Excess of lensing amplitude in the Planck CMB power spectrum

Precise measurements of the Planck cosmic microwave background (CMB) angular power spectrum (APS) at small angles have stimulated accurate statistical analyses of the lensing amplitude parameter $A_{L}$. To confirm if it satisfies the value expected by the flat-$\Lambda$CDM concordance model, i.e. $A_{L} = 1$, we investigate the spectrum difference obtained as: the difference of the measured Planck CMB APS and the Planck best-fit $\Lambda$CDM APS model. To know if this residual spectrum corresponds to statistical noise or if it has a hiden signature that can be accounted for with a larger lensing amplitude $A_{L} > 1$, we apply the Ljung-Box statistical test and find, with high statistical significance, that the spectrum difference is not statistical noise. This spectrum difference is then analysed in detail using simulated APS, based on the Planck $\Lambda$CDM best-fit model, where the lensing amplitude is a free parameter. We explore different binnations of the multipole order \,$\ell$\, and look for the best-fit lensing amplitude parameter that accounts for the spectrum difference in a $\chi^2$ procedure. We find that there is an excess of signal that is well explained by a $\Lambda$CDM APS with a non-null lensing amplitude parameter $A_{lens}$, with values in the interval $[0.10,0.29]$ at 68\% confidence level. Furthermore, the lensing parameter in the Planck APS should be $1 + A_{lens} > 1$ at $\sim 3 \sigma$ of statistical confidence. Additionally, we perform statistical tests that confirm the robustness of this result. Important to say that this excess of lensing amplitude, not accounted in the Planck's flat-$\Lambda$CDM model, could have an impact on the theoretical expectation of large-scale structures formation once the scales where it was detected correspond to these matter clustering processes.