Modified gravity versus shear viscosity: imprints on the scalar matter
  perturbations
  Cosmological scalar perturbation theory studied in the Newtonian gauge
depends on two potentials $\Phi$ and $\Psi$. In General Relativity (GR) they
must coincide ($\Phi=\Psi$) in the absence of anisotropic stresses sourced by
the energy momentum tensor. On the other hand, it is widely accepted in the
literature that potential deviations from GR can be parameterized by $\Phi\neq
\Psi$. The latter feature is therefore present in both GR cosmologies equipped
with shear viscous fluids or modified gravity. We study the evolution of scalar
matter density perturbations using the redshift-space-distortion based
$f(z)\sigma_8(z)$ data as a tool to differentiate and characterize the imprints
of both scenarios. We show that in the $f(z)\sigma_8(z)$ evolution both
scenarios yields to completely different imprints in comparison to the standard
cosmology. While the current available data is not sensitive to distinguish
modified gravity from viscous shear cosmologies, future precise data can be
used to break this indistinguishability.
