Scalar-tensor theories of gravity, neutrino physics, and the H0 tension

We use Planck 2018 data to constrain the simplest models of scalar-tensor theories characterized by a coupling to the Ricci scalar of the type F(sigma)R with F(sigma) = N-pl(2) + xi sigma(2). We update our results with previous Planck and BAO data releases obtaining the tightest constraints to date on the coupling parameters, that is xi < 5.5 x 10(-4) for N-pl = 0 (induced gravity or equivalently extended Jordan-Brans-Dicke) and (N-pl root 8 pi G) - 1 < 1.8 x 10(-5) for xi = -1/6 (conformal coupling), both at 95% CL. Because of a modified expansion history after radiation-matter equality compared to the ACDM model, all these dynamical models accommodate a higher value for H-0 and therefore alleviate the tension between Planck/BAO and distance-ladder measurement from SNe Ia data from 4.4 sigma at best to 2.7-3.2 sigma with CMB alone and 3.5-3.6 sigma including BAO data. We show that all these results are robust to changes in the neutrino physics. In comparison to the ACDM model, partial degeneracies between neutrino physics and the coupling to the Ricci scalar allow for smaller values N-eff similar to 2.8, 1 sigma lower compared to the standard N-eff = 3.046, and relax the upper limit on the neutrino mass up to 40%.