  We consider a set of solutions for a massless quartic scalar field, recently
devised, that satisfy a massive dispersion relation. We show that such
solutions have the property to give the correct behavior for the equation of
state of the dark energy. It seen that conformal invariance is restored and the
mass gap goes to zero on a time scale determined by the Hubble constant and the
strength of the self-interaction of the scalar field. When conformal invariance
is restored, the equation of state for the dark energy can apply.
