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

Understand

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 $\Omega_{m,0}$.