How many SNeIa do we need to detect the effect of weak lensing ?
  We show that as many as 4000 SNeIa may be required to detect the effect of weak lensing on their flux distribution with a high level of significance. However, if the intrinsic SNeIa magnitude dispersion is unknown one needs an even higher number of SNeIa (an order of magnitude more) to reach a similar level of statistical significance. Moreover, the ability to separate the lensing contribution from the intrinsic scatter depends sensitively on the amplitude of the latter. Using a Kolmogorov - Smirnov (K-S) test we check how the required number of SNeIa changes with level of significance. Our model incorporates a completely analytical description of weak lensing which has been tested extensively against numerical simulations. Thus, future missions such as SNAP may be able to detect non-Gaussianity at a lower significance level of 10% (through the K-S test) only if the intrinsic scatter is known from external data (e.g. from low redshift observations) whereas ALPACA with 100,000 SNe will definitely detect non-Gaussianity with a very high confidence even if the intrinsic magnitude dispersion is not known a priori. 
Dipak Munshi, Patrick Valageas