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Realizing Refsdal's original idea from 1964, we present estimates of theHubble constant that are complementary to and potentially competitive withthose of other cosmological probes. We use the observed positions of 89multiple images, with extensive spectroscopic information, from 28 backgroundsources and the measured time delays between the images S1-S4 and SX ofsupernova "Refsdal" ($z = 1.489$), which were obtained thanks to Hubble SpaceTelescope (HST) deep imaging and Multi Unit Spectroscopic Explorer (MUSE) data.We extend the strong lensing modeling of the Hubble Frontier Fields (HFF)galaxy cluster MACS J1149.5$+$2223 ($z = 0.542$), published by Grillo et al.(2016), and explore different $\Lambda$CDM models. Taking advantage of thelensing information associated to the presence of very close pairs of multipleimages at various redshifts and to the extended surface brightness distributionof the SN Refsdal host, we can reconstruct the total mass density profile ofthe cluster very precisely. The combined dependence of the multiple imagepositions and time delays on the cosmological parameters allows us to infer thevalues of $H_{0}$ and $\Omega_{\rm m}$ with relative (1$\sigma$) statisticalerrors of, respectively, 6% (7%) and 31% (26%) in flat (general) cosmologicalmodels, assuming a conservative 3% uncertainty on the final time delay of imageSX and, remarkably, no priors from other cosmological experiments. Our bestestimate of $H_{0}$, based on the model described in this work, will bepresented when the final time-delay measurement becomes available. Our resultsshow that it is possible to utilize time delays in lens galaxy clusters as animportant alternative tool for measuring the expansion rate and the geometry ofthe Universe.

Measuring the value of the Hubble constant "\`a la Refsdal"