  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.

General Relativity and Quantum Cosmology;Astrophysics;High Energy Physics - Theory