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

• Received 26 June 2018

DOI:https://doi.org/10.1103/PhysRevD.98.064008