Matter Growth in Imperfect Fluid Cosmology

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 $f \sigma_8$.