Morphology of CMB fields -- effect of weak gravitational lensing
  We study the morphology of the cosmic microwave background temperature and
polarization fields using the shape and alignment parameters, $\beta$ and
$\alpha$, 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 $\alpha$ and $\beta$, 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 $\alpha$ gets washed out at small angular
scales and become pronounced only at large angular scales. For $\beta$ 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.
