The cosmological background and the “external field” in modified gravity (MOG)

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