Swiss cheese and a cheesy CMB

Abstract

It has been argued that the Swiss-Cheese cosmology can mimic Dark Energy, when it comes to the observed luminosity distance-redshift relation. Besides the fact that this effect tends to disappear on average over random directions,we show in this work that based on the Rees-Sciama effect on the cosmic microwave background (CMB), the Swiss-Cheese model can be ruled out if allholes have a radius larger than about 35 Mpc. We also show that for smaller holes, the CMB is not observably affected, and that the small holes can still mimic Dark Energy, albeit in special directions, as opposed to previous conclusions in the literature.However, in this limit, the probability of looking in a special direction wherethe luminosity of supernovae is sufficiently supressed becomes very small, at leastin the case of a lattice of spherical holes considered in this paper.