Accurate Weak Lensing of Standard Candles. II. Measuring sigma8 with
  Supernovae
  Soon the number of type Ia supernova (SN) measurements should exceed 100,000.
Understanding the effect of weak lensing by matter structures on the supernova
brightness will then be more important than ever. Although SN lensing is
usually seen as a source of systematic noise, we will show that it can be in
fact turned into signal. More precisely, the non-Gaussianity introduced by
lensing in the SN Hubble diagram dispersion depends rather sensitively on the
amplitude sigma8 of the matter power spectrum. By exploiting this relation, we
are able to predict constraints on sigma8 of 7% (3%) for a catalog of 100,000
(500,000) SNe of average magnitude error 0.12 without having to assume that
such intrinsic dispersion is known a priori. The intrinsic dispersion has been
assumed to be Gaussian; possible intrinsic non-Gaussianities in the dataset
(due to the SN themselves and/or to other transients) could be potentially
dealt with by means of additional nuisance parameters describing higher moments
of the intrinsic dispersion distribution function. This method is independent
of and complementary to the standard methods based on CMB, cosmic shear or
cluster abundance observables.
