[@WillZag89], [@DEF92], [@DEF96a], [@DEF96b] or in the cosmological context in [@NaChiSu02]. The self–interaction potential $V$ in turn can play a role of the cosmological constant and give rise a mass term in the linearized theory.

In what follows we consider the massive Brans-Dicke theory in which the coupling parameter $\omega$ is given by the constant Brans–Dicke parameter, $\omega(\phi)=\omega_{BD}$. The field equations obtained by varying the action $S[g_{\mu\nu},\phi]$ with respect to the metric $g_{\mu\nu}$ and the scalar field $\phi$ are given by [@FM2003] $$\begin{aligned}
\label{eq:feq:BDM}
R_{\mu\nu} - \frac12g_{\mu\nu}R - \frac{V(\phi)}{\phi }& = & \frac{8\pi T_{\mu\nu}}{\phi} +
\frac{\omega_{BD}}{\phi^2}\left( \phi_{,\mu}\phi_{,\mu}-\frac12 g_{\mu\nu}\phi_{,\alpha}{}^{,\alpha} \right)
+ \frac{\phi_{,\mu\nu} - \Box_{g}\phi}{\phi}, \\
\Box_{g}\phi + \frac{\phi V'(\phi) - 2V(\phi)}{3+2\omega_{BD}} & = & \frac{8\pi T}{3+2\omega_{BD}}  \nonumber,\end{aligned}$$ where $R_{\mu\nu}$ is the Ricci tensor, $\Box_{g}\equiv (-g)^{-1/2}\partial_{\mu}(-g)^{1/2}g^{\mu\nu}\partial_{\nu}$, $T^{\mu\nu}\equiv\frac{2}{\sqrt{-g}}\frac{\delta S}{\delta g_{\mu\nu}}$, $T\equiv g_{\mu\nu}T^{\mu\nu}$ and $V'\equiv\frac{dV}{d\phi}$. We consider small perturbations over the background configuration of the Minkowski metric $\eta_{\mu\nu}$ and a constant field $\phi(x)=\phi_{0}$, $$\begin{aligned}
\label{eq:gp:lin}
& g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}, \quad \phi = \phi_{0} + \delta\phi,
\qquad |h_{\mu\nu}|\ll 1,\qquad|\delta\phi|\ll 1 &.\end{aligned}$$ To preserve the asymptotic flatness of solutions and to neglect higher–order self–interaction terms for the scalar field beside the mass term we assume [@ABWZ12] $V(\phi)=\frac12V''(\phi_0)\delta\phi^2$. Substituting (\[eq:gp:lin\]) into the field equations (\[eq:feq:BDM\]) 