A classification scheme for non-rotating inhomogeneous cosmologies

This paper describes a classification scheme for irrotational cosmological models which is not based on the existence of a group of local isometries hence is suitable for studying inhomogeneous cosmologies. The scheme is based on the algebraic structure of three trace-free symmetric two-index tensors which are defined in such models, namely the shear tensor of the fluid congruence, assumed irrotational, and the trace-free Ricci and Cotton-York tensors associated with the hypersurfaces orthogonal to the fluid. The restrictions that are imposed on these tensors by the existence of various groups of local isometries are derived, thereby relating the present approach to the usual classifications involving Killing vectors. These results lead to the conjecture that the algebraic structure the Cotton-York tensor (whose vanishing is a necessary and sufficient condition for the hypersurfaces to be conformally flat) is related to the nature of the gravitational waves that might be present. (author)