Effect of lensing magnification on type Ia supernova cosmology
  Effect of gravitational magnification on the measurement of distance modulus
of type Ia supernovae is presented. We investigate a correlation between
magnification and Hubble residual to explore how the magnification affects the
estimation of cosmological parameters. We estimate magnification of type Ia
supernovae in two distinct methods: one is based on convergence mass
reconstruction under the weak lensing limit and the other is based on the
direct measurement from galaxies distribution. Both magnification measurements
are measured from Subaru Hyper Suprime-Cam survey catalogue. For both
measurements, we find no significant correlation between Hubble residual and
magnification. Furthermore, we correct for the apparent supernovae fluxes
obtained by Supernova Legacy Survey 3-year sample using direct measurement of
the magnification. We find $\Omega_{\rm m0} = 0.287 ^{+0.104} _{-0.085}$ and $w
= -1.161 ^{+0.595}_{-0.358}$ for supernovae samples corrected for lensing
magnification when we use photometric redshift catalogue of Mizuki, while
$\Omega_{\rm m0} = 0.253 ^{+0.113} _{-0.087}$ and $w = -1.078 ^{+0.498}
_{-0.297}$ for DEmP photo-z catalogue. Therefore, we conclude that the effect
of magnification on the supernova cosmology is negligibly small for the current
surveys; however, it has to be considered for the future supernova survey like
LSST.
