Archimedean-type force in a cosmic dark fluid: I. Exact solutions for
  the late-time accelerated expansion
  We establish a new self-consistent model in order to explain from a unified
viewpoint two key features of the cosmological evolution: the inflation in the
early Universe and the late-time accelerated expansion. The key element of this
new model is the Archimedean-type coupling of the dark matter with dark energy,
which form the so-called cosmic dark fluid. We suppose that dark matter
particles immersed into the dark energy reservoir are affected by the force
proportional to the four-gradient of the dark energy pressure. The
Archimedean-type coupling is shown to play a role of effective energy-momentum
redistributor between the dark matter and the dark energy components of the
dark fluid, thus providing the Universe's evolution to be a quasiperiodic
and/or multistage process. In the first part of the work we discuss a
theoretical base and new exact solutions of the model master equations. Special
attention is focused on the exact solutions for which the scale factor is
presented by the anti-Gaussian function: these solutions describe the late-time
acceleration and are characterized by a nonsingular behavior in the early
Universe. The second part contains qualitative and numerical analysis of the
master equations; we focus there on the solutions describing a
multi-inflationary Universe.
