Impact of correlations on the modeling and inference of beyond vacuum–general relativistic effects in extreme-mass-ratio inspirals
Shubham Kejriwal, Lorenzo Speri, Alvin J. K. Chua
Abstract
In gravitational-wave astronomy, extreme-mass-ratio-inspiral (EMRI) sources for the upcoming LISA observatory have the potential to serve as high-precision probes of astrophysical environments in galactic nuclei, and of potential deviations from general relativity (GR). Such ``beyond vacuum-GR'' effects are often modeled as perturbations to the evolution of vacuum EMRIs under GR. Many studies have reported unprecedented constraints on these effects by examining the inference of one effect at a time. However, in a more realistic analysis, the simultaneous inference of multiple such effects is required since the parameters describing them are generally significantly correlated with each other and the vacuum EMRI parameters. Here, in a general framework, we show that these correlations remain even if any modeled effect is absent in the actual signal, and that they cause inference bias when any effect in the signal is ignored in the analysis model. This worsens the overall measurability of the whole parameter set, challenging the constraints found by previous studies, and posing a general problem for the modeling and inference of beyond vacuum-GR effects in EMRIs.