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.
