Construction of inhomogeneous universes which are Friedmann-Lemaître-Robertson-Walker on average

The understanding of our Universe is based on the working hypothesis that the homogeneous and isotropic models give a successful description on a very large scale, despite the nonlinear inhomogeneity of the matter distribution in the present Universe. We consider the compatibility problem between the overall homogeneity and isotropy and the local inhomogeneity. A scheme to construct inhomogeneous irrotational dust universes which are homogeneous and isotropic on average is shown in the framework of general relativity; they represent ‘‘relativistic pancake solutions’’ analogous to those in Newtonian cosmology.