Gravitational Waves Induced by non-Gaussian Scalar Perturbations

Abstract

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 $k_{\ast }$, 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 $k/k_{\ast }=4/\sqrt{3}$, and has a sharp cutoff at $k=4k_{\ast }$. The non-Gaussian part can exceed the Gaussian part if ${\mathcal{P}}_{\mathcal{R}}(k)f_{\text{NL}}^2\gtrsim 1$. If both a slope ${\Omega }_{\text{GW}}(k)\propto k^{\beta }$ with $\beta \sim 3$ 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 $10^{20}\text{g}$ 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 $f_{\text{NL}}$.

8 pages, 4 figures. Typos corrected. Published version

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