Exploring Statistical Isotropy Violations in the CMB sky: Real-Space Analysis

Abstract

Observations of cosmic microwave background (CMB) anisotropies have been instrumental in advancing modern cosmology. The availability of high-resolution CMB maps has significantly enhanced our understanding of the universe’s origin, dynamics, and components. The exquisitely measured maps of fluctuations in the CMB present the possibility of systematically testing the principle of statistical isotropy of the Universe. The isotropy of the CMB has been a subject of close scrutiny since the release of full-sky CMB data from missions like COBE, WMAP, and Planck. There are compelling reasons to investigate the isotropic nature of the universe. A systematic approach based on strong mathematical formulation allows any non-statistical isotropic (nSI) feature to be traced to the nature of physical effects or observational artifacts. Bipolar spherical harmonics (BipoSH) representation has emerged as an overarching general formalism for quantifying the departures from statistical isotropy for a field on a 2D sphere. The BipoSH coefficients extend the traditional CMB angular power spectrum, offering deeper insights into the early universe. The detection of non-zero BipoSH coefficients suggests a potential violation of isotropy. Statistical isotropy, which quantifies the isotropic nature of the universe studied through isotropic angular correlation function, plays a critical role in these studies. In this thesis, we study a natural generalization of the well-known isotropic angular correlation function that can also capture nSI features in random maps on a 2-sphere. We utilize a reduction technique for BipoSH that results in new basis functions called mBipoSH functions. In this new basis, new measures quantifying nSI features emerge as an additional set of the real space angular correlation functions that we refer to as mBipoSH angular correlation functions. ix In the specific domain of our interest, which involves the detailed study of observed maps depicting the anisotropy in the CMB, these maps offer a new set of observables in real space that complement the harmonic space BipoSH representation used earlier in the literature. Introducing new approaches often helps shed new light on the nature of the phenomena underlying the observed nSI signals. As an illustrative example, we derive and plot the mBipoSH angular correlation functions for the well-known nSI effects induced in CMB maps due to the Doppler boost, Cosmic hemispherical asymmetry and Non-circular beam cases. We emphasize that the work presented in this thesis can be effectively employed in the wider context to investigate random distributions on a 2D sphere, encompassing diverse applications ranging from celestial sky maps to geographical maps.