New Two-Metric Theory of Gravity with Prior Geometry

We present a Lagrangian-based metric theory of gravity with three adjustable constants and two tensor fields, one of which is a nondynamical "flat-space metric" $\ensuremath{\eta}$. With a suitable cosmological model and a particular choice of the constants, the "post-Newtonian limit" of the theory agrees, in the current epoch, with that of general relativity theory (GRT); consequently our theory is consistent with current gravitation experiments. Because of the role of $\ensuremath{\eta}$, the gravitational "constant" $G$ is time-dependent and gravitational waves travel null geodesics of $\ensuremath{\eta}$ rather than the physical metric $g$. Gravitational waves possess six degrees of freedom. The general exact static spherically-symmetric solution is a four-parameter family. Future experimental tests of the theory are discussed.