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

We present a novel approach to measuring the expansion rate and the geometryof the Universe, which combine time-delay cosmography in lens galaxy clusterswith pure samples of 'cosmic chronometers' (CCs) by probing the membergalaxies. The former makes use of the measured time delays between the multipleimages of time-varying sources strongly lensed by galaxy clusters, while thelatter exploits the most massive and passive cluster member galaxies to measurethe differential time evolution of the Universe. We applied two differentstatistical techniques, adopting realistic errors on the measured quantities,to assess the accuracy and the gain in precision on the values of thecosmological parameters. We demonstrate that the proposed combined methodallows for a robust and accurate measurement of the value of the Hubbleconstant. In addition, this provides valuable information on the othercosmological parameters thanks to the complementarity between the two differentprobes in breaking parameter degeneracies. Finally, we showcase the immediateobservational feasibility of the proposed joint method by taking advantage ofthe existing high-quality spectro-photometric data for several lens galaxyclusters.