Do the Early Galaxies observed by JWST disagree with Planck's CMB polarization measurements?

The recent observations from the James Webb Space Telescope have led to a surprising discovery of a significant density of massive galaxies with masses of $M \ge 10^{10.5} M_{\odot}$ at redshifts of approximately $z\sim 10$. This corresponds to a stellar mass density of roughly $\rho_*\sim 10^6 M_{\odot} Mpc^{-3}$. Despite making conservative assumptions regarding galaxy formation, this finding may not be compatible with the standard $\Lambda$CDM cosmology that is favored by observations of CMB Anisotropies from the Planck satellite. In this paper, we confirm the substantial discrepancy with Planck's results within the $\Lambda$CDM framework. Assuming a value of $\epsilon=0.2$ for the efficiency of converting baryons into stars, we indeed find that the $\Lambda$CDM model is excluded at more than $99.7 \%$ confidence level (C.L.). An even more significant exclusion is found for $\epsilon \sim 0.1$, while a better agreement, but still in tension at more than $95 \%$, is obtained for $\epsilon =0.32$. This tension, as already discussed in the literature, could arise either from systematics in the JWST measurements or from new physics. Here, as a last-ditch effort, we point out that disregarding the large angular scale polarization obtained by Planck, which allows for significantly larger values of the matter clustering parameter $\sigma_8$, could lead to better agreement between Planck and JWST within the $\Lambda$CDM framework. Interestingly, the model compatible with Planck temperature-only data and JWST observation also favors a higher Hubble constant $H_0=69.0\pm1.1$ km/s/Mpc at $68\%$ C.L., in better agreement with observations based on SN-Ia luminosity distances.