The cosmological background and the "external field" in Modified Gravity (MOG)

We investigate the contributions of the Friedmann-Lema\^itre-Robertson-Walker metric of the standard cosmology as an asymptotic boundary condition on the first-order approximation of the gravitational field in Moffat's theory of modified gravity (MOG). We also consider contributions due to the fact that the MOG theory does not satisfy the shell theorem or Birkhoff's theorem, resulting in what is known as the "external field effect" (EFE). We show that while both these effects add small contributions to the radial acceleration law, the result is orders of magnitude smaller than the radial acceleration in spiral galaxies.