(kpeak)/(23δ c ) ∼ O(10−2). Whether the PBH abundance is suppressed or enhanced depends on the fNL being positive or negative, respectively. In our model, non-Gaussianity parameter fNL(kpeak, kpeak, kpeak) ∼ O(1) takes positive sign, thus PBH abundance is suppressed dramatically. On the contrary, SIGWs are insensitive to primordial non-Gaussianity and hardly affected, so they are still within the sensitivities of space-based GWs observatories and Square Kilometer Array. ∗ [email protected] † [email protected] ‡ Corresponding author. [email protected] 1 ar X iv :2 10 6. 10 79 2v 2 [ gr -q c] 8 S ep 2 02 1