  In this manuscript we investigate the intrinsically flat (space-flat)
spacetimes as viable cosmological models. We show that they have a natural
geometric structure which is suitable to describe inhomogeneous matter
distributions forming a periodic pattern throughout the space. We prove
theorems for their local representation and for existence and uniqueness of the
Einstein's equations with these periodic boundary conditions. We also find an
interesting class of exact solutions, which illustrates the applicability of
such spacetimes in cosmology, with an early time behavior close to homogeneity
and isotropy and a late time aspect with peaks and voids in the matter
distribution.
