Post-Newtonian Metric for a General Class of Scalar-Tensor Gravitational Theories and Observational Consequences.

A general class of scalar-tensor gravitational theories is considered in which the c parameter of the Brans-Dicke theory is allowed to be an arbitrary (positive definite) function of the scalar field (co co () ). The weak-field metric for slowly moving mass sources is obtained to order 1/c4 for goo, allowing us to examine phenomenologically the question of whether experiments within the solar system can detect a possible co' dw/d 0. The post-Newtonian (1/c4) metric is dependent only on the two parameters co (o) and co' (o), where o is the scalar-field value at this time in the Universe. A variety of experimental consequences of co' 0 are found, including a contribution to the rate of precession of Mercury's perihelion.