model (top).[]{data-label="fig:FL_VS_SC"}](FL_vs_SC.pdf){width="\columnwidth"}

The propagation of light in a Swiss-cheese universe was first investigated by Kantowski [@Kan69], and later by Dyer and Roeder [@DR74]. Both concluded that the effect, on the Hubble diagram, of introducing “clumps” of matter was to lower the apparent deceleration parameter. The issue was revived within the backreaction and averaging debates, and the Swiss-cheese models have been extended to allow for more generic distributions of matter inside the holes—instead of just concentrating it at the center—where spacetime geometry is described by the Lemaître-Tolman-Bondi (LTB) solution. The optical properties of such models have been extensively studied (see Refs. [@Brouzakis:2006dj; @Biswas:2007gi; @Marra:2007pm; @Vanderveld:2008vi; @Brouzakis:2008; @Vanderveld:2011; @Clifton:2009nv; @Valkenburg:2009iw; @Szybka:2010ky]) to finally conclude that the average luminosity-redshift relation remains unchanged with respect to the purely homogeneous case, contrary to the early results of Refs. [@Kan69; @DR74].

In general, the relevance of “LTB holes” in Swiss-cheese models is justified by the fact that they allow one to reproduce the actual large-scale structure of the Universe (with voids and walls). However, though inhomogeneous, the distribution of matter in this class of models remains continuous at all scales. On the contrary, the old-fashioned approach with “clumps” of matter inside the holes *breaks the continuous 