Observational effects of a running Planck mass

We consider observational effects of a running effective Planck mass in the scalar-tensor gravity theory. At the background level, an increasing effective Planck mass allows a larger Hubble constant H₀, which is more compatible with the local direct measurements. At the perturbative level, for cosmic microwave background (CMB) anisotropies, an increasing effective Planck mass (i) suppresses the unlensed CMB power at 30 via the integrated Sachs-Wolfe effect and (ii) enhances CMB lensing power. Both effects slightly relax the tension between the current CMB data from the Planck satellite and the standard model predictions. However, these impacts on the CMB secondary anisotropies are subdominant, and the overall constraints are driven by the background measurements. Combining CMB data from the Planck satellite and an H₀ prior from Riess et al. , we find a 2 hint of a positive running of the effective Planck mass. However, the hint goes away when we add other low-redshift observational data including type Ia supernovae, baryon acoustic oscillations, and an estimation of the age of the Universe using the old stars.