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 follo ws a geodesic of the metric connection. The theory behaves in the Newt onian limit as the Newtonian theory with a correction which is proport ional to the matter density at the field point. This behavior can be p roduced by a Yukawa potential with an atomic scale characteristic rang e lambda and a coupling constant ct proportional to 1/lambda(2). This type of potential is not excluded by the present experimental data.