Relativistic quantum chaos in Robertson-Walker cosmologies

Open Robertson-Walker cosmologies of multiple spatial connectivity provide a challenging example for the possible influence of the global topological structure of space-time on the laws of microscopic motion. Free geodesic motion is investigated in such cosmologies in the context of first quantization. A unique localized wave field, a solution of the Klein-Gordon equation, is found as a consequence of the topological structure of the spacelike slices t=const of the manifold. This solution is closely related to the collection of the bounded chaotic trajectories. The link is provided by the quasi-self-similar limit set of the group of covering transformations on the boundary of the universal covering space of the spacelike sections. It is this fractal set from which the covering geodesics of the bounded trajectories emerge, its Hausdorff measure and dimension determine the localized wave field.