Dark energy as a fixed point of the Einstein Yang-Mills Higgs Equations
  We study the Einstein Yang-Mills Higgs equations in the $SO(3)$
representation on a isotropic and homogeneous flat Universe, in the presence of
radiation and matter fluids. We map the equations of motion into an autonomous
dynamical system of first-order differential equations and we find the
equilibrium points. We show that there is only one stable fixed point that
corresponds to an accelerated expanding Universe in the future. In the past,
instead, there is an unstable fixed point that implies a stiff-matter
domination. In between, we find three other unstable fixed points,
corresponding, in chronological order, to radiation domination, to matter
domination, and, finally, to a transition from decelerated expansion to
accelerated expansion. We solve the system numerically and we confirm that
there are smooth trajectories that correctly describe the evolution of the
Universe, from a remote past dominated by radiation to a remote future
dominated by dark energy, passing through a matter-dominated phase.
