The Impact of Spin Priors on Parameterized Tests of General Relativity

Abstract

Spin priors play a fundamental role in gravitational-wave parameter estimation, yet their impact on parameterized tests of General Relativity (GR) remains insufficiently understood. In this work, we systematically investigate how spin prior choices affect the 1.5PN deviation parameter $δ\hatϕ_3$ using real gravitational-wave events. We quantify prior-induced effects through the Jensen--Shannon divergence (JSD) and median shifts of posterior distributions. We find that the effective precession spin parameter $χ_p$ exhibits significantly stronger prior sensitivity than the effective inspiral spin $χ_{\rm eff}$. While $δ\hatϕ_3$ is generally robust across most events, GW231123\_135430 exhibits a noticeable discrepancy, with a JSD at the $\mathcal{O}(0.4)$ level. Examining the median shift, we note that events with very short inspiral durations, such as GW231028\_153006, GW231123\_135430, and GW191109\_010717, show more pronounced shifts, indicating increased sensitivity in low-information regimes. We further explore the relationship between the prior sensitivity of spin parameters and that of $δ\hatϕ_3$. No significant correlation is observed when spin parameters are inferred within the standard GR framework. However, when $δ\hatϕ_3$ is included in the analysis, a strong correlation emerges between $χ_{\rm eff}$ and $δ\hatϕ_3$, which we attribute to partial parameter degeneracy at the 1.5PN order. A leave-one-out test shows that the observed correlation is sensitive to the inclusion of specific events, indicating that it is partially driven by a subset of high-sensitivity events. Our results demonstrate that spin-prior choices can propagate into parameterized tests of GR in a non-trivial and model-dependent manner, and may mimic or reshape apparent deviations from GR.