Study of the shape and alignment of lensed CMB and large scale structure inferred from the CMB using Minkowski Tensors

Abstract

The large scale structure in the universe causes arcminute angular scale deflections of the paths of CMB photons, leading to blurring of the acoustic peaks and correlations between different modes. This effect can be exploited to reconstruct the matter distribution in the universe, or equivalently the lensing potential map, integrated along the line of sight. The aim of this thesis is to carry out a careful investigation of the imprint of the large scale structure on the CMB fields, and the morphology of the matter distribution inferred from the observed CMB data. This thesis begins with an introduction to the field of CMB lensing and CMB lensing reconstruction. Then in the third chapter we introduce the morphological descriptors, namely Minkowski functionals and Minkowski Tensors used in our analysis. As the first step we study the effect of gravitational lensing on the morphology of the intensity patterns of the CMB temperature and polarization fields using Minkowski tensors (MT). We calculate the distortion of the CMB patterns at different angular scales which are manifested as magnification and shearing, by measuring the alignment and shape parameters, α and β that are constructed from the MTs. We demonstrate that lensing makes all structures of the fields increasingly more anisotropic as we probe down to smaller scales. Further, we find that lensing does not induce statistical anisotropy of the fields, which shows consistency with the isotropic distribution of matter on large scales. This work constitutes the fourth chapter of this thesis. Next, in the fifth chapter we test the statistical isotropy of the universe using the reconstructed lensing potential data from a global as well as local perspective. This analysis is vital in the wake of the detection of CMB anomalies in the data of concluded and ongoing CMB missions. From the global analysis we find that the matter distribution is consistent with statistical isotropy of the universe. From the local analysis we identify several anomalous sky patches in the observed matter distribution which exhibit levels of alignment that are significantly higher than expected from isotropic fields having the same power spectrum. In the last part of the work we clarify the geometrical meaning of statistical isotropy and extend the analytic calculation of MTs to anisotropic Gaussian random fields. We also calculate the signatures of local type primordial non-Gaussianity on the MTs. Our results will be useful for accurate searches for non-Gaussianity and departure from isotropy using high precision cosmological datasets.