Chaos and Topological Evolution in Cosmology

Abstract

An elementary account on the chaoticity of galactic world-lines in an open universe is given. A new type of cosmic evolution by global metrical deformations, unpredicted by Einstein's equations, is pointed out. Physical effects of this evolution are backscattering of electromagnetic fields and particle creation in quantum fields. We review in an untechnical way how global metrical deformations of the open and multiply connected spacelike slices induce angular fluctuations in the temperature of the cosmic microwave background radiation.Our contemporary understanding of the global structure of the Universe is based on the assumption of a space-time continuum, a curved fourdimensional world. The observational evidence for this is actually scarce, but it offers at any rate a very simple qualitative explanation of the cosmic redshifts [Weinberg, 1972]. The second motivation to model the Universe as a Riemannian four-manifold, was the successful application of Riemannian geometry in explaining planetary perihelion shifts, and the deflection of light by gravitating bodies. These are local phenomena, which can be explained by introducing a Riemannian metric on a single coordinate chart. In cosmology, however, we are concerned with the global structure, with the topology of the four-manifold.In local problems of general relativity, on a single co-ordinate chart, Einstein's equations completely determine the evolution of the metric, once the energy-momentum tensor of the local gravitational sources is known. In cosmology we have to consider the evolution of the metric as well as the evolution of the topology of space-time. Einstein's equations certainly do not give any hint on the topology, and the evolution of the metric is likewise undetermined, because we do not know the energy-momentum tensor of the matter distribution in the Universe, nor the boundary conditions to be imposed. It is in my opinion pointless to hunt for elusive laws of cosmic evolution, the modeling employed in such endeavors is always copied from finite classical or quantum systems, and there is no reason to assume that the Universe is a finite Hamiltonian system like any other. A much more promising approach to cosmology is to figure out possibilities of cosmic evolution, and to think over which local physical manifestations they can have.Cosmology deals with the global structure of the Universe, local inhomogeneities are averaged out. This means that we assume the spacelike sections of the Universe as constantly curved, which reflects local homogeneity and isotropy. The threedimensional, real space should be of constant curvature. Taking the space expansion into account, which is essential to explain the red-shifts, we end up with a Robertson-Walker (RW) line element 1847