Post-Newtonian approximations in scale covariant gravitation

The scale covariant theory of gravitation, outlined by Dirac (1973), later developed by Canutoet al. (1977), revisited by Maeder and Bouvier (1978, 1979), takes into account the possible relative changes in the system of units associated with different physical interactions; in this respect, it represents a generalization of the General Relativity Theory. In the line of the latter aforementioned papers, we study here the case of a weak gravitational field, well suited to the inner motions of a star or galaxy cluster, in order to see whether the post-Newtonian approximation scheme can consistently fit into the scale covariant formalism. Such a task turns out to be feasible when the gauge terms met in the field equations are handled in an appropriate way, but only if the gauge or metrical connection vector is inversely proportional to cosmic time, as it should be in consequence of the outer boundary condition imposed on the solution of the field equations describing the Newtonian and the first post-Newtonian approximation.