Diagnosing multiplicative error by lensing magnification of type Ia
  supernovae
  Weak lensing causes spatially coherent fluctuations in flux of type Ia
supernovae (SNe Ia). This lensing magnification allows for weak lensing
measurement independent of cosmic shear. It is free of shape measurement errors
associated with cosmic shear and can therefore be used to diagnose and
calibrate multiplicative error. Although this lensing magnification is
difficult to measure accurately in auto correlation, its cross correlation with
cosmic shear and galaxy distribution in overlapping area can be measured to
significantly higher accuracy. Therefore these cross correlations can put
useful constraint on multiplicative error, and the obtained constraint is free
of cosmic variance in weak lensing field. We present two methods implementing
this idea and estimate their performances. We find that, with $\sim 1$ million
SNe Ia that can be achieved by the proposed D2k survey with the LSST telescope
(Zhan et al. 2008), multiplicative error of $\sim 0.5\%$ for source galaxies at
$z_s\sim 1$ can be detected and larger multiplicative error can be corrected to
the level of $0.5\%$. It is therefore a promising approach to control the
multiplicative to the sub-percent level required for stage IV projects. The
combination of the two methods even has the potential to diagnose and calibrate
galaxy intrinsic alignment, which is another major systematic error in cosmic
shear cosmology.
