The nonpolarized points (NPP) of the $Q$ and $U$ Stokes parameters of the CMB can be classified according to the geometry of the polarization field. We describe a procedure to identify these points in the pixelized sky and present the shape of the polarization angles in the vicinity of NPPs. We design a test of Gaussianity using the Kullback-Leibler divergence. We show that the total number density of nonpolarized points of the E and B families is closely related to the presence of lensing and the tensor-to-scalar ratio $r$. We further show that in the absence of lensing, the total number of NPPs of all types does not depend on $r$, while the lensing effect removes this degeneracy. This analysis is applied to the CMB maps from the 2018 Planck release. We show that there is a general consistency of SMICA and NILC maps compared to a reference set of Gaussian simulations. The strongest discrepancies are found in the Commander (with corresponding $p$ value 0.07) and SEVEM ($p=0.01$) maps.

• Received 27 January 2021
• Accepted 4 May 2021

DOI:https://doi.org/10.1103/PhysRevD.104.023502