We present a new approach to the mathematical objects of General Relativity in terms of which a generic f(R)-gravity theory gravitation is written in a first-order (à la Palatini) formalism, and introduce the concept of Dark Metric which could bypass the emergence of disturbing concepts as Dark Energy and Dark Matter. These issues are related to the fact that General Relativity could not be the definitive theory of Gravitation due to several shortcomings that come out both from theoretical and experimental (...) viewpoints. At large scales, the attempts to match it with the recent observational data lead to invoke Dark Energy and Dark Matter as the bulk components of the cosmic fluid. Since no final evidence, at fundamental level, exists for such ingredients, it could be useful to reconsider the gravitational sector in order to see if suitable extensions of General Relativity could solve the shortcomings present at infrared scales. (shrink)

On Avicenna, 980-1037, a Muslim philosopher.