Assessing the systematic errors of extreme-mass-ratio inspirals waveforms for testing general relativity

Gravitational wave (GW) observations from extreme-mass-ratio inspirals (EMRIs) are powerful tools for testing general relativity (GR). However, systematic errors arising from waveform models could potentially lead to incorrect scientific conclusions. These errors can be divided into two main categories: fundamental bias (due to limitations in the validity of the Einstein field equations) and modeling error (due to inaccuracies in waveform templates). Using Bayesian inference, we investigate the impact of these systematic errors on tests of GR. Regarding fundamental bias, we find that at low signal-to-noise ratios (SNR), there is a risk of misidentifying a non-GR EMRI signal as a GR-EMRI one, and vice versa. However, this risk diminishes as the SNR increases to around 40 or higher. Additionally, modeling errors might reduce the SNR of detected EMRI signals and could be misinterpreted as deviations from GR, leading Bayesian inference to favor non-GR scenarios, especially at high SNR. We emphasize the importance of developing sufficiently accurate waveform templates based on alternative gravity theories for testing GR.