Pancakes as opposed to Swiss cheese

We examine a novel class of toy models of cosmological inhomogeneities by smoothly matching along a suitable hypersurface an arbitrary number of sections of 'quasi flat' inhomogeneous and anisotropic Szekeres-II models to sections of any spatially flat cosmology that can be described by the Robertson–Waker metric (including de Sitter, anti de Sitter and Minkowski spacetimes). The resulting 'pancake' models are quasi-flat analogues to the well known spherical 'Swiss-cheese' models found in the literature. Since Szekeres-II models can be, in general, compatible with a wide range of sources (dissipative fluids, mixtures of non-comoving fluids, mixtures of fluids with scalar or magnetic fields or gravitational waves), the pancake configurations we present allow for a description of a wide collection of localized sources embedded in a Robertson–Waker geometry. We provide various simple examples of arbitrary numbers of Szekeres-II regions (whose sources are comoving dust and energy flux interpreted as a field of peculiar velocities) matched with Einstein de Sitter, ΛCDM and de Sitter backgrounds. We also prove that the Szekeres-II regions can be rigorously regarded as 'exact' covariant perturbations on a background defined by the matching discussed above. We believe that these models can be useful to test ideas on averaging and backreaction and on the effect of inhomogeneities on cosmic evolution and observations. (paper)