Testing Strong-Field Gravity Using Gravitational-Wave–Only Constraints on the I–Love Universal Relation

Binary neutron stars provide a unique laboratory for testing gravity in the strong-field, matter-dominated regime. A key prediction of General Relativity (GR) and alternative theories of gravity is the I–Love universal relation, which posits a nearly equation-of-state–independent connection between the neutron star moment of inertia (I) and tidal deformability (Love number), with each theory predicting a distinct form. Traditional tests of this relation require combining electromagnetic and gravitational-wave (GW) observations from different astrophysical systems, introducing systematics from mismatched source properties and environments. Recent advances in modeling dynamical tidal interactions now enable direct extraction of the neutron star spin frequency through mode resonances in GW signals, allowing simultaneous inference of both the moment of inertia and tidal deformability from a single GW event. In this work, I present the first constraints on the I–Love relation derived exclusively from GW observations, assess improvements with future detector sensitivities, and explore implications for testing deviations from GR. These results establish GW observations as a clean and self-consistent probe of neutron star structure and offer a robust new avenue for testing universal predictions of strong-field gravity.