Analyses of Type Ia Supernova Data in Cosmological Models with a Local Void

Abstract

The data of type Ia supernovae observed by the High-z SN Search Team and Supernova Cosmology Project are analyzed in inhomogeneous cosmological models with a local void on scales of about 200 Mpc, to derive the best-fit values of model parameters and the confidence contours. The $χ^2$ fitting is found to be slightly better than that in homogeneous models. It is shown that (1) the best-fit values are most sensitive to the ratio $R$ of the outer Hubble constant ($H_0^{\rm II}$) to the inner Hubble constant ($H_0^{\rm I}$), (2) the best-fit outer density parameter ($Ω_0^{\rm II}$) (and cosmological constant parameter ($λ_0^{\rm II}$)) increases (and decreases) with the increase of $R$, respectively, and (3) $(Ω_0^{\rm II}, λ_0^{\rm II})$ can be $(1, 0)$ for $R \approx 0.8$. Moreover it is shown that these models may be naturally consistent with the new supernova data (SN1997ff) for $z = 1.7$.