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

TL;DR

This paper introduces a new set of generalized isotropic angular correlation functions derived from BipoSH formalism, enabling detailed analysis of statistical isotropy violations in CMB maps, which could reveal new cosmological insights.

Contribution

It develops a novel formalism of generalized angular correlation functions (mBipoSH) to quantify non-Statistical Isotropy features in CMB data, extending the BipoSH approach.

Findings

New mBipoSH functions effectively capture nSI features.

The formalism provides a compact, observable measure of SI violations.

Potential to identify physical effects or artifacts causing nSI.

Abstract

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.