Lensing-like tensions in the Planck legacy release

Abstract

We analyze the final release of the Planck satellite data to constrain the gravitational lensing potential in a model-independent manner. The amount of lensing determined from the smoothing of the acoustic peaks in the temperature and polarization power spectra is 2$\sigma$ too high when compared with the measurements using the lensing reconstruction and 2.8$\sigma$ too high when compared with $\Lambda$CDM expectation based on the "unlensed" portion of the temperature and polarization power spectra. The largest change from the previous data release is the $\Lambda$CDM expectation, driven by improved constraints to the optical depth to reionization. The anomaly still is inconsistent with actual gravitational lensing, given that the lensing reconstruction constraints are discrepant independent of the model. Within the context of $\Lambda$CDM, improvements in its parameter constraints from lensing reconstruction bring this tension to 2.1$\sigma$ and from further adding baryon acoustic oscillation and Pantheon supernova data to a marginally higher 2.2$\sigma$. Once these other measurements are included, marginalizing this lensing-like anomaly cannot substantially resolve tensions with low-redshift measurements of $H_0$ and $S_8$ in $\Lambda$CDM, $\Lambda$CDM+$N_\mathrm{eff}$ or $\Lambda$CDM+$\sum m_\nu$; furthermore the artificial strengthening of constraints on $\sum m_\nu$ is less than 20%.