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 $H_0$, 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 $\ell \lesssim 30$ 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 $\Lambda$CDM model predictions. However, those 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 $H_0$ prior from Riess $et$ $al$, we find a $\sim 2\sigma$ hint of a positive running of 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 Universe age estimation using the oldest stars.