New probe of non-Gaussianities with primordial black hole induced gravitational waves

We propose a new probe of primordial non-Gaussianities (NGs) through the observation of gravitational waves (GWs) induced by ultra-light ($M_{\text{PBH}}< 10^{9}\rm{g}$) primordial black holes (PBHs). Interestingly enough, the existence of primordial NG can leave imprints on the clustering properties of PBHs and the spectral shape of induced GW signals. Focusing on a scale-dependent local-type NG, we identify a distinct double-peaked GW energy spectrum that, contingent upon $M_{\text{PBH}}$ and the abundance of PBHs at the time of formation, denoted as $\Omega_\mathrm{PBH,f}$, may fall into the frequency bands of upcoming GW observatories, including LISA, ET, SKA, and BBO. Thus, such a signal can serve as a novel portal for probing primordial NGs. Intriguingly, combining BBN bounds on the GW amplitude, we find for the first time the joint limit on the product of the effective non-linearity parameter for the primordial tri-spectrum, denoted by $\bar{\tau}_\mathrm{NL}$, and the primordial curvature perturbation power spectrum $\mathcal{P}_{\cal R}(k)$, which reads as $\bar{\tau}_\mathrm{NL} \mathcal{P}_{\cal R}(k) < 4\times 10^{-20} \Omega^{-17/9}_\mathrm{PBH,f} \left( \frac{M_{\rm PBH}}{10^4\mathrm{g}} \right)^{-17/9}$.