The percent precision achieved on the values of the cosmological parameters defining the expansion rate and the geometry of the universe has recently revealed some tension between measurements from local and early-Universe cosmological probes. The best strategy forward is then to explore complementary and independent techniques. The use of the time delays of time-varying sources, supernovae (SNe) and quasars (QSOs), that are multiply imaged by galaxy clusters represents an alternative and competitive cosmological probe.
I will review recent efforts aimed at measuring the value of the cosmological parameters with cluster lenses, and in particular the value of the Hubble constant (H0). I will then focus on SDSS J1029+2623, which is one of the few currently known lens galaxy clusters with (three) multiple images of a background QSO. In addition, the QSO host galaxy is lensed into a ~22”.5 long tangential arc. I will present the methodology we adopt to derive accurate and precise estimates of the value of H0 with multi-band HST photometry and VLT/MUSE spectroscopic data. The best-fit model reproduces well, over more than 77k HST pixels, the flux of the QSO and the surface brightness distribution of its host galaxy, for the first time on such a complex and large-scale system. The combination of the positions of 26 spectroscopically confirmed multiple images, one time-delay measurement between the multiple images of the QSO, and the extended surface brightness modelling of the multiply lensed QSO host galaxy allows us to precisely determine the lens Fermat potential/total mass distribution and therefore provide a new measurement of the value of H0.
These first results will pave the way for using a statistically significant sample of similar cluster-scale strong lensing systems that will be discovered in forthcoming surveys, like Vera C. Rubin – LSST and Euclid, as a competitive cosmological probe.