Testing modified gravity with the eccentric neutron star-black hole merger GW200105

Direct detections of gravitational waves offer a unique opportunity to test gravity in the highly dynamical and strong field regime. Current tests are typically performed assuming signals from quasicircular binaries. However, the complex waveform morphology induced by orbital eccentricity can enhance our ability to probe gravity with greater precision. A recent analysis of the neutron star-black hole event GW200105 identified strong evidence for orbital eccentricity. We extend an eccentric-precessing waveform model to test alternative models with this signal by incorporating eccentric corrections induced by Brans-Dicke, Einstein-dilaton-Gauss-Bonnet, and dynamical Chern-Simons gravity at leading post-Newtonian order. We show that analyzing this event with a quasi-circular model leads to a false deviation from general relativity, while the inclusion of eccentricity improves the bounds on the models. Our analysis of GW200105 places tight constraints on Einstein-dilaton-Gauss-Bonnet gravity, $α^{1/2}_{\rm{EdGB}} \lesssim 2.38\,\text{km}$, and Brans-Dicke gravity, $ω_{\rm{BD}} \gtrsim 3.5$, while dynamical Chern-Simons gravity remains unconstrained due to the low spin content.