Gravitational Waves Induced by non-Gaussian Scalar Perturbations

TL;DR

This paper investigates how non-Gaussian scalar perturbations in the early universe induce gravitational waves, analyzing their spectrum, and explores how future observations could detect or constrain primordial non-Gaussianity and primordial black holes.

Contribution

It provides a detailed calculation of the gravitational wave spectrum induced by non-Gaussian curvature perturbations and discusses observational signatures and constraints from future detectors and primordial black hole data.

Findings

Non-Gaussian contributions to GWs can dominate over Gaussian ones under certain conditions.

The GW spectrum exhibits a peak at a specific scale and a sharp cutoff, serving as a signature of non-Gaussianity.

Detection of a specific slope and multiple peaks in the GW spectrum can indicate primordial non-Gaussianity.

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 $k_*$, 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 $f_\text{NL}$.