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, Ω_{GW}(k), given that the power spectrum of the curvature perturbation P_{R}(k) has a narrow peak at some small scale k_{*}, with a local-type non-Gaussianity, and constrain the nonlinear parameter f_{NL} 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 Ω_{GW} increases as k^{3}, peaks at k/k_{*}=4/sqrt[3], and has a sharp cutoff at k=4k_{*}. The non-Gaussian part can exceed the Gaussian part if P_{R}(k)f_{NL}^{2}≳1. If both a slope Ω_{GW}(k)∝k^{β} with β∼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 P_{R} or f_{NL}.