On vacuum density, the initial singularity and dark energy
  Standard cosmology poses a number of important questions. Apart from its
singular origin, it possesses early and late accelerating phases required to
account for observations. The vacuum energy has been considered as a possible
way to resolve some of these questions. The vacuum energy density induced by
free fields in an early de Sitter phase has earlier been estimated to be
proportional to $H^4$, while more recently it has been suggested that the QCD
condensate induces a term proportional to H at late times. These results have
been employed in models which are non-singular and inflationary at early times
and accelerating at late times. Here we cast these models in terms of scalar
fields and study the corresponding spectrum of primordial perturbations. At
early times the spectrum is found to be not scale-invariant, thus implying that
slow-roll inflation is still required after the phase transition induced by the
vacuum. At late times the corresponding scalar-field potential is harmonic,
with a mass of the order of the Hubble scale, a result that may be understood
in the light of the holographic conjecture.
