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

Understand

We study the cosmological constraints on the variation of the Newton's constant and on post-Newtonian parameters for simple models of scalar-tensor theory of gravity beyond the extended Jordan-Brans-Dicke theory.

• We restrict ourselves to an effectively massless scalar field with a potential $V \propto F^2$, where $F(\sigma)=N_{pl}^2+\xi\sigma^2$ is the coupling to the Ricci scalar considered.
• We derive the theoretical predictions for cosmic microwave background (CMB) 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 adiabatic initial condition for scalar fluctuations.
• When comparing these models with $Planck$ 2015 and a compilation of baryonic acoustic oscilation (BAO) data, all these models accomodate a marginalized value for $H_0$ higher than in $\Lambda$CDM.