The Impact of Spin Priors on Parameterized Tests of General Relativity

TL;DR

This study examines how different spin prior choices influence gravitational-wave tests of General Relativity, revealing that prior assumptions can significantly affect the interpretation of deviations from GR.

Contribution

It provides a systematic analysis of spin prior effects on parameterized GR tests using real gravitational-wave data, highlighting the importance of prior selection.

Findings

Effective precession spin parameter shows stronger prior sensitivity than effective inspiral spin.

Most events have robust $ ext{delta}\hat{ ext{phi}}_3$ estimates, but some show notable prior-induced discrepancies.

Including $ ext{delta}\hat{ ext{phi}}_3$ in the analysis introduces a correlation with $ ext{chi}_{ ext{eff}}$, driven by specific high-sensitivity events.

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 $\delta \hat{\phi}_3$ 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 $\chi_p$ exhibits significantly stronger prior sensitivity than the effective inspiral spin $\chi_{\rm eff}$. While $\delta \hat{\phi}_3$ 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 $\delta \hat{\phi}_3$. No significant correlation is observed when spin parameters are inferred within the standard GR framework. However, when $\delta \hat{\phi}_3$ is included in the analysis, a strong correlation emerges between $\chi_{\rm eff}$ and $\delta \hat{\phi}_3$, 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.