Growth rate in inhomogeneous interacting vacuum models
  We study the effects of vacuum energy perturbations on the evolution of the
dark matter growth rate in a decomposed Chaplygin gas model with interacting
dark matter and vacuum energy. We consider two different cases: (i) geodesic
dark matter with homogeneous vacuum, and (ii) a covariant ansatz for vacuum
density perturbations. In the latter case, we show that the vacuum
perturbations are very tiny as compared to dark matter perturbations on
sub-horizon scales. In spite of that, depending on the value of the Chaplygin
gas parameter {\alpha}, vacuum perturbations suppress or enhance the dark
matter growth rate as compared to the geodesic model.
