Distinguishing Standard from Modified Gravity in the Local Group and beyond

The works in this portfolio test the hypothesis that it is not possible to extrapolate the Newtonian inverse square law of gravity from Solar System to galaxy scales. In particular, I look into various tests of Modified Newtonian Dynamics (MOND), which posits a modification below a very low acceleration threshold. Although discrepancies with Newtonian dynamics are indeed observed, they can usually be explained by invoking an appropriate distribution of invisible mass known as dark matter (DM). This leads to the standard cosmological paradigm, $Λ$CDM. I consider how it may be distinguished from MOND using collision velocities of galaxy clusters, which should sometimes be much faster in MOND. I focus on measuring these velocities more accurately and conclude that this test ought to be feasible in the near future. For the time being, I look at the much nearer and more accurately observed Local Group (LG) of galaxies. Its main constituents $-$ the Milky Way (MW) and Andromeda (M31) $-$ should have undergone a past close flyby in MOND but not in $Λ$CDM. The fast MW-M31 relative motion around the time of their flyby would have allowed them to gravitationally slingshot any passing LG dwarf galaxies out at high speed. I consider whether there is any evidence for such high-velocity galaxies (HVGs). Several candidates are found in two different $Λ$CDM models of the LG, one written by a founding figure of the paradigm. The properties of these HVGs are similar to what might be expected in MOND, especially their tendency to lie close to a plane. Being more confident of its validity, I then used MOND to determine the escape velocity curve of the MW over the distance range 8$-$50 kpc, finding reasonable agreement with the latest observations. I finish by discussing possible future directions for MOND research.