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We establish a nonlinear version of the SU(N) symmetric theory, whichdescribes self-consistently the interaction between the gravitational, gauge,vector and pseudoscalar (axion) fields. In the context of this theory the SU(N)symmetric multiplet of vector fields is associated with the color aether, thedecay of which in the early Universe produced the canonic dynamic aether andthe axionic dark matter. The SU(N) symmetric Yang-Mills field, associated withthe color aether, forms the source, which transfers the energy of the decayingcolor aether to the axion field. The nonlinear modification of the model usesexplicitly the requirement of discrete symmetry, prescribed by the axion field,and is based on the analogy with nonlinear physical pendulum. We show that inthe framework of this nonlinear regular model the axion field can grow to anarbitrarily large value, thus explaining the abundance of the axionic darkmatter in the Universe.

Einstein-Yang-Mills-aether theory with nonlinear axion field: Decay of color aether and the axionic dark matter production