The periastron advance in curvature based extended gravity and dark energy

In the context of the periastron advance as a fundamental test for gravity theories, we show an approach to deduce constraints on the sizes of the new forces arising in the weak field limit of the Extended Theories of Gravity (ETG). It is also studied the force motivated by Quintessence Fields deforming the Schwarzschild geometry and associated to the Dark Energy, responsible of the acceleration of the Universe. As for the ETG, we consider the more general Scalar-Tensor Fourth Order Gravity (STFOG) and the NonCommutative Spectral Gravity (NCSG) as a special case. The solutions of the linearized field equations provide corrections to the Newtonian potential in the Yukawa-like form V (r) = α e−βr r , where α is the parameter related to the strength of the potential and β to the range of the force. Quintessence Fields lead to a power-law correction with parameters related to the Dark Energy. By analysing the periastron advance with the use of the current data, we find improvements on the parameters of the gravitational models as well as on the bounds of the parameter β by several orders of magnitude.