Friedmann cosmology with decaying vacuum density
  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. 
H. A. Borges and S. Carneiro