Discrimination between Lambda-CDM, quintessence, and modified gravity models using wide area surveys

In the past decade or so observations of supernovae, Large Scale Structures (LSS), and the Cosmic Microwave Background (CMB) have confirmed the presence of what is called dark energy - the cause of accelerating expansion of the Universe. They have also measured its density as well as the value of other cosmological parameters according to the concordance $\Lambda$CDM model with few percent uncertainties. Next generation of surveys should allow to constrain this model with better precisions, or distinguish between a LCDM and alternative models such as modified gravity and (interacting)-quintessence models. In this work we parametrize both homogeneous and anisotropic components of matter density in the context of interacting dark energy models with the goal of discriminating between f(R) modified gravity and its generalizations, and interacting dark energy models, for which we also propose a phenomenological description of energy-momentum conservation equations inspired by particle physics. It is based on the fact that the simplest interactions between particles/fields are elastic scattering and decay. The parametrization of growth rate proposed here is nonetheless general and can be used to constrain other interactions. As an example of applications, we present an order of magnitude estimation of the accuracy of the measurement of these parameters using Euclid and Planck surveys data, and leave a better estimation to a dedicated work.