A larger value for $H_0$ by an evolving gravitational constant

We provide further evidence that a massless cosmological scalar field with a non-minimal coupling to the Ricci curvature of the type $M^2_{\rm pl}(1+\xi \sigma^n/M_{\rm pl}^n) $ alleviates the existing tension between local measurements of the Hubble constant and its inference from CMB anisotropies and baryonic acoustic oscillations data in presence of a cosmological constant. In these models, the expansion history is modified compared to $\Lambda$CDM at early time, mimicking a change in the effective number of relativistic species, and gravity weakens after matter-radiation equality. Compared to $\Lambda$CDM, a quadratic ($n=2$) coupling increases the Hubble constant when {\em Planck} 2018 (alone or in combination with BAO and SH0ES) measurements data are used in the analysis. Negative values of the coupling, for which the scalar field decreases, seem favored and consistency with Solar System can be naturally achieved for a large portion of the parameter space without the need of any screening mechanism. We show that our results are robust to the choice of $n$, also presenting the analysis for $n=4$.
Comment: 11 pages, 4 figures, 3 tables; v2 references added, minor changes, accepted for publication in PRD