A dynamical systems approach to geodesics in Bianchi cosmologies

To understand the observational properties of cosmological models, in parti cular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conju nction 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 a ugment the Einstein field equations with the geodesic equations, all writte n in dimensionless form, obtaining an extended system of first-order ordina ry differential equations that simultaneously describes the evolution of th e gravitational field and the behavior of the associated geodesics. It is s hown that the extended system is a powerful tool for investigating the effe ct of space-time anisotropies on the temperature of the cosmic microwave ba ckground radiation, and that it can also be used for studying geodesic chao s.