HAMILTONIAN STRUCTURES FOR COMPACT HOMOGENEOUS UNIVERSES

Hamiltonian structures for spatially compact locally homogeneous vacuu m universes are investigated, provided that the set of dynamical varia bles contains the Teichmuller parameters, parameterizing the purely gl obal geometry. One of the key ingredients of our arguments is a suitab le mathematical expression for quotient manifolds, where the universal cover metric carries all the degrees of freedom of geometrical variat ions, i.e., the covering group is fixed. We discuss general problems c oncerned with the use of this expression in the context of general rel ativity, and demonstrate the reduction of the Hamiltonians for some ex amples. For our models, all the dynamical degrees of freedom in Hamilt onian view are unambiguously interpretable as geometrical deformations , in contrast to the conventional open models. (C) 1997 American Insti tute of Physics.