Mathematics

Mathematical physics

Spectral density

Astrophysics

Quantum mechanics

Primordial black hole

Curvature

Binary black hole

Particle physics

Scalar curvature

Omega

Gravitational wave

Geometry

Statistics

Cutoff

Scalar (mathematics)

Physics

Physical Review Letters

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...

Gravitational Waves Induced by Non-Gaussian Scalar Perturbations