An important goal of this Action is to perform a detailed theoretical and phenomenological analysis of the relation between the effective field yielding dark energy and non-canonical Lagrangians and non-linear gauge kinetic functions. Generalizations of the action functional can be approached in several ways. For instance, some prescriptions replace the linear scalar curvature term in the Einstein-Hilbert action by a function of the scalar curvature, f(R), or by more general scalar invariants of the theory. An interesting novel possibility that will be analyzed in great detail includes a non- minimal coupling between the scalar curvature and the matter Lagrangian density. Another prescription considers one (or more) scalar fields coupled to the geometry, and playing a gravitational role. In this context, infrared modifications of GR will be extensively explored. All modified gravity models induce observational signatures at the post-Newtonian level, which are described by the parameterized post-Newtonian (PPN) metric coefficients arising from these extensions of GR. These ETGs will be tested against large-scale structure and lensing, astrophysical and laboratory measurements, as well as laboratory and space-based Equivalence Principle experiments. The tests from the solar system, large scale structure and lensing essentially restrict the range of allowed modified gravity models, and thus offer a window into understanding the perplexing nature of the cosmic acceleration and of gravity itself. These tests will be the milestones of WG1 for the project that have to be combined with results and deliverables of WG2 and WG3. Specifically, the WG2 and WG3 will be fundamental in the construction of viable ETGs.