An Extension of General Relativity Depending on the Independent Powers of Rμv

We present an extension of General Relativity governed by a scalar Lagrangian density, function of all the independent invariant scalars one is able to build by the powers of the Ricci tensor. The new terms arising in the generalized Einstein filed equations, in the viewpoint of usual General Relativity, may be interpreted as dark matter and dark energy contributions. Metricity condition fulfilled by a new tensor different than the usual metric tensor is also obtained. More it is shown that Schwarzschild-De Sitter, Robertson-Walker-De Sitter and Kerr-De Sitter metrics are exact solutions to the new field equations. Remarkably the form of the equation of the geodesic trajectories of particle motions across space-time remains the same as in Einstein General Relativity unless the cosmological constant is no longer a constant becoming a function of the space-time co-ordinates.