Augmenting the power of time-delay cosmography in lens galaxy clusters by probing their member galaxies - I. Type Ia supernovae

We present a simple and promising new method to measure the expansion rate and the geometry of the universe that combines observations related to the time delays between the multiple images of time-varying sources, strongly lensed by galaxy clusters, and Type Ia supernovae, exploding in galaxies belonging to the same lens clusters. By means of two different statistical techniques that adopt realistic errors on the relevant quantities, we quantify the accuracy of the inferred cosmological parameter values. We show that the estimate of the Hubble constant is robust and competitive, and depends only mildly on the chosen cosmological model. Remarkably, the two probes separately produce confidence regions on the cosmological parameter planes that are oriented in complementary ways, thus providing in combination valuable information on the values of the other cosmological parameters. We conclude by illustrating the immediate observational feasibility of the proposed joint method in a well-studied lens galaxy cluster, with a relatively small investment of telescope time for monitoring from a 2 to 3 m class ground-based telescope.