A model independent comparison of supernova and strong lensing cosmography: implications for the Hubble constant tension

We use supernovae measurements, calibrated by the local determination of the Hubble constant $H_0$ by SH0ES, to interpolate the distance-redshift relation using Gaussian process regression. We then predict, independent of the cosmological model, the distances that are measured with strong lensing time delays. We find excellent agreement between these predictions and the measurements. The agreement holds when we consider only the redshift dependence of the distance-redshift relation, independent of the value of $H_0$. Our results disfavor the possibility that lens mass modeling contributes a 10\% bias or uncertainty in the strong lensing analysis, as suggested recently in the literature. In general our analysis strengthens the case that residual systematic errors in both measurements are below the level of the current discrepancy with the CMB determination of $H_0$, and supports the possibility of new physical phenomena on cosmological scales. With additional data our methodology can provide more stringent tests of unaccounted for systematics in the determinations of the distance-redshift relation in the late universe.