We study the morphology of the cosmic microwave background temperature and polarization fields using the shape and alignment parameters, β and α, that are constructed from the contour Minkowski tensor. The primary goal of our paper is to understand the effect of weak gravitational lensing on the morphology of the CMB fields. In order to isolate different physical effects that can be potentially confused with the effect of lensing, we first study the effect of varying the cosmology on α and β, and show that they are relatively insensitive to variation of cosmological parameters. Next we analyze the signatures of hemispherical anisotropy, and show that information of such anisotropy in α gets washed out at small angular scales and become pronounced only at large angular scales. For β we find characteristic distortions which vary with the field threshold. We then study the effect of weak gravitational lensing using simulations of lensed temperature and E and B modes. We quantify the distortion induced in the fields across different angular scales. We find that lensing makes structures of all fields increasingly more anisotropic as we probe down to smaller scales. We find distinct behaviour of morphological distortions as a function of threshold for the different fields. The effect is small for temperature and E mode, while it is significantly large for B mode. Further, we find that lensing does not induce statistical anisotropy, as expected from the isotropic distribution of large scale structure of matter. We expect that the results obtained in this work will provide insights on the reconstruction of the lensing potential.

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The small but measurable effect of weak gravitational lensing on the cosmic microwave background radiation provide information about the large-scale distribution of matter in the universe. We use the all sky distribution of matter, as represented by the convergence map that is inferred from CMB lensing measurement by Planck survey, to test the fundamental assumption of Statistical Isotropy (SI) of the universe. For the analysis we use the α statistic that is devised from the contour Minkowski tensor, a tensorial generalization of the scalar Minkowski functional, the contour length. In essence, the α statistic captures the ellipticity of iso-field contours at any chosen threshold value of a smooth random field and provides a measure of anisotropy. The SI of the observed convergence map is tested against the suite of realistic simulations of the convergence map provided by the Planck collaboration. We first carry out a global analysis using the full sky data after applying the galactic and point sources mask. We find that the observed data is consistent with SI. Further we carry out a local search for departure from SI in small patches of the sky using α. This analysis reveals several sky patches which exhibit deviations from simulations with statistical significance higher than 95% confidence level (CL). Our analysis indicates that the source of the anomalous behaviour of most of the outlier patches is inaccurate estimation of noise. We identify two outlier patches which exhibit anomalous behaviour originating from departure from SI at higher than 95% CL. Most of the anomalous patches are found to be located roughly along the ecliptic plane or in proximity to the ecliptic poles.