  Recently, the Cubic Galileon Gravity (CGG) model has been suggested as an
alternative gravity theory to General Relativity. The model consists of an
extra field potential term which can serve as the `fifth-force'. In this
article, we examine the possibility whether this extra force term can explain
the missing mass problem in galaxies without the help of dark matter. By using
the Milky Way rotation curve and the Spitzer Photomery & Accurate Rotation
Curves (SPARC) data, we show that this CGG model can satisfactorily explain the
shapes of these rotation curves without dark matter. The CGG model can be
regarded as a new alternative theory to challenge the existing dark matter
paradigm.
