Model-independent $H_0$ within FLRW: Joint constraints from GWTC-3 standard sirens and strong lensing time delays

Abstract: We use 47 gravitational-wave (GW) standard sirens from the third Gravitational-Wave Transient Catalog to calibrate distances in the strong gravitational lensing (SGL) system RXJ1131-1231 and constrain the Hubble constant ($H_0$) via the distance sum rule, without assuming a specific cosmological model. For $\Omega_K = 0$, we obtain $H_0 = 73.22^{+5.95}_{-5.43}$ ${\rm km}~{\rm s}^{-1}~{\rm Mpc}^{-1}$ and $H_0 = 70.40^{+8.03}_{-5.60}$ ${\rm km}~{\rm s}^{-1}~{\rm Mpc}^{-1}$ by breaking the mass-sheet transform using lens galaxy's mass models and stellar kinematics, respectively. Allowing $\Omega_K$ to vary increases the central value of $H_0$ and reduces its precision. We find that GW dark sirens have significant potential for calibrating SGL systems, due to their relatively higher redshifts. By combining 42 binary black holes and RXJ1131-1231, we obtain an $H_0$ constraint with a precision approximately $40\%$ better than the measurement from GW170817 using the Hubble law. This suggests that high-precision, model-independent $H_0$ measurements can be achieved with this method as the redshift range of GW dark sirens expands, even without the need for GW bright sirens.