Forecasts of cosmological constraints from Type Ia supernovae including the weak-lensing convergence

We investigate how the cosmological constraints from SNe Ia are improved by including the effects of weak-lensing convergence. To do so, we introduce the lognormal function as the convergence PDF modeling the lensing scatter of SN Ia magnitude, and apply a sample selection for SNe Ia to avoid strongly lensed samples. Comparing with the contribution of other uncertainties (e.g., the intrinsic magnitude scatter), we find that the lensing effect is dominant at $z > 1$. Then forecasting the parameter constraints for the Wide-Field InfraRed Survey Telescope survey, we show that considering the weak-lensing effect, the constraints on the density parameters $\Omega_m$ or $\Omega_{\Lambda}$, and the dark energy equation of state $w$ are improved, especially for SNe Ia samples at higher redshift $z > 1$. Furthermore, we see that the degeneracy between the total mass of neutrino $\Sigma m_{\nu}$ and the (cold) dark matter density parameter $\Omega_{c}$ can be resolved.