Archimedean-type force in a cosmic dark fluid: III. Big Rip, Little Rip
  and Cyclic solutions
  We analyze late-time evolution of the Universe in the framework of the
self-consistent model, in which the dark matter is influenced by the
Archimedean-type force proportional to the four-gradient of the dark energy
pressure. The dark energy is considered as a fluid with the equation of state
of the relaxation type, which takes into account a retardation of the dark
energy response to the Universe accelerated expansion. The dark matter is
guided by the Archimedean-type force, which redistributes the total energy of
the dark fluid between two its constituents, dark energy and dark matter, in
the course of the Universe accelerated expansion. We focus on the constraints
for the dark energy relaxation time parameter, for the dark energy equation of
state parameter, and for the Archimedean-type coupling constants, which
guarantee the Big Rip avoidance. In particular, we show that the
Archimedean-type coupling protects the Universe from the Big Rip scenario with
asymptotically infinite negative dark energy pressure, and that the Little Rip
is the fate of the Universe with the Archimedean-type interaction inside the
dark fluid.
