Full analysis of the scalar-induced gravitational waves for the curvature perturbation with local-type non-Gaussianities

TL;DR

This paper provides a comprehensive analysis of scalar-induced gravitational waves from primordial curvature perturbations with local-type non-Gaussianities, including full non-Gaussian contributions and their spectral scaling, enhancing understanding of PBH-related signals.

Contribution

It extends previous models by incorporating full non-Gaussian diagrams up to G_NL order and deriving the spectral scaling, offering more accurate predictions of SIGW signals for various primordial spectra.

Findings

Derived semi-analytical formulas for SIGW spectra with non-Gaussianities.

Numerically evaluated SIGW spectra for a log-normal primordial power spectrum.

Identified the infrared scaling behavior of the SIGW energy spectrum.

Abstract

Primordial black holes (PBHs) are supposed to form through the gravitational collapse of regions with large density fluctuations. The formation of PBHs inevitably leads to the emission of scalar-induced gravitational wave (SIGW) signals, offering a unique opportunity to test the hypothesis of PBHs as a constituent of dark matter (DM). Previous studies have calculated the energy spectrum of SIGWs in local-type non-Gaussian models, primarily considering the contributions from the $F_{\mathrm{NL}}$-order or the $G_{\mathrm{NL}}$-order while neglecting connected diagrams. In this study, we extend the previous work by (i) considering the full contribution of non-Gaussian diagrams up to the $G_{\mathrm{NL}}$-order; (ii) deriving the generic scaling of the SIGW energy spectrum in the infrared region. We derive semi-analytical results applicable to arbitrary primordial power spectra and numerically evaluate the energy spectrum of SIGWs for a log-normal power spectrum.