Determining Cosmological-model-independent $H_0$ with Gravitationally Lensed Supernova Refsdal

Abstract

{The reappearance of supernova Refsdal with detailed modeling of the lens cluster allows us to measure the time-delay distance,} which serves as a powerful tool to determine the Hubble constant ($H_0$). We give a cosmological-model-independent method to estimate $H_0$ through Gaussian process regression, using time-delay measurements from this lensed supernova in combination with supernova data from the Pantheon+ sample. {Using eight mass models for the lens cluster,} we infer $H_0 = 64.2^{+4.4}_{-4.3} \, \rm{km\,s^{-1}\,Mpc^{-1}}$ and using two cluster models most consistent with the observations, we infer $H_0 = 66.3^{+3.8}_{-3.6} \, \rm{km\,s^{-1}\,Mpc^{-1}}$. Our estimates of the value of $H_0$ are in $1σ$ agreement with the results assuming a flat $Λ$CDM model and the uncertainties are comparable. Our constraint results on $H_0$ from the eight lens models and the two lens models indicate $2σ$ and $1.8σ$ tensions with that estimated by Supernova H0 for the Equation of State, respectively. However, our median values of $H_0$ from the two sets of lens models show good consistency with $H_0$ inferred from Planck cosmic microwave background observations assuming $Λ$CDM model within $1σ$. We also find that our results for $H_0$ indicate $2σ$ deviations and $1.7σ$ deviations from the constraint results of $H_0$ using six time-delay quasars by H0LiCOW with the same analysis method.