  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 all
holes 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 where the luminosity of supernovae is
sufficiently supressed becomes very small, at least in the case of a lattice of
spherical holes considered in this paper.
