Dynamics of expansion of the Universe in the models with non-minimally
  coupled dark energy
  We consider the dark energy model with barotropic equation of state, which
interacts with dark matter through gravitation and another force, causing the
energy-momentum exchange between them. Both components are described in
approximation of ideal fluids, which are parametrized by density and equation
of state parameters. Three types of interactions between dark components are
considered: the interaction independent from their densities, the one
proportional to density of dark energy and the one proportional to density of
dark matter. The equations which describe the expansion dynamics of homogeneous
and isotropic Universe and evolution of densities of both components for
different values of interaction parameter are obtained on the bases of the
general covariant conservation equations and Einstein's ones. For three kinds
of interactions we show the existence of the range of values of parameters of
dark energy for which the densities of dark components and their sum are
negative. We find the conditions of positivity of density of dark energy and
dark matter. The constraints on the value of parameter of interaction are
derived. The dynamics of expansion of the Universe with these interactions of
dark energy and dark matter is analysed.
