Search for a new measure to quantify violation of statistical isotropy in the CMB

Abstract

Studying the Cosmic Microwave Background (CMB) is one of the most significant ways to gain insight into the physics of the early Universe. Having an accurate knowledge of the early Universe is crucial to our understanding of the current Universe and how it evolves. It is thus essential to interpret the CMB data correctly and efficiently. One of the ways in which the CMB is currently analysed is through the angular power spectrum, which is derived from a spherical harmonic decomposition of the temperature field. While that works perfectly fine in the case of a statistically isotropic Universe, it lacks significantly while analysing violation of statistical isotropy. Hajian and Souradeep [1] proposed the Bipolar Spherical Harmonic (BipoSH) formalism as a natural generalisation of the angular power spectrum in the absence of the assumed statistical isotropy in cosmology. Manakov et al. [2] further proposed the minimal BipoSH formalism in the context of scattering cross sections in atomic processes where a general BipoSH function can be written in terms of a certain set of BipoSH functions called minimal harmonics. This thesis is an investigation into the properties of the minimal BipoSH formalism and speculations on the impact it can have on speeding up the analysis of CMB data.

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