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

The data of type Ia supernovae observed by the High-z SN Search Team andSupernova Cosmology Project are analyzed in inhomogeneous cosmological modelswith a local void on scales of about 200 Mpc, to derive the best-fit values ofmodel parameters and the confidence contours. The $\chi^2$ fitting is found tobe slightly better than that in homogeneous models. It is shown that (1) thebest-fit values are most sensitive to the ratio $R$ of the outer Hubbleconstant ($H_0^{\rm II}$) to the inner Hubble constant ($H_0^{\rm I}$), (2) thebest-fit outer density parameter ($\Omega_0^{\rm II}$) (and cosmologicalconstant parameter ($\lambda_0^{\rm II}$)) increases (and decreases) with theincrease of $R$, respectively, and (3) $(\Omega_0^{\rm II}, \lambda_0^{\rmII})$ can be $(1, 0)$ for $R \approx 0.8$. Moreover it is shown that thesemodels may be naturally consistent with the new supernova data (SN1997ff) for$z = 1.7$.Comment: 12 pages, 6 figures, Accepted for publication in Prog. Theor. Phys. (Vol.106, No.5, 2001