Determining Model-independent $H_0$ and Consistency Tests

We determine the Hubble constant $H_0$ precisely ($2.3\%$ uncertainty) in a manner independent of cosmological model through Gaussian process regression, using strong lensing and supernova data. Strong gravitational lensing of a variable source can provide a time-delay distance $D_{\Delta t}$ and angular diameter distance to the lens $D_{\rm{d}}$. These absolute distances can anchor Type Ia supernovae, which give an excellent constraint on the shape of the distance-redshift relation. Updating our previous results to use the H0LiCOW program's milestone dataset consisting of six lenses, four of which have both $D_{\Delta t}$ and $D_{\rm{d}}$ measurements, we obtain $H_0=72.8_{-1.7}^{+1.6}\rm{\ km/s/Mpc}$ for a flat universe and $H_0=77.3_{-3.0}^{+2.2}\rm{\ km/s/Mpc}$ for a non-flat universe. We carry out several consistency checks on the data and find no statistically significant tensions, though a noticeable redshift dependence persists in a particular systematic manner that we investigate. Speculating on the possibility that this trend of derived Hubble constant with lens distance is physical, we show how this can arise through modified gravity light propagation, which would also impact the weak lensing $\sigma_8$ tension.