SIMBAD references

In recent years, a crisis in the standard cosmology has been caused by inconsistencies in the measurements of some key cosmological parameters, the Hubble constant H₀ and cosmic curvature parameter Ω_K, for example. It is necessary to remeasure them with the cosmological model-independent methods. In this paper, based on the distance sum rule, we present such a way to constrain H₀ and Ω_K simultaneously in the late universe from strong gravitational lensing time-delay (SGLTD) data and gravitational wave (GW) standard siren data simulated from the future observation of the Einstein Telescope (ET). Based on the data for six currently observed SGLTDs, we find that the constraint precision of H₀ from the combined 100 GW events can be comparable with the measurement from the SH0ES collaboration. As the number of GW events increases to 700, the constraint precision of H₀ will exceed that of the Planck 2018 results. Considering 1000 GW events as the conservative estimation of ET in the 10 yr observation, we obtain H₀ = 73.69 ± 0.36 km s^–1 Mpc^–1 with a 0.5% uncertainty and ${{\rm{\Omega }}}_{K}={0.076}_{-0.087}^{+0.068}$. In addition, we simulate 55 strong gravitational lensing (SGL) systems with a 6.6% uncertainty for the measurement of time-delay distance. By combining with 1000 GWs, we infer that H₀ = 73.65 ± 0.35 km s^–1 Mpc^–1 and Ω_K = 0.008 ± 0.048. Our results suggest that this approach can play an important role in exploring cosmological tensions.