Curvature coupling in Einstein-Yang-Mills theory and non-minimal self-duality (Q2457715)

A self-consistent non-minimal non-abelian-Einstein-Yang-Mills model, containing three phenomenological coupling constants, is formulated. The ansatz of a vanishing Yang-Mills induction is considered as a particular case of the self-duality requirement for the gauge field. Such an ansatz is shown to allow obtaining an exact solution of the self-consistent set of equations when the space-time has a constant curvature. An example describing a pure magnetic gauge field in the de Sitter cosmological background is discussed in detail.