  We study the stellar bar growth in high resolution numerical galaxy models
with and without dark matter halos. In all models the galactic disk is
exponential and the halos are rigid or live Plummer spheres. More specifically,
when there is no dark matter halo, we modify the gravitational force between
point particles. To do so we use the weak field limit of an alternative theory
of dark matter known as MOG in the literature. The galaxy model in MOG has the
same initial conditions as in galaxy models with dark matter halo. On the other
hand, the initial random velocities and the Toomre's local stability parameter
are the same for all the models. We show that the evolution and growth of the
bar in MOG is substantially different from the standard cases including dark
matter halo. More importantly, we find that the bar growth rate and its final
magnitude is smaller in MOG. On the other hand, the maximum value of the bar in
MOG is smaller than the Newtonian models. It is shown that although the live
dark matter halo may support the bar instability, MOG has stabilizing effects.
Furthermore, we show that MOG supports fast pattern speeds, and unlike in the
dark matter halo models pattern speed does not decrease with time. Theses
differences, combined with the relevant observations, may help to distinguish
between dark matter an modified gravity in galactic scales.
