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The aim of this paper is to constrain modified gravity with redshift spacedistortion observations and supernovae measurements. Compared with a standardLCDM analysis, we include three additional free parameters, namely the initialconditions of the matter perturbations,the overall perturbation normalization,and a scale-dependent Y parameter modifying the Poisson equation, in an attemptto perform a more model-independent analysis. First, we constrain the Poissonparameter Y (also called Geff ) by using currently available fsigma_8 data andthe recent SN catalog JLA. We find that the inclusion of the additional freeparameters makes the constraints significantly weaker than when fixing them tothe standard cosmological value. Second, we constrain Y by using forecastgrowth-rate data for Euclid and SKA missions. Here again we point out theweakening of the constraints when the additional parameters are included.Finally, we adopt as modified gravity Poisson parameter the specific Horndeskiform, and use scale-dependent forecasts to build an exclusion plot for theYukawa potential akin to the ones realized in laboratory experiments, both forthe Euclid and the SKA surveys.

Model-independent constraints on modified gravity from current data and from the Euclid and SKA future surveys