Testing MOG, Non-Local Gravity and MOND with rotation curves of dwarf galaxies

Abstract: Modified Gravity (MOG) and Non-Local Gravity (NLG) are two alternative theories to General Relativity. They are able to explain the rotation curves of spiral galaxies and clusters of galaxies without including dark matter (Moffat & Rahvar 2013, 2014; Rahvar & Mashhoon 2014). In the weak-field approximation these two theories have similar forms, with an effective gravitational potential that has two components: (i) Newtonian gravity with the gravitational constant enhanced by a factor $(1+\alpha)$ and (ii) a Yukawa type potential that produces a repulsive force with length scale $1/\mu$. In this work we compare the rotation curves of dwarf galaxies in the LITTLE THINGS catalog with predictions of MOG, NLG and Modified Newtonian Dynamics (MOND). We find that the universal parameters of these theories, can fit the rotation curve of dwarf galaxies with a larger stellar mass to the light ratio compared to the nearby stars in the Milky Way galaxy. Future direct observations of mass function of stars in the dwarf galaxies can examine different modified gravity models.