BIANCHI COSMOLOGICAL MODELS AND GAUGE SYMMETRIES

We analyse carefully the problem of gauge symmetries for Bianchi models, from both the geometrical and dynamical points of view. Some of the geometrical definitions of gauge symmetries (i.e. 'homogeneity preserving diffeomorphisms') given in the literature do not incorporate the crucial feature that local gauge transformations should be independent at each point of the manifold of the independent variables (i.e. time for Bianchi models), i.e. should be arbitrarily localizable (in time). We give a geometrical definition of homogeneity preserving diffeomorphisms that does not possess this shortcoming. The proposed definition has the further advantage of coinciding with the dynamical definition based on the invariance of the action in Lagrangian or Hamiltonian form. We explicitly verify the equivalence of the Lagrangian-covariant phase space with the Hamiltonian reduced phase space. Remarks on the use of the Ashtekar variables in Bianchi models are also given.