Millilensing induced systematic biases in parametrized tests of general relativity

Tests of general relativity (GR) can be systematically biased when our waveform models are inaccurate. We perform a proof-of-principle study of systematic biases in tests of general relativity induced by neglecting lensing effects for millilensed gravitational-wave signals, where the lens mass is typically in the ${10}^{3}{M}_{\ensuremath{\bigodot}}--{10}^{5}{M}_{\ensuremath{\bigodot}}$ range. In particular, we use a nested-sampling Bayesian parameter estimation and model selection analysis of a millilensed signal (without a noise realization) with an unlensed parametrized post-Einsteinian (ppE) recovery model. We find that at the signal-to-noise ratios of 30 and higher, there is a significant bias in the ppE parameter, especially when the source is aligned with the lens mass (the lensing effect is pronounced) and when its total mass is low (the signal duration is long). We use a toy model and the linear signal and Laplace approximations to provide a semianalytic explanation for the trends in the systematic errors found in the nested sampling analysis. Moreover, a Bayes factor analysis reveals that the (unlensed) ppE model is weakly favored over the (unlensed) GR model, and a fitting factor study shows there is a significant loss of signal-to-noise ratio when using the (unlensed) ppE model. Thus, for the typical source parameters and SNRs considered in this work, millilensing-induced systematic biases are unlikely to result in false positive GR deviations.