We investigate the possibility of measuring the Hubble constant , the fractional energy density components and the equation of state parameter of the “ dark energy ” using lensed multiple images of high-redshift supernovae .
With future instruments , such as the SNAP and NGST satellites , it will become possible to observe several hundred lensed core-collapse supernovae with multiple images .
Accurate measurements of the image separation , flux-ratio , time-delay and lensing foreground galaxy will provide complementary information to the cosmological tests based on , e.g. , the magnitude-redshift relation of Type Ia supernovae , especially with regards to the Hubble parameter that could be measured with a statistical uncertainty at the one percent level .
Assuming a flat universe , the statistical uncertainty on the mass density is found to be \sigma ^ { stat } _ { \Omega _ { M } } \raise 1.29 pt \hbox { $ < $ } \kern - 7.5 pt { \lower 2. % 795 pt \hbox { $ \sim$ } } 0.05 .
However , systematic effects from the uncertainty of the lens modeling are likely to dominate .
E.g. , if the lensing galaxies are extremely compact but are ( erroneously ) modeled as singular isothermal spheres , the mass density is biased by \sigma ^ { syst } _ { \Omega _ { M } } \sim 0.1 .

We argue that wide-field near-IR instruments such as the one proposed for the SNAP mission are critical for collecting large statistics of lensed supernovae .