Systematic biases due to waveform mismodeling in parametrized post-Einsteinian tests of general relativity: The impact of neglecting spin precession and higher modes (2410.06254v3)

Abstract: We study the robustness of parametrized post-Einsteinian (ppE) tests of General Relativity (GR) with gravitational waves, due to waveform inaccuracy. In particular, we determine the properties of the signal -- signal-to-noise ratio (SNR) and source parameters -- such that we are led to falsely identify a ppE deviation in the post-Newtonian (PN) inspiral phase at -1PN, 1PN, or 2PN order, due to neglecting spin precession or higher models in the recovery model. To characterize the statistical significance of the biases, we compute the Bayes factor between the ppE and GR models, and the fitting factor of the ppE model. For highly-precessing, edge-on signals, we find that mismodeling the signal leads to a significant systematic bias in the recovery of the ppE parameters, even at an SNR of 30. However, these biased inferences are characterized by a significant loss of SNR and a weak preference for the ppE model. At a higher SNR, the biased inferences display a strong preference for the ppE model and a significant loss of SNR. For edge-on signals containing asymmetric masses, at an SNR of 30, we find that excluding higher modes does not impact the ppE tests as much as excluding spin precession. Our analysis, therefore, identifies the spin-precessing and mass-asymmetric systems for which parametrized tests of GR are robust. With a toy model and using the linear signal approximation, we illustrate these regimes of bias and characterize them by obtaining bounds on the ratio of systematic to statistical error and the effective cycles incurred due to mismodeling. As a by-product of our analysis, we connect various measures and techniques commonly used to estimate systematic errors -- linear-signal approximation, Laplace approximation, fitting factor, effective cycles, and Bayes factor -- that apply to all studies of systematic uncertainties in gravitational wave parameter estimation.