Tensions between direct measurements of the lens power spectrum from Planck data

We apply a recently developed method to directly measure the gravitational lensing power spectrum from CMB power spectra to the Planck satellite data. This method allows us to analyze the tension between the temperature power spectrum and lens reconstruction in a model independent way. Even when allowing for arbitrary variations in the lensing power spectrum, the tension remains at the 2.4$\sigma$ level. By separating the lensing and unlensed high redshift information in the CMB power spectra, we also show that under $\Lambda$CDM the two are in tension at a similar level whereas the unlensed information is consistent with lensing reconstruction. These anomalies are driven by the smoother acoustic peaks relative to $\Lambda$CDM at $\ell \sim 1250 - 1500$. Both tensions relax slightly when polarization data are considered. This technique also isolates the one aspect of the lensing power spectrum that the Planck CMB power spectra currently constrain and can be straightforwardly generalized to future data when CMB power spectra constrain multiple aspects of lensing which are themselves correlated with lensing reconstruction.