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

Abstract 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 H 0 . 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 H 0 . 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 H 0 with a strong lens sample with small statistics but H 0 sensitivity gives a precise H 0 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 H 0 = 72.2 ± 2.1 km s −1 Mpc −1 , a precision of 2.9%. Allowing for cosmic curvature with a prior of Ω k = −0.2, 0.2, the constraint becomes .