We consider the massive scalar-tensor theory in the Jordan frame $F(\Phi) =K^{ 2}\Phi^2$ and $U(\Phi) =(1/2)m^{ 2}\Phi^2$, where $F(\Phi)$ corresponds to a constant Brans-Dicke parameter $\omega_{ BD}=1/4K^2$. The constraint of the Solar System experiments is $K^2<(1/400)^2$. For dustlike matter in a spatially flat homogeneous isotropic universe, we reduce the equations of motion to a system of two differential equations of first order which can be exactly solved. We obtain simple and explicit expressions for $\frac{ \Phi(z)}{ \Phi(0)}$ and $\frac{ H(z)}{ H_{ 0}}$ that depend only on two parameters, $K^2$ and $\Omega_{ m,0}$. For $K\leq1/400$ the expansion rate $H(z)$ can be practically superposed on the $\Lambda$CDM solution $H_{ \Lambda}(z)$, up to high redshift $z$, but the equation of state $w_{ DE}(z)$ of the dark energy is not constant: it presents a very slight crossing of the phantom divide line $w=-1$ in the neighborhood of $z=0$ and becomes very slightly positive at high redshifts.
Categories: astro-ph.CO gr-qc