Large-scale CMB temperature and polarization cross-spectra likelihoods

TL;DR

This paper introduces a cross-spectra based likelihood approach for analyzing large-scale CMB data to improve constraints on reionization, primordial perturbations, and tensor-to-scalar ratio, effectively handling noise and systematics.

Contribution

It develops a novel cross-spectra likelihood method with two solutions for non-Gaussianity, validated on realistic simulations, enhancing large-scale CMB analysis accuracy.

Findings

Validated likelihoods on simulations with realistic noise levels

Effectively eliminate noise bias and residual systematics

Handle multipole and mode correlations in combined temperature and polarization data

Abstract

We present a cross-spectra based approach for the analysis of CMB data at large angular scales to constrain the reionization optical depth $\tau$, the tensor to scalar ratio $r$ and the amplitude of the primordial scalar perturbations $A_s$. With respect to the pixel-based approach developed so far, using cross-spectra has the unique advantage to eliminate spurious noise bias and to give a better handle over residual systematics, allowing to efficiently combine the cosmological information encoded in cross-frequency or cross-dataset spectra. We present two solutions to deal with the non-Gaussianity of the $\hat{C}_\ell$ estimator distributions at large angular scales: the first one relies on an analytical parametrization of the estimator distribution, while the second one is based on modification of the Hamimache\&Lewis likelihood approximation at large angular scales. The modified HL method (oHL) is powerful and complete. It allows to deal with multipole and mode correlations for a combined temperature and polarization analysis. We validate our likelihoods on numerous simulations that include the realistic noise levels of the \wmap, \planck-LFI and \planck-HFI experiments, demonstrating their validity over a broad range of cross-spectra configurations.