Measuring the Hubble constant using strongly lensed gravitational wave signals

The measurement of the Hubble constant H-0 plays an important role in the study of cosmology. In this work, we propose a new method to constrain the Hubble constant using the strongly lensed gravitational wave (SLGW) signals. Through reparameterization, we find that the lensed waveform is sensitive to the H-0. Assuming the scenario that no electromagnetic counterpart of the GW source can be identified, our method can still give meaningful constraints on the H-0 with the information of the lens redshift. We then apply Fisher information matrix and Markov Chain Monte Carlo to evaluate the potential of this method. For the space-based GW detector, TianQin, the H-0 can be constrained within a relative error of similar to 1% with a single SLGW event.