Cosmological constraints on post-Newtonian parameters in effectively massless scalar-tensor theories of gravity

We study the cosmological constraints on the variation of Newton's constant and on post-Newtonian parameters for simple models of the scalar-tensor theory of gravity beyond the extended Jordan-Brans-Dicke theory. We restrict ourselves to an effectively massless scalar field with a potential V∝F2, where F(σ)=Npl2+ξσ2 is the coupling to the Ricci scalar considered. We derive the theoretical predictions for cosmic microwave background anisotropies and matter power spectra by requiring that the effective gravitational strength at present is compatible with the one measured in a Cavendish-like experiment and by assuming an adiabatic initial condition for scalar fluctuations. When comparing these models with Planck 2015 and a compilation of baryonic acoustic oscillations data, all these models accommodate a marginalized value for H0 higher than in ΛCDM. We find no evidence for a statistically significant deviation from Einstein's general relativity. We find ξ