Probing quadratic gravity with black-hole ringdown gravitational waves measured by LIGO-Virgo-KAGRA detectors

Quadratic–gravity theories arise in the low–energy limits of several high‑energy and quantum‑gravity frameworks. We perform ringdown‑only tests of these theories using quasinormal‑mode spectra computed with the METRICS framework, which are accurate for moderately spinning black holes (dimensionless spin up to 0.75). Analyzing the ringdown of the high‑SNR events GW150914, GW190521_074359 and GW200129_065458, we find no evidence for deviations from general relativity. We thereby place bounds on the effective coupling length scales of axi–dilaton, dynamical Chern–Simons, and scalar Gauss–Bonnet gravity. Combining the three events yields (90\% credible) constraints of $\ell_{\rm AD} < 34\,$km, $\ell_{\rm dCS} < 49\,$km, and $\ell_{\rm sGB} < 47\,$km. Our analysis provides the first observational constraint on axi–dilaton gravity.