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.

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