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We study the form of the luminosity distance as a function of redshift in thepresence of large scale inhomogeneities, with sizes of order 10 Mpc or larger.We approximate the Universe through the Swiss-cheese model, with each sphericalregion described by the Tolman-Bondi metric. We study the propagation of lightbeams in this background, assuming that the locations of the source and theobserver are random. We derive the optical equations for the evolution of thebeam area and shear. Through their integration we determine the configurationsthat can lead to an increase of the luminosity distance relative to thehomogeneous cosmology. We find that this can be achieved if the Universe iscomposed of spherical void-like regions, with matter concentrated near theirsurface. For inhomogeneities consistent with the observed large scalestructure, the relative increase of the luminosity distance is of the order ofa few percent at redshifts near 1, and falls short of explaining thesubstantial increase required by the supernova data. On the other hand, theeffect we describe is important for the correct determination of the energycontent of the Universe from observations.Comment: 27 pages, 5 figures Revised version. References added. Conclusions  clarifie

The effect of large scale inhomogeneities on the luminosity distance