The Dynamical Degrees of Freedom in Spatially Homogeneous Cosmology*

The true analogues of superspace and conformal superspace for spatially homogeneous cosmology are introduced and discussed in relation to the kinematics of the evolution of Cauchy data from a spatially homogeneous initial value surface using a spatially homogeneous lapse function. Having fixed the slicing of spatially homogeneous spacetimes to be the natural one, an obvious restriction on the freedom of choice of the shift vector field occurs, and its relation to the three-dimensional diffeomorphism gauge group of the problem is explained. In this context the minimal distortion shift equation of Smarr and York naturally arises. Finally these ideas are used to simplify the dynamics.