Showing papers by "John Wainwright published in 2000"

The asymptotic regimes of tilted Bianchi II cosmologies

Abstract: In this paper we give, for the first time, a complete description of the dynamics of tilted spatially homogeneous cosmologies of Bianchi type II. The source is assumed to be a perfect fluid with equation of state $p = (\gamma -1) \mu$, where $\gamma$ is a constant. We show that unless the perfect fluid is stiff, the tilt destabilizes the Kasner solutions, leading to a Mixmaster-like initial singularity, with the tilt being dynamically significant. At late times the tilt becomes dynamically negligible unless the equation of state parameter satisfies $\gamma > {10/7}$. We also find that the tilt does not destabilize the flat FL model, with the result that the presence of tilt increases the likelihood of intermediate isotropization.

Non-tilted Bianchi VII 0 models - the radiation fluid

Abstract: We consider the late time behaviour of non-tilted perfect fluid Bianchi VII0 models when the source is a radiation fluid, thereby completing the analysis of the Bianchi VII0 models initiated by Wainwright et al in a recent paper. The models exhibit the phenomena of asymptotic self-similarity breaking and Weyl-curvature dominance at late times. The late time dynamics of the VII0 perfect fluid models, and in particular that of the radiation fluid, is a prime example of the complexity inherent in the field equations of general relativity.

Asymptotic Self-similarity Breaking in Cosmology

Abstract: We discuss the role of self-similarity in the evolution of cosmological models. The simplest model, the flat Friedmann–Lemaįtre universe is exactly self-similar. On the other hand, the open Friedmann–Lemaįtre universe and the anisotropic Bianchi I universes, are not exactly self-similar, but are asymptotically self-similar, both near the initial singularity and at late times. In general, however, cosmological models are not asymptotically self-similar, and our goal is to describe the different mechanisms that lead to asymptotic self-similarity breaking in Bianchi universes. The discussion will also serve to give an overview of our current understanding of the dynamics of Bianchi universes.

A Dynamical Systems Approach to Geodesics in Bianchi Cosmologies

Abstract: To understand the observational properties of cosmological models, in particular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conjunction with the orthonormal frame approach, has proved to be an invaluable tool for analyzing spatially homogeneous cosmologies. It is thus natural to use such techniques to study the geodesics of these models. We therefore augment the Einstein field equations with the geodesic equations, all written in dimensionless form, obtaining an extended system of first-order ordinary differential equations that simultaneously describes the evolution of the gravitational field and the behavior of the associated geodesics. It is shown that the extended system is a powerful tool for investigating the effect of spacetime anisotropies on the temperature of the cosmic microwave background radiation, and that it can also be used for studying geodesic chaos.