  We consider an isotropic homogeneous cosmological model with five interacting
elements: first, the dynamic aether presented by a unit timelike vector field,
second, the pseudoscalar field describing an axionic component of the dark
matter, third, the cosmic dark energy, described by a rheologic fluid, fourth,
the non-axionic dark matter coupled to the dark energy, fifth, the gravity
field. We show that the early evolution of the Universe described by this model
can include two specific epochs: the first one can be characterized as a
super-inflation, the second epoch is associated with an oscillatory regime. The
dynamic aether carries out a regulatory mission; the rheologic dark fluid
provides the specific features of the spacetime evolution. The oscillations of
the scale factor and of the Hubble function are shown to switch on the
parametric (Floquet - type) mechanism of the axion number growth.
