Inhomogeneous generalizations of the Robertson-Walker cosmological models

Solutions of Einstein's equations are discussed in which the flow of matter is hypersurface-orthogonal and shearfree, but accelerating, the hypersurfaces being conformally flat. The field equations require integrability conditions which are solved. In 4 of the 8 cases the field equations are reduced to a single ordinary differential equation of 2nd order, the other 4 cases are under investigation. In some solutions at an initial instant the matter density is a periodic function of the distance along the curves orthogonal to the orbits of the symmetry group. When the amplitude of the spatial variation of density goes to zero, the flat FLRW model is obtained