Cosmography using strongly lensed gravitational waves from binary black holes

Third generation gravitational wave (GW) detectors are expected to detect millions of binary black hole (BBH) mergers during their operation period. A small fraction of them ($\sim 1\mathrm{\%}$) will be strongly lensed by intervening galaxies and clusters, producing multiple observable copies of the GW signals. The expected number of lensed events and the distribution of the time delay between lensed events depend on the cosmology. We develop a Bayesian analysis method for estimating cosmological parameters from the detected number of lensed events and their time delay distribution. The expected constraints are comparable to that obtained from other cosmological measurements, but probing a different redshift regime ($z\sim 10$) that is not explored by other probes.