Cosmography with supernova Refsdal through time-delay cluster lensing: Independent measurements of the Hubble constant and geometry of the Universe

We present new measurements of the values of the Hubble constant, matter density, dark energy density, and dark energy density equation-of-state (EoS) parameters. These results have been obtained from a full strong-lensing analysis of the observed positions of 89 multiple images and 4 measured time delays of the supernova (SN) Refsdal in the Hubble Frontier Fields galaxy cluster MACS J1149.5+2223. By strictly following the identical modelling methodology (as done in our previous work undertaken before time delays were available), our cosmographic measurements are essentially blind, based on the frozen procedure. Without using any priors from other cosmological experiments, in an open $w$CDM cosmological model and via our reference cluster mass model, we measure the following values: $H_0 = 65.1^ $ km s$^ $ Mpc$^ DE $, and $w=-0.92^ $ (at the 68.3 confidence level). No other single cosmological probe has been able to simultaneously measure all these parameters. Remarkably, our estimated values of the cosmological parameters, in particular that of $H_0$, are very robust and do not significantly depend on the assumed cosmological model or the cluster mass modelling details. The latter aspect introduces systematic uncertainties on the values of $H_0$ and $w,$ which are found to be largely subdominant compared to the statistical errors. The results of this study demonstrate that the combination of time delays in lens galaxy clusters with extensive photometric and spectroscopic information offers a novel and competitive cosmological tool.