Distance-redshift relation in a realistic inhomogeneous universe

We investigate the distance-redshift relation in a realistic inhomogeneous universe where the mass distribution is described by the mass function of Sheth and Tormen. It is found that the derived distance deviates systematically from the standard distance up to 10% depending on the choice of the lowest halo mass in which baryonic matter condensed to form luminous object such as galaxies. Remarkably the derived distance is well approximated by the Dyer-Roeder distance if we choose the clumpiness parameter α calculated by our model. We also discuss the effect of inhomogeneities in the determination of dark energy parameter in the supernovae observation, and find that this effect must be taken into account for the future high redshift supernovae observation.