Flattened bispectrum of the scalar-induced gravitational waves

Abstract: Recent pulsar timing array collaborations have reported evidence of the stochastic gravitational wave background. The gravitational waves induced by primordial curvature perturbations, referred to as scalar-induced gravitational waves (SIGWs), could potentially be the physical origins of the gravitational wave background. Due to nonlinearity of Einstein's gravity, there is non-Gaussianity of SIGWs even when the sourced primordial curvature perturbation is Gaussian. This paper investigates the intrinsic non-Gaussianity of SIGWs influenced by formation of primordial black holes. Specifically, we examine whether spectral width of Gaussian primordial curvature perturbations can affect non-Gaussianity of SIGWs. In order to ensure us to correctly quantify the degree of non-Gaussianity, we introduce an oscillation average scheme that can conserve the exact results of skewness of SIGWs. In this framework, the oscillation of SIGWs not only suppresses the bispectrum amplitude but also leads to a flattened-type bispectrum. Based on our results of skewness, it is found that the primordial curvature power spectrum with a narrower width can enhance the intrinsic non-Gaussianity.