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, $\Omega_\text{GW}(k)$, given that the power spectrum of the curvature
perturbation $\mathcal{P}_\mathcal{R}(k)$ has a narrow peak at some small scale
$k_*$, with a local-type non-Gaussianity, and constrain the nonlinear parameter
$f_\text{NL}$ 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 $\Omega_\text{GW}$ 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
$\mathcal{P}_\mathcal{R}(k)f_\text{NL}^2\gtrsim1$. If both a slope
$\Omega_\text{GW}(k)\propto k^\beta$ with $\beta\sim3$ 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
$10^{20}\text{g}$ to $10^{22}\text{g}$ are identified as cold dark matter of
the Universe, the corresponding GWs must be detectable by LISA-like detectors,
irrespective of the value of $\mathcal{P}_\mathcal{R}$ or $f_\text{NL}$.
