  Extensions of Einstein's General Relativity (GR) can formally be given a GR
structure in which additional geometric degrees of freedom are mapped on an
effective energy-momentum tensor. The corresponding effective cosmic medium can
then be modeled as an imperfect fluid within GR. The imperfect fluid structure
allows us to include, on a phenomenological basis, anisotropic stresses and
energy fluxes which are considered as potential signatures for deviations from
the cosmological standard $\Lambda$-cold-dark-matter ($\Lambda$CDM) model. As
an example, we consider the dynamics of a scalar-tensor extension of the
standard model, the $e_{\Phi}\Lambda$CDM model. We constrain the magnitudes of
anisotropic pressure and energy flux with the help of redshift-space distortion
(RSD) data for the matter growth function $f \sigma_8$.
