Exact cosmological solution of a Scalar-Tensor Gravity theory compatible
  with the $\Lambda CDM$ model
  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.
