Cosmological models with Yang-Mills fields

TL;DR

This paper explores cosmological models with SU(2) Yang-Mills fields, demonstrating that minimal coupling models lack de Sitter solutions, while non-minimal coupling models can produce de Sitter solutions without a cosmological constant.

Contribution

It introduces a reconstruction program for Yang-Mills cosmological models and compares minimal and non-minimal coupling effects on de Sitter solutions.

Findings

Minimal coupling models lack de Sitter solutions.

Non-minimal coupling models can produce de Sitter solutions without a cosmological constant.

A reconstruction method for Yang-Mills cosmological models is proposed.

Abstract

Cosmological models with an SU(2) Yang-Mills field are studied. For a specific model with a minimally coupled Yang-Mills Lagrangian, which includes an arbitrary function of the second-order term and a fourth-order term, a corresponding reconstruction program is proposed. It is shown that the model with minimal coupling has no de Sitter solutions, for any nontrivial function of the second-order term. To get de Sitter solutions, a gravitational model with nonminimally coupled Yang-Mills fields is then investigated. It is shown that the model with non-minimal coupling has in fact a de Sitter solution, even in absence of the cosmological constant term.