Hamiltonian reduction of Bianchi cosmologies

Abstract

It was noted recently that the ADM diffeomorphism constraint does not generate all observed symmetries for several Bianchi models. We will suggest not using the ADM constraint restricted to homogeneous variables, but some equivalent, which is derived from a restricted action principle. This will generate all homogeneity preserving diffeomorphisms, which will be shown to be automorphism generating vector fields, in class A and class B models. Following Dirac's constraint formalism one will naturally be restricted to the unimodular part of the automorphism group.