Constraints on non-Gaussian primordial curvature perturbation from the LIGO-Virgo-KAGRA third observing run

The scalar-induced gravitational wave (SIGWs), arising from large amplitude primordial density fluctuations, provide a unique observational test for directly probing the epoch of inflation. In this work, we provide constraints on the SIGW background by taking into account the non-Gaussianity in the primordial density fluctuations, using the first three observing runs (O1-O3) data of the LIGO-Virgo-KAGRA collaboration. We find that the non-Gaussianity gives a non-negligible effect on the GW energy density spectrum and starts to affect the analysis of the O1-O3 data when the non-Gaussianity parameter is F NL > 3.55. Furthermore, the constraints exhibit asymptotic behavior given by F NL A g = const. at large F NL limit, where A g denotes the amplitude of the curvature perturbations. In the limit of large F NL , we placed a 95% credible level upper limit F NL A g ≤ 0.115, 0.106, 0.112 at fixed scales of 10 16 , 10 16.5 , 10 17 Mpc -1 , respectively.