of the scalar-tensor Brans-Dicke theory and in [@Mohseni11] in the case of the nonlinear massive dRGT gravity model [@dRGT11].

The nonrelativistic sector of gravitational interactions in these theories is also modified. For example if the scalar field in massive BD theory satisfies the Klein–Gordon equation with the mass parameter $m$ one expects that the effective Newtonian gravitational potential in the near zone of a source will be modified by the Yukawa–type corrections, $\sim \exp{(-m r)}$. This corrections would manifest themselves as a deviation from the Keppler’s third law and can be investigated by observing the dynamics of the planets of the Solar System [@BGS2011]. The uncertainty of those measurements can be interpreted as providing the upper bounds on the mass parameter. The strongest upper bound, $m<4.4\times 10^{-22}$eV, comes from observations of Mars [@Will98]. But whatever the Solar System bounds might be one must take notice that in theories predicting massive scalar waves the mass parameter may have a dynamical origin. For example in massive ST theories it is defined by the local minimum of some potential $V(\phi)$ which determines the dynamics of $\phi$. However one can also consider potentials having a number of local extrema which, depending on the external 