Luminosity distance in 'Swiss cheese' cosmology with randomized voids: I. Single void size

摘要

Recently there have been suggestions that the Type Ia supernova data can beexplained using only general relativity and cold dark matter with no darkenergy. In "Swiss cheese" models of the Universe, the standardFriedmann-Robertson-Walker picture is modified by the introduction of masscompensating spherical inhomogeneities, typically described by theLemaitre-Tolman-Bondi metric. If these inhomogeneities correspond to underdensecores surrounded by mass-compensating overdense shells, then they can modifythe luminosity distance-redshift relation in a way that can mimic acceleratedexpansion. It has been argued that this effect could be large enough to explainthe supernova data without introducing dark energy or modified gravity. We showthat the large apparent acceleration seen in some models can be explained interms of standard weak field gravitational lensing together with insufficientrandomization of void locations. The underdense regions focus the light lessthan the homogeneous background, thus dimming supernovae in a way that canmimic the effects of acceleration. With insufficient randomization of thespatial location of the voids and of the lines of sight, coherent defocusingcan lead to anomalously large demagnification effects. We show that a properrandomization of the voids and lines of sight reduces the effect to the pointthat it can no longer explain the supernova data.