Model-independent constraints on the Hubble constant using lensed quasars and the latest supernova

Abstract The Hubble constant , a key parameter quantifying the present expansion rate of the universe, remains a subject of significant debate due to the persistent tension between early- and late-universe measurements. Strong gravitational lensing (SGL) time delays provide an independent avenue to constrain . In this paper, we utilize seven SGL systems from the TDCOSMO sample to constrain , employing the model-independent approaches: deep neural networks (DNN), Gaussian process (GP), polynomial fitting (polyfit) and Padé approximant (PA). Using these methods, we reconstruct unanchored luminosity distances from the Pantheon+ SNe Ia dataset and obtain km s −1 Mpc −1 , km s −1 Mpc −1 , km s −1 Mpc −1 and km s −1 Mpc −1 , respectively. These estimates are consistent within 1 σ level and align with local distance ladder results. Notably, the GP method achieves uncertainties that are half those of the DNN approach, whereas the DNN method offers more reliable confidence intervals in reconstruction at high redshifts. Our findings underscore the potential of these methodologies to refine constraints on and contribute to resolving the Hubble tension with future advancements.