  We consider the nonlinearly extended Einstein-Maxwell-axion theory, which is
based on the account for two symmetries: first, the discrete symmetry
associated with the properties of the axion field, second, the Jackson's
symmetry, prescribing to the electrodynamics to be invariant with respect to
the rotation in the plane coordinated by the electric and magnetic fields. We
derive the master equations of the nonlinearly extended theory, and apply them
to the Bianchi-I model with magnetic field. The main result, describing the
behavior of the nonlinearly coupled axion, electromagnetic and gravitational
fields is the anomalous growth of the axionically induced electric field in the
early magnetized Universe. The character of behavior of this anomalous electric
field can be indicated by the term flare. We expect, that these electric flares
can produce the electron-positron pair creation, significant acceleration of
the born charged particles, and emission of the electromagnetic waves by these
accelerated particles.
