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(σ) R with F(σ) = N_pl² + ξ σ². We update our results with previous Planck and BAO data releases obtaining the tightest constraints to date on the coupling parameters, that is ξ < 5.5 × 10^-4 for N_pl=0 (induced gravity or equivalently extended Jordan-Brans-Dicke) and (N_pl √8 π G)-1 < 1.8 × 10^-5 for ξ = -1/6 (conformal coupling), both at 95% CL. Because of a modified expansion history after radiation-matter equality compared to the ΛCDM model, all these dynamical models accommodate a higher value for H₀ and therefore alleviate the tension between Planck/BAO and distance-ladder measurement from SNe Ia data from 4.4σ at best to 2.7-3.2σ with CMB alone and 3.5-3.6σ including BAO data. We show that all these results are robust to changes in the neutrino physics. In comparison to the ΛCDM model, partial degeneracies between neutrino physics and the coupling to the Ricci scalar allow for smaller values N_eff ~ 2.8, 1σ lower compared to the standard N_eff = 3.046, and relax the upper limit on the neutrino mass up to 40%.