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

The scalar-induced gravitational waves (SIGW), 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 third observing run (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 O3 data when the non-Gaussianity parameter is $F_{\rm NL} > 3.55$. Furthermore, the constraints exhibit asymptotic behavior given by $F_{\rm NL} A_g = \rm{const.}$ at large $F_{\rm NL}$ limit, where $A_g$ denotes the amplitude of the curvature perturbations. In the limit of large $F_{\rm NL}$, we placed a 95% confidence level upper limit $F_{\rm NL} A_g \leq 0.13, 0.09, 0.10$ at fixed scales of $10^{16}, 10^{16.5}, 10^{17}~{\rm Mpc}^{-1}$, respectively.