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

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