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Massive galaxy clusters at intermediate redshifts act as gravitational lensesthat can magnify supernovae (SNe) occurring in background galaxies. We assessthe possibility to use lensed SNe to put constraints on the mass models ofgalaxy clusters and the Hubble parameter at high redshift. Due to the standardcandle nature of Type Ia supernovae (SNe Ia), observational information on thelensing magnification from an intervening galaxy cluster can be used toconstrain the model for the cluster mass distribution. A statistical analysisusing parametric cluster models was performed to investigate the possibleimprovements from lensed SNe Ia for the accurately modeled galaxy cluster A1689and the less well constrained cluster A2204. Time delay measurements obtainedfrom SNe lensed by accurately modeled galaxy clusters can be used to measurethe Hubble parameter. For a survey of A1689 we estimate the expected rate ofdetectable SNe Ia and of multiply imaged SNe. The velocity dispersion and coreradius of the main cluster potential show strong correlations with thepredicted magnifications and can therefore be constrained by observations ofSNe Ia in background galaxies. This technique proves especially powerful forgalaxy clusters with only few known multiple image systems. The mainuncertainty for measurements of the Hubble parameter from the time delay ofstrongly lensed SNe is due to cluster model uncertainties. For the extremelywell modeled cluster A1689, a single time delay measurement could be used todetermine the Hubble parameter with a precision of ~ 10%. We conclude thatobservations of SNe Ia behind galaxy clusters can be used to improve the massmodeling of the large scale component of galaxy clusters and thus thedistribution of dark matter. Time delays from SNe strongly lensed by accuratelymodeled galaxy clusters can be used to measure the Hubble constant at highredshifts.

Near-IR search for lensed supernovae behind galaxy clusters: III. Implications for cluster modeling and cosmology