Bayesian inference on the sphere beyond statistical isotropy

TL;DR

This paper introduces a Bayesian method using Bipolar Spherical Harmonics to analyze and quantify violations of statistical isotropy in CMB sky maps, accounting for physical effects and observational artifacts.

Contribution

It presents a novel Bayesian framework for inferring non-isotropic covariance structures on the sphere, adaptable to physical models and capable of assessing SI violations in CMB data.

Findings

Successfully recovers input SI violation signals in simulated maps

Provides full posterior distributions for BipoSH spectra

Demonstrates applicability to Doppler boost parameter inference

Abstract

We present a general method for Bayesian inference of the underlying covariance structure of random fields on a sphere. We employ the Bipolar Spherical Harmonic (BipoSH) representation of general covariance structure on the sphere. We illustrate the efficacy of the method as a principled approach to assess violation of statistical isotropy (SI) in the sky maps of Cosmic Microwave Background (CMB) fluctuations. SI violation in observed CMB maps arise due to known physical effects such as Doppler boost and weak lensing; yet unknown theoretical possibilities like cosmic topology and subtle violations of the cosmological principle, as well as, expected observational artefacts of scanning the sky with a non-circular beam, masking, foreground residuals, anisotropic noise, etc. We explicitly demonstrate the recovery of the input SI violation signals with their full statistics in simulated CMB maps. Our formalism easily adapts to exploring parametric physical models with non-SI covariance, as we illustrate for the inference of the parameters of a Doppler boosted sky map. Our approach promises to provide a robust quantitative evaluation of the evidence for SI violation related anomalies in the CMB sky by estimating the BipoSH spectra along with their complete posterior.