Double-peaked inflation model: Scalar induced gravitational waves and primordial-black-hole suppression from primordial non-Gaussianity
Fengge Zhang, Jiong Lin, Yizhou Lu
Abstract
A significant abundance of primordial black hole (PBH) dark matter can be produced by curvature perturbations with power spectrum ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\zeta}}^{2}({k}_{\mathrm{peak}})\ensuremath{\sim}\mathcal{O}({10}^{\ensuremath{-}2})$ 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 $\mathcal{O}({10}^{\ensuremath{-}2})$ 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 $|{f}_{\mathrm{NL}}({k}_{\mathrm{peak}},{k}_{\mathrm{peak}},{k}_{\mathrm{peak}})|\ensuremath{\gtrsim}{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\zeta}}^{2}({k}_{\mathrm{peak}})/(23{\ensuremath{\delta}}_{c}^{3})\ensuremath{\sim}\mathcal{O}({10}^{\ensuremath{-}2})$. Whether the PBH abundance is suppressed or enhanced depends on the ${f}_{\mathrm{NL}}$ being positive or negative, respectively. In our model, non-Gaussianity parameter ${f}_{\mathrm{NL}}({k}_{\mathrm{peak}},{k}_{\mathrm{peak}},{k}_{\mathrm{peak}})\ensuremath{\sim}\mathcal{O}(1)$ 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.