Curvature Dependence of Gravitational-Wave Tests of General Relativity

High-energy extensions to general relativity modify the Einstein-Hilbert action with higher-order curvature corrections and theory-specific coupling constants. The order of these corrections imprints a universal curvature dependence on observations while the coupling constant controls the deviation strength. In this Letter, we leverage the theory-independent expectation that modifications to the action of a given order in spacetime curvature (Riemann tensor and contractions) lead to observational deviations that scale with the system length scale to a corresponding power. For gravitational-wave observations, the relevant scale is the binary total mass, and deviations scale as a power of mass p related to the action order. For example, p=4, 6 arise in effective field theory for cubic and quartic theories, respectively. We incorporate this insight into the inspiral phase test of general relativity with current gravitational-wave observations, and directly infer the curvature scaling without compromising the agnostic nature of the test. This introduces a flexible yet highly interpretable new paradigm for tests of general relativity spanning many length scales.