A foreground model independent estimation of joint posterior of CMB E-mode polarization over large angular scales

Abstract

The advent of precision cosmology has led to a very accurate observational data. In order to extract cosmological information, we therefore need robust and accurate Cosmic Microwave Background (CMB) reconstruction techniques with reliable statistical error estimates associated with them. We show the performance of our algorithm using simulations of the future Probe of Inflation and Cosmic Origins (PICO) missions. To generate samples from the joint distribution, we employ the internal linear combination (ILC) technique with prior information of CMB E-mode covariance matrix augmented by a Gibbs sampling technique of Sudevan and Saha 2020. We estimate the marginalized densities of [Formula: see text] and [Formula: see text] using the samples from full-posterior. The best-fit cleaned E-mode map and the corresponding angular power spectrum are consistent with the input E-mode map and the sky power spectrum implying accurate reconstruction. Using the samples [Formula: see text] of all Gibbs chains, we estimate the likelihood function [Formula: see text]) of any arbitrary [Formula: see text] given simulated observed maps (data, D) of PICO mission using a Blackwell–Rao estimator. The likelihood function can be seamlessly integrated to the cosmological parameter estimation method. Apart from producing an accurate estimate of E-mode signal over large angular scales, our method also builds a connection between the component reconstruction and reliable cosmological parameter estimation using CMB E-mode observations over large angular scales. The entire method does not assume any explicit models for E-mode foreground components in order to remove them, which is an attractive property since foreground modeling uncertainty does not pose as a challenge in this case.