Cosmology with Modified Newtonian Dynamics (MOND)

It is well-known that the application of Newtonian dynamics to an expanding spherical region leads to the correct relativistic expression (the Friedmann equation) for the evolution of the cosmic scale factor. Here, the cosmological implications of Milgrom's modified Newtonian dynamics (MOND) are considered by means of a similar procedure. Earlier work by Felten demonstrated that in a region dominated by modified dynamics, the expansion cannot be uniform (separations cannot be expressed in terms of a scale factor) and that any such region will eventually re-collapse regardless of the initial expansion velocity and mean density. Here I show that, because of the acceleration threshold for the MOND phenomenology, a region dominated by MOND will have a finite size which, in the early Universe ($z > 3$), is smaller than the horizon scale. Therefore, uniform expansion and homogeneity on horizon scale are consistent with MOND-dominated non-uniform expansion and the development of inhomogeneities on smaller scale. In the radiation-dominated era, the amplitude of MOND-induced inhomogeneities is much smaller than that implied by observations of the cosmic background radiation, and the thermal and dynamical history of the Universe is identical to that of the standard Big Bang. When matter first dominates the energy density of the Universe, the cosmology diverges from that of the standard model. Objects of galaxy mass are the first virialized objects to form (by z=10) and larger structure develops rapidly. At the present epoch, the Universe would be inhomogeneous out to a substantial fraction of the Hubble radius.