Testing Source Dependence in Gravitational-Wave Tests of General Relativity with Mutual Information

Abstract

Phenomenological deviation parameters used in gravitational-wave tests of general relativity need not represent universal fundamental properties of the sources. Instead, a deviation parameter can be a derived quantity that depends on source properties. Apparent violations of general relativity arising from waveform systematics or data-quality issues can also depend on source properties. In addition to diagnosing individual events, it is helpful to identify systematic trends at the population level. We introduce a nonparametric framework that uses mutual information to test whether the deviations depend on source properties. We validate the framework using simulations with massive graviton waveforms. Assuming we do not have prior knowledge of the underlying theory, massive graviton effects can be captured by a parameterized post-Einstein coefficient that is expected to depend on the luminosity distance and source mass. The results show that the mass and distance dependencies become clear for graviton masses of $\geq 1\times10^{-22}\,\mathrm{eV}$ at detector sensitivities representative of the current fourth observing run, while the controlled general relativity simulations yield null results. We then analyze public real-data products for tests of general relativity from GWTC-4.0 and 4-OGC, including phenomenological parameterized tests, modified dispersion tests, and parity violation tests. The phenomenological deviation parameters have tentative correlations with effective spin, and correlations of modified-dispersion or parity-violation parameters with source mass are visible. These results demonstrate that catalog-level dependence can identify patterns and thus be used to diagnose the origin of deviations in testing general relativity. The framework therefore complements single-event analyses and parameterized hierarchical population tests.