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The weak lensing magnification of Type Ia Supernovae (SNe Ia) is sensitive tothe clustering of matter, and provides an independent cosmological probecomplementary to SN Ia distance measurements. The Nancy Grace Roman SpaceTelescope is uniquely sensitive to this measurement as it can discover highredshift SNe Ia and measure them with high precision. We present a methodologyfor reconstructing the probability distribution of the weak lensingmagnification $\mu$ of SNe Ia, $p(\mu)$, from observational data, and using itto constrain cosmological parameters. We find that the reconstructed $p(\mu)$can be fitted accurately by a stretched Gaussian distribution, and used tomeasure the variance of $\mu$, $\xi_\mu$, which can be compared to theoreticalpredictions in a likelihood analysis. Applying our methodology to a set ofrealistically simulated SNe Ia expected from the Roman Space Telescope, we findthat using the weak lensing magnification of the SNe Ia constrains acombination 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 distancemeasurements result in a $\sim$ 10\% measurement on $\sigma_8$. The SNe Ia fromRoman will be powerful in constraining the cosmological model.

Forecasting Cosmological Constraints from the Weak Lensing Magnification of Type Ia Supernovae Measured by the Nancy Grace Roman Space Telescope