The Effect of Weak Lensing on Distance Estimates from Supernovae
  Using a sample of 608 Type Ia supernovae from the SDSS-II and BOSS surveys,
combined with a sample of foreground galaxies from SDSS-II, we estimate the
weak lensing convergence for each supernova line-of-sight. We find that the
correlation between this measurement and the Hubble residuals is consistent
with the prediction from lensing (at a significance of 1.7sigma. Strong
correlations are also found between the residuals and supernova nuisance
parameters after a linear correction is applied. When these other correlations
are taken into account, the lensing signal is detected at 1.4sigma. We show for
the first time that distance estimates from supernovae can be improved when
lensing is incorporated by including a new parameter in the SALT2 methodology
for determining distance moduli. The recovered value of the new parameter is
consistent with the lensing prediction. Using CMB data from WMAP7, H0 data from
HST and SDSS BAO measurements, we find the best-fit value of the new lensing
parameter and show that the central values and uncertainties on Omega_m and w
are unaffected. The lensing of supernovae, while only seen at marginal
significance in this low redshift sample, will be of vital importance for the
next generation of surveys, such as DES and LSST, which will be systematics
dominated.
