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, ΩGW(k), given that the power spectrum of the curvature perturbation PR(k) has a narrow peak at some small scale k*, with a local-type non-Gaussianity, and constrain the nonlinear parameter fNL 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 ΩGW increases as k³, peaks at k/k*=4/√3, and has a sharp cutoff at k=4k*. The non-Gaussian part can exceed the Gaussian part if PR(k)fNL²1. If both a slope ΩGW(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 10²⁰ to 10²² 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 PR or fNL.