Augmenting the power of time-delay cosmography in lens galaxy clusters by probing their member galaxies

We present a novel approach to measuring the expansion rate and the geometry of the Universe, which combines time-delay cosmography in lens galaxy clusters with pure samples of 'cosmic chronometers' by probing the member galaxies. The former makes use of the measured time delays between the multiple images of time-varying sources strongly lensed by galaxy clusters, while the latter exploits the most massive and passive cluster member galaxies to measure the differential time evolution of the Universe. We applied two different statistical techniques, adopting realistic errors on the measured quantities, to assess the accuracy and the gain in precision on the values of the cosmological parameters. We demonstrate that the proposed combined method allows for a robust and accurate measurement of the value of the Hubble constant. In addition, this provides valuable information on the other cosmological parameters thanks to the complementarity between the two different probes in breaking parameter degeneracies. Finally, we showcased the immediate observational feasibility of the proposed joint method by taking advantage of the existing high-quality spectro-photometric data for several lens galaxy clusters.