The Newtonian limit in a family of metric affine theories of gravitation

A brief review of a first order theory with a quadratic Lagrangian L = R + omega(0)R(2) is presented. It is shown that a test particle follows a geodesic of the metric connection. The theory behaves in the Newtonian limit as the Newtonian theory with a correction which is proportional to the matter density at the field point. This behavior can be produced by a Yukawa potential with an atomic scale characteristic range lambda and a coupling constant ct proportional to 1/lambda(2). This type of potential is not excluded by the present experimental data.