Fitting rotation curve of galaxies by de Rham-Gabadadze-Tolley massive gravity

We investigate effects of massive graviton on the rotation curves of the Milky Way, spiral galaxies and Low Surface Brightness~(LSB) galaxies. Using a simple de Rham, Gabadadze, and Tolley (dRGT) massive gravity model, we find static spherically symmetric metric and a modified Tolman-Oppenheimer-Volkoff (TOV) equation. The dRGT nonlinear graviton interactions generate density and pressures which behave like a dark energy that can mimic the gravitational effects of a dark matter halo. We found that rotation curves of most galaxies can be fitted well by a single constant-gravity parameter $\gamma \sim m_{g}^{2}C \sim 10^{-28}~{\rm m^{-1}}$ corresponding to the graviton mass in the range $m_g\sim {10}^{-21}-{10}^{-30}\mathrm{e}\mathrm{V}$ depending on the choice of the fiducial metric parameter $C\sim 1-{10}^{18}\text{ m}$. Fitting rotation curve of the Milky Way puts strong constraint on the Yukawa-type coupling of the massive graviton exchange as a result of the shell effects.