Double-peaked inflation model: Scalar induced gravitational waves and
  primordial-black-hole suppression from primordial non-Gaussianity
  A significant abundance of primordial black hole (PBH) dark matter can be
produced by curvature perturbations with power spectrum
$\Delta_\zeta^2(k_{\mathrm{peak}})\sim \mathcal{O}(10^{-2})$ 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 $\mathcal{O}(10^{-2})$ 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
$|f_{\mathrm{NL}}(k_{\text{peak}},k_{\text{peak}},k_{\text{peak}})|\gtrsim
\Delta^2_{\zeta}(k_{\mathrm{peak}})/(23\delta^3_c) \sim \mathcal{O}(10^{-2})$.
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
$f_{\mathrm{NL}}(k_{\mathrm{peak}},k_{\mathrm{peak}},k_{\mathrm{peak}})\sim
\mathcal{O}(1)$ 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.
