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.