Dark sirens, i.e., gravitational-wave (GW) sources without electromagnetic counterparts, are new probes of the expansion of the universe. The efficacy of this method relies on correctly localizing the host galaxies. However, recent theoretical studies have shown that astrophysical environments could mislead the spatial localization by distorting the GW signals. It is unclear whether and to what degree the incorrect spatial localizations of dark sirens would impair the accuracy of the measurement of the cosmological parameters. To address this issue, we consider the future observations of dark sirens using the Cosmic Explorer and the Einstein Telescope, and we design a Bayesian framework to access the precision of measuring the Hubble–Lemaître constant H
0. Interestingly, we find that the precision is not compromised when the number of well-localized dark sirens is significantly below 300, even in the extreme scenario that all the dark sirens are localized incorrectly. As the number exceeds 300, the incorrect spatial localizations start to produce statistically noticeable effects, such as a slow convergence of the posterior distribution of H
0. We propose several tests that can be used in future observations to verify the spatial localizations of dark sirens. Simulations of these tests suggest that incorrect spatial localizations will dominate a systematic error of H
0 if as much as 10% of a sample of 300 well-localized dark sirens are affected by their environments. Our results have important implications for the long-term goal of measuring H
0 to a precision of <1% using dark sirens.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.