Reconstructing the weak lensing magnification distribution of Type Ia
  supernovae
  Weak lensing of Type Ia supernovae (SNe Ia) is a systematic uncertainty in
the use of SNe Ia as standard candles, as well as an independent cosmological
probe, if the corresponding magnification distribution can be extracted from
data. We study the peak brightness distribution of SNe Ia in the Pantheon
sample, and find that the high $z$ sub-sample shows distinct weak lensing
signatures compared to the low $z$ subsample: a long tail at the bright end due
to high magnifications and a shift of the peak brightness toward the faint end,
consistent with findings from earlier work. We have developed a technique to
reconstruct the weak lensing magnification distribution of SNe Ia, $p(\mu)$,
from the measured SN Ia flux distribution, and applied it to the Pantheon
sample. We find that $p(\mu)$ can be reconstructed at a significance better
than 2$\sigma$ for the subsample of SNe Ia at $z>0.7$ (124 SNe Ia), and at a
lower significance for the SNe Ia at $z>0.9$ (49 SNe Ia), due to the small
number of SNe Ia at high redshifts. The large number of $z>1$ SNe Ia from
future surveys will enable the use of $p(\mu)$ reconstructed from SNe Ia as an
independent cosmological probe.
