A Model-independent Determination of the Hubble Constant from Lensed Quasars and Supernovae Using Gaussian Process Regression

Strongly lensed quasar systems with time delay measurements provide "time delay distances," which are a combination of three angular diameter distances and serve as powerful tools to determine the Hubble constant H0. However, current results often rely on the assumption of the ΛCDM model. Here we use a model-independent method based on Gaussian process to directly constrain the value of H0. By using Gaussian process regression, we can generate posterior samples of unanchored supernova distances independent of any cosmological model and anchor them with strong lens systems. The combination of a supernova sample with large statistics but no sensitivity to H0 with a strong lens sample with small statistics but H0 sensitivity gives a precise H0 measurement without the assumption of any cosmological model. We use four well-analyzed lensing systems from the state-of-art lensing program H0LiCOW and the Pantheon supernova compilation in our analysis. Assuming the universe is flat, we derive the constraint H0 = 72.2 ± 2.1 km s−1 Mpc−1, a precision of 2.9%. Allowing for cosmic curvature with a prior of Ωk = [−0.2, 0.2], the constraint becomes ${H}_{0}={73.0}_{-3.0}^{+2.8}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$.