Model-independent constraints on modified gravity from current data and
  from the Euclid and SKA future surveys
  The aim of this paper is to constrain modified gravity with redshift space
distortion observations and supernovae measurements. Compared with a standard
LCDM analysis, we include three additional free parameters, namely the initial
conditions of the matter perturbations,the overall perturbation normalization,
and a scale-dependent Y parameter modifying the Poisson equation, in an attempt
to perform a more model-independent analysis. First, we constrain the Poisson
parameter Y (also called Geff ) by using currently available fsigma_8 data and
the recent SN catalog JLA. We find that the inclusion of the additional free
parameters makes the constraints significantly weaker than when fixing them to
the standard cosmological value. Second, we constrain Y by using forecast
growth-rate data for Euclid and SKA missions. Here again we point out the
weakening of the constraints when the additional parameters are included.
Finally, we adopt as modified gravity Poisson parameter the specific Horndeski
form, and use scale-dependent forecasts to build an exclusion plot for the
Yukawa potential akin to the ones realized in laboratory experiments, both for
the Euclid and the SKA surveys.
