  Among the several proposals to solve the incompatibility between the observed
small value of the cosmological constant and the huge value obtained by quantum
field theories, we can find the idea of a decaying vacuum energy density,
leading from high values at early times of universe evolution to the small
value observed nowadays. In this paper we consider a variation law for the
vacuum density recently proposed by Schutzhold on the basis of quantum field
estimations in the curved, expanding background, characterized by a vacuum
density proportional to the Hubble parameter. We show that, in the context of
an isotropic and homogeneous, spatially flat model, the corresponding solutions
retain the well established features of the standard cosmology, and, in
addition, are in accordance with the observed cosmological parameters. Our
scenario presents an initial phase dominated by radiation, followed by a dust
era long enough to permit structure formation, and by an epoch dominated by the
cosmological term, which tends asymptotically to a de Sitter universe. Taking
the matter density equals to half of the vacuum energy density, as suggested by
observation, we obtain a universe age given by Ht = 1.1, and a decelerating
parameter equals to -1/2.
