Abstract

The Pioneer anomalous acceleration remains inadequately explained. Here, is an attempt to shed some light on the dilemma by invoking a gauge variant theory of gravity. Since the gauge transformations in this theory are absolute there is an anisotropic cosmological frame effect in the vicinity of the solar system. The acceleration is not a true acceleration but a combination of an artifact of the anisotropic metric and an apparent acceleration due to a gravitational blue-shift. First, an alternative proposal of a theory of gravity is introduced that permits an extra scalar field into the field equations, but is related to the metric tensorially. In the process of justifying this theory, a meta-theory is proposed. Secondly, a cosmological model is solved. This is relevant to the anomalous acceleration due to the fact that the anisotropic solar system is nested in the isotropic and homogeneous background. Although there is a frame effect, it is velocity independent due to the relative nature of the tensorial fields. Thirdly, a quasi-static exterior spherically symmetric solution is derived. Fourthly, since there isn't any gauge invariance, there is no gravitational radiation. However, there is an apparent decrease in the period of the binary pulsar PSR 1913+16. Here I show how the decrease of the period is decrease of the period by an energy dissipation through the scalar field, but is cancelled by an anomalous galactic acceleration. Fifthly, from an analysis of the binary pulsar PSR 1534+12, an anomalous galactic term related to the critical cosmological density is predicted in the galactic acceleration terms of that system. Sixthly, the rate of the change in the eccentricity of these systems is formulated. Finally, from the PPN parameters, if this theory is correct, some verifying predictions are made, like a slight violation of the equivalence principle.