Distances and Lensing in Cosmological Void Models

We study the distances and gravitational lensing in spherically symmetricinhomogeneous cosmological models consisting of inner and outer homogeneousregions which are connected by a single shell or double shells at the redshift$z_1 \sim 0.067$. The density and Hubble parameters in the inner region areassumed to be smaller and larger, respectively, than those in the outer region.It is found that at the stage $z_1 < z < 1.5$ the distances from an observer inthe inner void-like region are larger than the counterparts (with equal $z$) inthe corresponding homogeneous Friedmann models, and hence the magnitudes forthe sources at this stage are larger. This effect of the void-like low-densityregion may explain the deviations of the observed [magnitude-redshift] relationof SNIa from the relation in homogeneous models, independently of thecosmological constant. When the position of the observer deviates from thecenter, moreover, it is shown that the distances are anisotropic and the imagesof remote sources are systematically deformed. The above relation at $z \geq1.0$ and this anisotropy will observationally distinguish the role of the abovevoid-like region from that of the positive cosmological constant. The influenceon the time-delay measurement is also discussed.Comment: 14 pages, 11 postscript figures Equation numbers were corrected, Apj 529(2000) No.1 in pres