A dynamical systems approach to geodesics in Bianchi cosmologies

TL;DR

This paper develops a dynamical systems framework combining Einstein's equations and geodesic equations to analyze null geodesics in Bianchi cosmologies, aiding understanding of cosmic microwave background anisotropies.

Contribution

It introduces an extended system of equations that simultaneously models gravitational dynamics and geodesic behavior in anisotropic cosmologies, enabling new insights into CMB properties.

Findings

Extended system effectively models geodesic evolution.

Framework reveals impact of anisotropies on CMB temperature.

Potential to study geodesic chaos in cosmological models.

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.