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

TL;DR

This paper investigates how spatial topologies influence the dynamics of locally U(1)×U(1) symmetric cosmological models, revealing the role of topology in inhomogeneous universe evolution through classification and symmetry analysis.

Contribution

It provides a systematic classification of spatial topologies in locally U(1)×U(1) symmetric models and analyzes their influence on dynamics via symmetry operators.

Findings

Classification of possible spatial topologies in the models.

Identification of symmetry operators commuting with dynamics.

Insights into the influence of topology on cosmological evolution.

Abstract

We show examples which reveal influences of spatial topologies to dynamics, using a class of spatially {\it closed} inhomogeneous cosmological models. The models, called the {\it locally U(1)$\times$U(1) symmetric models} (or the {\it generalized Gowdy models}), are characterized by the existence of two commuting spatial {\it 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 the influence of spatial topologies on dynamics by obtaining translation and reflection operators which commute with the dynamical flow in the phase space.