Foundations of Classical and Quantum Chaos in Extended Robertson-Walker Cosmologies

A topological explanation for the recently observed anisotropy of the background radiation is given in terms of a cosmology that evolves from a totally chaotic initial state, and whose spacelike slices are infinite and multiply connected. Keywords: Robertson-Walker cosmology, relativistic chaos, Bernoulli property, chaotic nucleus, homogeneity, isotropy, quantum chaos, background radiation, anisotropy, hyperbolic three-manifold, deformation space, quasi-Fuchsian group, Schottky group, limit set, Hausdorff dimension, convex hull.