We study the feasibility of detecting weak lensing spatial correlations between Supernova (SN) Type Ia magnitudes with present (Dark Energy Survey, DES) and future (Large Synoptic Survey Telescope, LSST) surveys. We investigate the angular auto-correlation function of SN magnitudes (once the background cosmology has been subtracted) and cross-correlation with galaxy catalogues. We examine both analytical and numerical predictions, the latter using simulated galaxy catalogues from the MICE Grand Challenge Simulation. We predict that we will be unable to detect the SN auto-correlation in DES, while it should be detectable with the LSST SN deep fields (15,000 SNe on 70 deg^2) at ~6sigma level of confidence (assuming 0.15 magnitudes of intrinsic dispersion). The SN-galaxy cross-correlation function will deliver much higher signal-to-noise, being detectable in both surveys with an integrated signal-to-noise of ~100 (up to 30 arcmin separations). We predict joint constraints on the matter density parameter (Omega_m) and the clustering amplitude (sigma_8) by fitting the auto-correlation function of our mock LSST deep fields. When assuming a Gaussian prior for Omega_m, we can achieve a 25% measurement of sigma_8 from just these LSST supernovae (assuming 0.15 magnitudes of intrinsic dispersion). These constraints will improve significantly if the intrinsic dispersion of SNe Ia can be reduced.
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