  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.
