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Cosmological scalar perturbation theory studied in the Newtonian gaugedepends on two potentials $\Phi$ and $\Psi$. In General Relativity (GR) theymust coincide ($\Phi=\Psi$) in the absence of anisotropic stresses sourced bythe energy momentum tensor. On the other hand, it is widely accepted in theliterature that potential deviations from GR can be parameterized by $\Phi\neq\Psi$. The latter feature is therefore present in both GR cosmologies equippedwith shear viscous fluids or modified gravity. We study the evolution of scalarmatter density perturbations using the redshift-space-distortion based$f(z)\sigma_8(z)$ data as a tool to differentiate and characterize the imprintsof both scenarios. We show that in the $f(z)\sigma_8(z)$ evolution bothscenarios yields to completely different imprints in comparison to the standardcosmology. While the current available data is not sensitive to distinguishmodified gravity from viscous shear cosmologies, future precise data can beused to break this indistinguishability.

Modified gravity versus shear viscosity: imprints on the scalar matter perturbations