Cosmological model with variable equations of state for matter and dark
  energy
  We construct a cosmological model which is physically reasonable,
mathematically tractable, and extends the study of CDM models to the case where
the equations of state (EoS) for matter and dark energy (DE) vary with time. It
is based on the assumptions of (i) flatness, (ii) validity of general
relativity, (iii) the presence of a DE component that varies between two
asymptotic values, (iv) the matter of the universe smoothly evolves from an
initial radiation stage - or a barotropic perfect fluid - to a phase where it
behaves as cosmological dust at late times. The model approximates the CDM ones
for small $z$ but significantly differ from them for large $z$. We focus our
attention on how the evolving EoS for matter and DE can modify the CDM
paradigm. We discuss a number of physical scenarios. One of them includes, as a
particular case, the so-called generalized Chaplygin gas models where DE
evolves from non-relativistic dust. Another kind of models shows that the
current accelerated expansion is compatible with a DE that behaves like
pressureless dust at late times. We also find that a universe with variable DE
can go from decelerated to accelerated expansion, and vice versa, several
times.
