Model-independent tests of gravity with present data and future surveys

The large freedom in the free functions affecting linear perturbations in theories of modified gravity and dark energy leads to the burden of parametrization, which means that the observational constraints depend strongly on the way these free functions are parametrized. Using a model-independent test of gravity, alleviates this problem and it even frees us from assumptions about initial conditions, galaxy bias or the nature of dark matter. In this talk I will present the first model-independent reconstruction of the gravitational slip as a function of redshift, using present data on large scale structure and the Hubble function. For future data I will show how we can use these tests to rule out entire classes of modified gravity models and how we have to handle, in a Bayesian way, the constraints from models which are very close to LCDM and might not even be clearly distinguishable, even with next generation surveys.