Forecasting Cosmological Constraints from the Weak Lensing Magnification
  of Type Ia Supernovae Measured by the Nancy Grace Roman Space Telescope
  The weak lensing magnification of Type Ia Supernovae (SNe Ia) is sensitive to
the clustering of matter, and provides an independent cosmological probe
complementary to SN Ia distance measurements. The Nancy Grace Roman Space
Telescope is uniquely sensitive to this measurement as it can discover high
redshift SNe Ia and measure them with high precision. We present a methodology
for reconstructing the probability distribution of the weak lensing
magnification $\mu$ of SNe Ia, $p(\mu)$, from observational data, and using it
to constrain cosmological parameters. We find that the reconstructed $p(\mu)$
can be fitted accurately by a stretched Gaussian distribution, and used to
measure the variance of $\mu$, $\xi_\mu$, which can be compared to theoretical
predictions in a likelihood analysis. Applying our methodology to a set of
realistically simulated SNe Ia expected from the Roman Space Telescope, we find
that using the weak lensing magnification of the SNe Ia constrains a
combination of matter density $\Omega_m$ and matter clustering amplitude
$\sigma_8$. SN Ia distances alone lead to a better than 1\% measurement of
$\Omega_m$. The combination of SN Ia weak lensing magnification and distance
measurements result in a $\sim$ 10\% measurement on $\sigma_8$. The SNe Ia from
Roman will be powerful in constraining the cosmological model.
