Global Topology and Local Violation of Discrete Symmetries

Cosmological models that are locally consistent with general relativity and the standard model are constructed, in which an object transported around the Universe undergoes $P,C$, and $\mathrm{CP}$ transformations. This leads to an enlargement of the gauge groups of electroweak and strong interactions to include antiunitary transformations. Gedanken experiments in these cosmological models show that if all interactions obey Einstein causality then $P,C$, and $\mathrm{CP}$ cannot be violated. But another model in which the sign of the charge may be reversed is allowed. Some possible implications to modifications of the standard model are considered.