COSMOLOGICAL OBSERVATIONS IN AN INHOMOGENEOUS UNIVERSE - DISTANCE-REDSHIFT RELATION

The distance-redshift relation in an inhomogeneous universe is studied. On the basis of relativistic optical equations, numerical calculations are performed to get a realistic distance-redshift relation. It is shown that the distance-redshift relation is coincident with that in the standard Friedmann-Robertson-Walker (FRW) model on average if galaxies or clusters of galaxies are assumed to be completely transparent. We also show that the effect of the shear along the light path is small if the scale of inhomogeneities is larger than galactic scale and that our numerical results are consistent with the analytical investigation recently done by Futamase and Sasaki.