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A local void and the accelerating Universe

Corresponding to the recent observational claims that we are in a local void (an underdense region) on scales of 200 - 300 Mpc, the magnitude-redshift relation in a cosmological model with a local void is investigated. It is already evident that the accelerating behavior of high-z supernovae can be explained in this model, because the local void plays a role similar to the positive cosmological constant. In this paper the dependence of the behavior on the gaps of cosmological parameters in the inner (low-density) region and the outer (high-density) region, the radius of the local void, and the clumpiness parameter is studied and its implication is discussed.