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.