Locally U(1)×U(1) Symmetric Cosmological Models: Topology and Dynamics

We show examples which reveal influences of spatial topologies to dynamics, using a class of spatially closed inhomogeneous cosmological models. The models, called the locally U(1)×U(1) symmetric models (or the generalized Gowdy models), are characterized by the existence of two commuting spatial local Killing vectors. For systematic investigations we first present a classification of possible spatial topologies in this class. We stress the significance of the locally homogeneous limits (i.e., the Bianchi types or the ‘geometric structures’) of the models. In particular, we show a method of reduction to the natural reduced manifold, and analyze the equivalences at the reduced level of the models as dynamical models. Based on these fundamentals, we examine influences of spatial topologies to dynamics by obtaining translation and reflection operators which commute with the dynamical flow in the phase space. JSPS Research Fellow. Electronic mail: [email protected]