Accounting for scalar non-Gaussianity in secondary gravitational waves

It is well known that enhancement in the primordial scalar perturbations over small scales generates detectable amplitudes of secondary gravitational waves (GWs), by sourcing the tensor perturbations at the second order. These stochastic gravitational waves are expected to carry the imprints of primordial non-Gaussianities. The scalar bispectrum that is typically produced in models of inflation leading to significant secondary GWs is non-trivial and highly scale dependent. In this work, we present a method to account for such general scale dependent scalar bispectrum arising from inflationary models in the calculation of the spectral density of secondary GWs. Using this method, we compute the contributions arising from the scalar bispectrum to the amplitude of secondary GWs in two specific models of inflation driven by the canonical scalar field. We find that these non-Gaussian contributions can be highly model dependent and have to be consistently taken into account while estimating the total amplitude of the secondary GWs. Beyond the models considered, we emphasize that the method discussed is robust, free from assumptions about the shape of the bispectrum and generalizes earlier approaches adopted in the literature. We argue that this method of accounting for the scalar bispectrum shall be helpful in future computations for exotic models generating larger amplitudes of scalar non-Gaussianities along with significant amount of secondary GWs.