Millilensing induced systematic biases in parameterized tests of General Relativity

TL;DR

This paper investigates how millilensing effects in gravitational-wave signals can cause systematic biases in tests of general relativity, potentially mimicking deviations, especially at high signal-to-noise ratios and specific source configurations.

Contribution

It introduces a Bayesian analysis framework to quantify biases caused by neglecting millilensing in gravitational-wave tests of GR, highlighting conditions under which false deviations may appear.

Findings

Bias toward false GR deviations at high SNRs with aligned lensing.

Weak preference for non-GR models in Bayesian analysis.

Significant signal-to-noise loss when using unlensed models.

Abstract

Tests of general relativity (GR) can be systematically biased when our waveform models are inaccurate. We here study 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 $10^3M_\odot$--$10^5M_\odot$ range. In particular, we use a nested-sampling Bayesian parameter estimation and model selection analysis of a millilensed signal with an unlensed parameterized post-Einsteinian (ppE) recovery model. We find that the ppE model is significantly biased toward a detection of a deviation from general relativity at signal-to-noise ratios of 30 and higher, 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 semi-analytic 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. This implies that although a parameter estimation study may incorrectly infer a deviation from general relativity, a residual signal-to-noise ratio test would reveal that the ppE model is not a good fit to the data. Thus, with current detectors, millilensing-induced systematic biases are unlikely to result in false positive detections of GR deviations.