Evolution of density perturbations in decaying vacuum cosmology: The   case of non-zero perturbations in the cosmological term
  We extend the results of a previous paper where a model of interacting dark energy, with a cosmological term decaying linearly with the Hubble parameter, is tested against the observed mass power spectrum. In spite of the agreement with observations of type Ia supernovas, baryonic acoustic oscillations and the cosmic microwave background, we had shown previously that no good concordance is achieved if we include the mass power spectrum. However, our analysis was based on the ad hoc assumption that the interacting cosmological term is strictly homogeneous. Now we perform a more complete analysis, by perturbing such a term. Although our conclusions are still based on a particular, scale invariant choice of the primordial spectrum of dark energy perturbations, we show that a cosmological term decaying linearly with the Hubble parameter is indeed disfavored as compared to the standard model. 
H. A. Borges, S. Carneiro, J. C. Fabris