The magnitude-redshift relation in a realistic inhomogeneous universe

The light rays from a source are subject to a local inhomogeneous geometry generated by inhomogeneous matter distribution as well as the existence of collapsed objects. In this paper we investigate the effect of inhomogeneities and the existence of collapsed objects on the propagation of light rays and evaluate changes in the magnitude-redshift relation from the standard relationship found in a homogeneous FRW universe. We give the expression of the correlation function and the variance for the perturbation of apparent magnitude, and calculate it numerically by using the non-linear matter power spectrum. We use the lognormal probability distribution function for the density contrast and spherical collapse model to truncate the power spectrum in order to estimate the blocking effect by collapsed objects. We find that the uncertainties in $\Omega_m$ is $\sim 0.02$, and that of $w$ is $\sim 0.04$. We also discuss a possible method to extract these effects from real data which contains intrinsic ambiguities associated with the absolute magnitude.Comment: 19 pages, 4 figures, accepted to JCA

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.Comment: 15 pages, 4 figures, accepted for publication in JCAP; some changes to match published versio