Swiss-cheese model is closer to the latter situation, because the Ricci tensor is zero inside the holes (see Fig. \[fig:FL\_VS\_SC\]). It is therefore hoped to capture the relevant optical properties of the Universe.

In fact, neither a Friedmann-Lemaître model nor a Swiss-cheese model can be considered a realistic description of the Universe. They share the property of being exact solutions of the Einstein equations which satisfy the Copernican principle, either strictly or statistically. Swiss-cheese models can be characterized by an extra-cosmological parameter describing the smoothness of their distribution of matter. Thus, a FL spacetime is nothing but a perfectly smooth Swiss cheese. It is legitimate to investigate to which extent observations can constrain the smoothness cosmological parameter, and therefore to quantify how close to a FL model the actual Universe is.

![The standard interpretation of SNe data assumes that light propagates in purely homogeneous and isotropic space (top). However, thin light beams are expected to probe the inhomogeneous nature of the actual Universe (bottom) down to a scale where the continuous limit is no longer valid. []{data-label="fig:FL_VS_reality"}](FL_vs_reality.pdf){width="\columnwidth"}

![Swiss-cheese models (bottom) allow us to model inhomogeneities beyond the continuous limit, while keeping the same dynamics and average properties as the FL 