Ten scenarios from early radiation to late time acceleration with a
  minimally coupled dark energy
  We consider General Relativity with matter, radiation and a minimally coupled
dark energy defined by an equation of state w. Using dynamical system method,
we find the equilibrium points of such a theory assuming an expanding Universe
and a positive dark energy density. Two of these points correspond to classical
radiation and matter dominated epochs for the Universe. For the other points,
dark energy mimics matter, radiation or accelerates Universe expansion. We then
look for possible sequences of epochs describing a Universe starting with some
radiation dominated epoch(s) (mimicked or not by dark energy), then matter
dominated epoch(s) (mimicked or not by dark energy) and ending with an
accelerated expansion. We find ten sequences able to follow this Universe
history without singular behaviour of w at some saddle points. Most of them are
new in dark energy literature. To get more than these ten sequences, w has to
be singular at some specific saddle equilibrium points. This is an unusual
mathematical property of the equation of state in dark energy literature, whose
physical consequences tend to be discarded by observations. This thus
distinguishes the ten above sequences from an infinity of ways to describe
Universe expansion.
