Constraining the Hubble constant and its lower limit from the proper motion of extragalactic radio jets

The Hubble constant (H-0) is a measurement to describe the expansion rate of the Universe in the current era. However, there is a 4.4 sigma discrepancy between the measurements from the early Universe and the late Universe. In this research, we propose a model-free and distance-free method to constrain H-0. Combining Friedman-Lemaltre-Robertson-Walker cosmology with geometrical relation of the proper motion of extragalactic jets, the lower limit (H-0,H-min) of H-0 can be determined using only three cosmology-free observables: the redshifts of the host galaxies, and the approaching and receding angular velocities of radio jets. Using these, we propose to use the Kolmogorov-Smirnov test (K-S test) between cumulative distribution functions of H-0,(min) to differentiate cosmology. We simulate 100, 200, and 500 extragalactic jets with three levels of accuracy of the proper motion (mu(a) and mu(r)), at 10, 5, and 1 per cent, corresponding to the accuracies of the current and future radio interferometers. We perform K-S tests between the simulated samples as theoretical distributions with different H-0 and power-law index of velocity distribution of jets and mock observational data. Our result suggests increasing sample sizes leads to tighter constraints on both power-law index and the Hubble constant at moderate accuracy (i.e. 10 and 5 per cent), while at 1 per cent accuracy, increasing sample sizes leads to tighter constraints on power-law index more. Improving accuracy results in better constraints in the Hubble constant compared with the power-law index in all cases, but it alleviates the degeneracy.