INHOMOGENEOUS SELF-SIMILAR COSMOLOGICAL MODELS

A class of self-similar spatially inhomogeneous models whose time evolution is determined by the similarity group is investigated. The self-similarity group is three-dimensional and acts transitively on timelike hypersurfaces, reducing the Einstein equations to a system of ordinary differential equations describing the dependence of the metric variables on the remaining spatial coordinate. This system of ordinary differential equations is given a Hamiltonian formulation which then serves as a starting point for a search for 'hidden' symmetries. Several cases are shown to allow such symmetries. Exploiting these symmetries makes it possible to integrate the field equations and thereby obtain several new classes of inhomogeneous self-similar exact solutions.