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_PBH< 10^9g) 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_PBH and the abundance of PBHs at the time of formation, denoted as Ω_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 τ̅_NL, and the primordial curvature perturbation power spectrum 𝒫_ R(k), which reads as τ̅_NL𝒫_ R(k) < 4× 10^-20Ω^-17/9_PBH,f( M_ PBH/10^4g)^-17/9.