Accurate weak lensing of standard candles. I. Flexible cosmological fits
  With the availability of thousands of type Ia supernovae in the near future
the magnitude scatter induced by lensing will become a major issue as it
affects parameter estimation. Current N-body simulations are too time consuming
to be integrated in the likelihood analyses used for estimating the
cosmological parameters. In this paper we show that in the weak lensing regime
a statistical numerical approximation produces accurate results orders of
magnitude faster. We write down simple fits to the second, third and fourth
central moments of the lensing magnification probability distribution as a
function of redshift, of the power spectrum normalization and of the
present-day matter density. We also improve upon existing models of lensing
variance and show that a shifted lognormal distribution fits well the numerical
one. These fits can be easily employed in cosmological likelihood analyses.
Moreover, our theoretical predictions make it possible to invert the problem
and begin using supernovae lensing to constrain the cosmological parameters.
