  In the framework of the extended Einstein-aether-axion theory we study the
model of a two-level aetheric control over the evolution of a spatially
isotropic homogeneous Universe filled with axionic dark matter. Two guiding
functions are introduced, which depend on the expansion scalar of the aether
flow, equal to the tripled Hubble function. The guiding function of the first
type enters the aetheric effective metric, which modifies the kinetic term of
the axionic system; the guiding function of the second type predetermines the
structure of the potential of the axion field. We obtained new exact solutions
of the total set of master equations of the model (with and without
cosmological constant), and studied in detail four analytically solvable
submodels, for which both guiding functions are reconstructed and illustrations
of their behavior are presented.
