Constraining model parameters from coupled dark energy and other beyond-ΛCDM models in the nonlinear regime

The next generation of galaxy surveys such as Euclid, LSST and SKA will probe even further the small scale galaxy clustering (GC) and weak lensing (WL) observables with an increased precision. In order to determine the correct cosmological model of the Universe, we need to understand alternative theories of modified gravity and dark energy at least in the mildly non-linear regime, provided we can take into account most of the possible sources of systematics. In this talk I will present some forecasts on the DM-DE coupling parameter β, using information from the non-linear scales for GC and WL observables with Euclid-like specifications (arXiv:1508.07208). I will also present some ongoing work in growing neutrino quintessence and general Horndeski models, where with the use of N-body simulations and renormalized perturbation theory, we can show that non-linearities might play a very important role when testing these models against observations.