Fundamental parameter-free solutions in modified gravity

Modified gravity (MOG) has been used successfully to explain the rotation curves of galaxies, the motion of galaxy clusters, the bullet cluster and cosmological observations without the use of dark matter or Einstein's cosmological constant. We now have the ability to demonstrate how these solutions can be obtained directly from the action principle, without resorting to the use of fitted parameters or empirical formulae. We obtain numerical solutions to the theory's field equations that are exact in the sense that no terms are omitted, in two important cases: the spherically symmetric, static vacuum solution and the cosmological case of a homogeneous, isotropic universe. We compare these results to selected astrophysical and cosmological observations.