Extended gravity from noncommutativity

We review the first order theory of gravity (vierbein formulation) on noncommutative spacetime studied in [1, 2]. The first order formalism allows to couple the theory to fermions. This NC action is then reinterpreted (using the Seiberg-Witten map) as a gravity theory on commutative spacetime that contains terms with higher derivatives and higher powers of the curvature and depend on the noncommutativity parameter \theta. When the noncommutativity is switched off we recover the usual gravity action coupled to fermions. The first nontrival corrections to the usual gravity action coupled to fermions are presented in a manifest Lorentz invariant form.