Global dynamics of Yang-Mills field and perfect-fluid Robertson-Walker cosmologies

TL;DR

This paper develops a global dynamical systems approach to analyze the behavior of flat Robertson-Walker cosmologies with Yang-Mills fields and perfect fluids, providing insights into their asymptotic dynamics and explicit solutions.

Contribution

It introduces a new global dynamical systems formulation for these cosmologies, enabling comprehensive analysis of their asymptotic behavior and explicit solution contextualization.

Findings

Proves asymptotic source-dominance in past and future directions.

Provides a global state space picture for pure massless Yang-Mills solutions.

Offers a unified framework for analyzing matter sources in cosmological models.

Abstract

We apply a new global dynamical systems formulation to flat Robertson-Walker cosmologies with a massless and massive Yang-Mills field and a perfect-fluid with linear equation of state as the matter sources. This allows us to give proofs concerning the global dynamics of the models including asymptotic source-dominance towards the past and future time directions. For the pure massless Yang-Mills field, we also contextualize well-known explicit solutions in a global (compact) state space picture.