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We present a simple and promising new method to measure the expansion rateand the geometry of the universe that combines observations related to the timedelays between the multiple images of time-varying sources, strongly lensed bygalaxy clusters, and Type Ia supernovae, exploding in galaxies belonging to thesame lens clusters. By means of two different statistical techniques that adoptrealistic errors on the relevant quantities, we quantify the accuracy of theinferred cosmological parameter values. We show that the estimate of the Hubbleconstant is robust and competitive, and depends only mildly on the chosencosmological model. Remarkably, the two probes separately produce confidenceregions on the cosmological parameter planes that are oriented in complementaryways, thus providing in combination valuable information on the values of theother cosmological parameters. We conclude by illustrating the immediateobservational feasibility of the proposed joint method in a well-studied lensgalaxy cluster, with a relatively small investment of telescope time formonitoring from a 2 to 3m class ground-based telescope.

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