Constraints on Newton's Constant from Cosmological Observations
  Newton's constant has observational effects on both the CMB power spectra and
the light curves of SNIa. We use Planck data, BAO data and the SNIa measurement
to constrain the varying Newton's constant $G$ during the CMB epoch and the
redshift ranges of PANTHEON samples, and find no evidence indicating that $G$
is varying with redshift. By extending the $\Lambda$CDM model with one free
parameter $G$, we get $G =(6.65635_{-0.18560}^{+0.18766} ) \times 10^{-11} \rm
m^3kg^{-1}s^{-2}$ and $H_0=67.62^{+1.24}_{-1.25} $ km s$^{-1}$ Mpc$^{-1}$ at
68$\%$ C.L. from Planck$+$BAO$+$uncalibrated PANTHEON. The results show the
value of $G$ is consistent with CODATA 2018, but the $H_0$ tension can't be
solved in this way.
