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

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.