  On the basis of a previously established scalar-tensor extension of the
$\Lambda$CDM model we develop an effective fluid approach for the matter growth
function. This extended $\Lambda$CDM (henceforth $e_{\Phi}\Lambda$CDM)
cosmology takes into account deviations from the standard model both via a
modified background expansion and by the inclusion of geometric anisotropic
stresses as well as of perturbations of the geometric dark-energy equivalent.
The background dynamics is governed by an explicit analytic expression for the
Hubble rate in which modifications of the standard model are given in terms of
a single constant parameter [1]. To close the system of fluid-dynamical
perturbation equations we introduce two phenomenological parameters through
which the anisotropic stress is related both to the total energy density
perturbation of the cosmic substratum and to relative perturbations in the
effective two-component system. We quantify the impact of deviations from the
standard background, of anisotropic stresses and of non-vanishing perturbations
of the effective dark-energy component on the matter growth rate function $f
\sigma_8$ and confront the results with recent redshift-space distortion (RSD)
measurements.
