Chaos in Cosmology

We consider open cosmological models with multiply connected spacelike slices. In these universes there is a finite, convex region in which the world lines turn chaotic. We point out some physical effects of the topology in wave fields, like particle creation-annihilation, violation of the space-reflection symmetry, and fluctuations in the temperature of the microwave background. The evolution of classical and quantum mechanical probability densities under the mixing horospherical flow is discussed.