  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.
