Dipanshu | Searcharxiv

arXiv2024

Statistical Isotropy Violations in CMB Temperature Anisotropy: Analysis Using Minimal Bipolar Spherical Harmonics

In this work, we present a follow-up to our previous work where the concept of minimal Bipolar spherical harmonics (mBipoSH) functions was introduced as a natural basis for studying angular correlations in the non-statistical isotropic (nSI) Cosmic Microwave Background (CMB) sky. In this study, we extend the formalism of mBipoSH functions and apply it to analyze two sources of statistical isotropy (SI) violation-cosmic hemispherical asymmetry (CHA) and non-circular (NC) beam shapes. We present the analytical expression for mBipoSH functions and plot the corresponding angular correlation functions for these cases, addressing the $L=1$ and $L=2$ multipole statistical isotropy violations within the BipoSH basis. Our results confirm the effectiveness of the proposed approach, as it successfully captures and explains the observed angular correlations in the CMB sky.

astro-ph.CO↗

arXiv2023

Capturing Statistical Isotropy violation with generalized Isotropic Angular Correlation Functions of CMB Anisotropy

The exquisitely measured maps of fluctuations in the Cosmic Microwave Background (CMB) present the possibility to test the principle of Statistical Isotropy (SI) of the Universe through systematic observable measures for non-Statistical Isotropy (nSI) features in the data. Recent measurements of the CMB temperature field provide tantalizing evidence of the deviation from SI. A systematic approach based on strong mathematical formulation allows any nSI feature to be traced to known physical effects or observational artefacts. Unexplained nSI features could have immense cosmological ramifications for the standard model of cosmology. BipoSH (Bipolar Spherical Harmonics) provides a general formalism for quantifying the departure from statistical isotropy for a field on a 2D sphere. We adopt a known reduction of the BipoSH functions, dubbed Minimal Harmonics (Manakov et al. 1996). We demonstrate that this reduction technique of BipoSH leads to a new generalized set of isotropic angular correlation functions (mBipoSH) that are observable quantifications of nSI features in a sky map. We show that any nSI feature in the CMB map captured by BipoSH at the bipolar multiple $L$ with projection $M$ can be studied by $(L+1)$ mBipoSH angular correlation functions in case of even parity and by $L$ functions in case of odd parity. We present in this letter a novel observable quantification of deviation from statistical isotropy in terms of generalized angular correlation functions that are compact and complementary to the BipoSH spectra that generalize angular power spectrum CMB fluctuations.

astro-ph.CO↗