Strong-lensing cosmography using third-generation gravitational-wave detectors

We present a detailed exposition of a statistical method for estimating cosmological parameters from the observation of a large number of strongly lensed binary-black-hole (BBH) mergers observable by third-generation gravitational-wave (GW) detectors. This method, first presented in $\href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.261401}{[1]}$, compares the observed number of strongly lensed GW events and their time delay distribution (between lensed images) with observed events to infer cosmological parameters. We show that the precision of the estimation of the cosmological parameters does not have a strong dependance on the assumed BBH redshift distribution model. An incorrect model for the distribution of lens properties and redshifts can lead to a biased cosmological inference. However, Bayesian model selection can assist in selecting the right model from a set of available parametric models for the distribution of lens redshift and properties. We also present a way to incorporate the effect of contamination in the data due to the limited efficiency of lensing identification methods, so that it will not bias the cosmological inference.
Comment: 17 pages, 5 figures