Exact cosmological solution of a scalar-tensor gravity theory compatible with the ΛCDM 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 Phi(z)/Phi(0) and H(z)/H-0 that depend only on two parameters, K-2 and Omega(m,0). For K <= 1/400, 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.