Nonminimal isotropic cosmological model with Yang-Mills and Higgs fields

TL;DR

This paper introduces a six-parameter nonminimal Einstein-Yang-Mills-Higgs model applied to cosmology, revealing a unique de Sitter solution and demonstrating how nonminimal coupling can restore isotropy by screening anisotropy.

Contribution

It formulates a novel six-parameter nonminimal Einstein-Yang-Mills-Higgs model and finds an exact de Sitter solution that shows how nonminimal coupling can restore isotropy in cosmology.

Findings

Existence of a unique de Sitter solution for specific coupling parameters.

Nonminimal coupling can effectively screen anisotropy caused by Yang-Mills fields.

The model relates coupling parameters to spacetime curvature for consistency.

Abstract

We establish a nonminimal Einstein-Yang-Mills-Higgs model, which contains six coupling parameters. First three parameters relate to the nonminimal coupling of non-Abelian gauge field and gravity field, two parameters describe the so-called derivative nonminimal coupling of scalar multiplet with gravity field, and the sixth parameter introduces the standard coupling of scalar field with Ricci scalar. The formulated six-parameter nonminimal Einstein-Yang-Mills-Higgs model is applied to cosmology. We show that there exists a unique exact cosmological solution of the de Sitter type for a special choice of the coupling parameters. The nonminimally extended Yang-Mills and Higgs equations are satisfied for arbitrary gauge and scalar fields, when the coupling parameters are specifically related to the curvature constant of the isotropic spacetime. Basing on this special exact solution we discuss the problem of a hidden anisotropy of the Yang-Mills field, and give an explicit example, when the nonminimal coupling effectively screens the anisotropy induced by the Yang-Mills field and thus restores the isotropy of the model.