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The signal of a stochastic gravitational wave (GW) background has been sought for several decades and has just come within the observational reach through the pulsar timing array. While several sources of GW background have been analysed in the literature, the phenomenon of scalar-induced GW emerges as a simple yet inevitable candidate. Scalar-induced GW are highly sensitive to primordial non-Gaussianity, such as three-point and four-point correlations of primordial scalar perturbations. In this talk, I shall discuss the unique imprints of scalar bispectrum and trispectrum on the scalar-induced GW. Using representative inflationary models, I shall illustrate that the bispectrum significantly affects the spectral density of GW. Further, a parity-odd component of the scalar trispectrum shall induce preferential helicity in GW. Over certain scales, the chirality of scalar-induced GW directly quantifies the parity-violation in non-Gaussian correlations, unobscured by Gaussian contributions. These inferences from GW will complement our knowledge of primordial non-Gaussianity and parity-violation gleaned from CMB and galaxy surveys. Time permitting, I shall also discuss potential tests of statistical homogeneity and isotropy of cosmological perturbations, by examining the cross-correlations between unequal wavenumbers and different polarizations of GW. Lastly, I shall close with the outlook of our results in light of ongoing and upcoming observational missions. |