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

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