Constraints on ultra-slow-roll inflation from the third LIGO-Virgo observing run

The nonattractor evolution in ultra-slow-roll (USR) inflation results in the amplification of superhorizon curvature perturbations and then induces a strong and detectable stochastic gravitational wave background. In this letter, we search for such a stochastic gravitational wave background in data from the third LIGO-Virgo observing run and place constraints on the USR inflationary models. The $e$-folding number of the USR phase are constrained to be $\mathrm{\Delta }N\lesssim 2.9$ at the 95% confidence level and the power spectrum of curvature perturbations amplified during the USR phase is constrained to be ${\log }_{10}{P}_{R\mathrm{p}}<-1.7$ at the scales $2.9\times {10}^5\mathrm{p}{\mathrm{c}}^{-1}\lesssim k\lesssim 1.7\times {10}^{11}\mathrm{p}{\mathrm{c}}^{-1}$. Besides, we forecast the ability of future experiments to constrain USR inflation, and find $P_{R\mathrm{p}}\lesssim {10}^{-3.6}$ for LISA and Taiji, $P_{R\mathrm{p}}\lesssim {10}^{-3.3}$ for Cosmic Explore and Einstein Telescope, $P_{R\mathrm{p}}\lesssim {10}^{-5.5}$ for DECIGO and Big Bang Observer and $P_{R\mathrm{p}}\lesssim {10}^{-5.2}$ for Square Kilometre Array.