Gravitational Waves Induced by Non-Gaussian Scalar Perturbations

We study gravitational waves (GWs) induced by non-Gaussian curvature perturbations. We calculate the density parameter per logarithmic frequency interval, ₆ₖ (k), given that the power spectrum of the curvature perturbation Pₑ (k) has a narrow peak at some small scale k*, with a local-type non-Gaussianity, and constrain the nonlinear parameter f₍₋ with the future LISA sensitivity curve as well as with constraints from the abundance of the primordial black holes (PBHs). We find that the non-Gaussian contribution to ₆ₖ increases as k^3, peaks at k/k*=4/3, and has a sharp cutoff at k=4k*. The non-Gaussian part can exceed the Gaussian part if Pₑ (k) f₍₋^21. If both a slope ₆ₖ (k) k^ with 3 and the multiple-peak structure around a cutoff are observed, it can be recognized as a smoking gun of the primordial non-Gaussianity. We also find that if PBHs with masses of 10^20 to 10^22 g are identified as cold dark matter of the Universe, the corresponding GWs must be detectable by LISA-like detectors, irrespective of the value of Pₑ or f₍₋.