Constraining cosmological parameters in FLRW metric with lensed GW+EM signals

We proposed a model-independent method to constrain the cosmological parameters using the Distance Sum Rule of the FLRW metric by combining the time delay distances and the comoving distances through a multi-messenger approach. The time delay distances are measured from lensed gravitational wave~(GW) signals together with their corresponding electromagnetic wave~(EM) counterpart, while the comoving distances are obtained from a parametrized fitting approach with independent supernova observations. With a series of simulations based on Einstein Telescope, Large Synoptic Survey Telescope and The Dark Energy Survey, we find that only 10 lensed GW+EM systems can achieve the constraining power comparable to and even stronger than 300 lensed quasar systems due to more precise time delay from lensed GW signals. Specifically, the cosmological parameters can be constrained to ~$k=0.01_{-0.05}^{+0.05}$ and ~$H_0=69.7_{-0.35}^{+0.35}$ (1$\sigma$). Our results show that more precise time delay measurements could provide more stringent cosmological parameter values, and lensed GW+EM systems therefore can be applied as a powerful tool in the future precision cosmology.