Galaxy Dynamics Predictions in the Nonsymmetric Gravitational Theory

In the weak field approximation, the nonsymmetric gravitational theory (NGT) has, in addition to the Newtonian gravitational potential, a Yukawa-like potential produced by the exchange of a spin $1^+$ boson between fermions. If the range $r_0=\mu^{-1}$ is $25$ kpc, then this additional potential due to the interaction with matter in the halos of galaxies can explain the flat rotation curves of galaxies and the Tully-Fisher law ($L\sim v^4$) without the dark matter hypothesis. Possible fits to clusters of galaxies and gravitational lensing observations are discussed. The results are based on a linear approximation to a new perturbatively consistent version of the NGT field equations, which does not violate the weak equivalence principle.