A minimal power-spectrum-based moment expansion for CMB B-mode searches

TL;DR

This paper introduces a power-spectrum-based moment expansion method to model polarized foregrounds in CMB B-mode searches, reducing biases and uncertainties in estimating the tensor-to-scalar ratio r, especially for large sky surveys.

Contribution

The paper presents a novel, minimal-parameter moment expansion technique for foreground modeling in power-spectrum analysis, improving bias mitigation in B-mode polarization measurements.

Findings

Successfully unbiased estimate of r with .003 uncertainty in simulations

Upper bound r<0.06 (95% C.L.) from BICEP2/Keck data

Method compatible with existing forecasts and other analysis approaches

Abstract

The characterization and modeling of polarized foregrounds has become a critical issue in the quest for primordial $B$-modes. A typical method to proceed is to factorize and parametrize the spectral properties of foregrounds and their scale dependence (i.e. assuming that foreground spectra are well described everywhere by their sky average). Since in reality foreground properties vary across the Galaxy, this assumption leads to inaccuracies in the model that manifest themselves as biases in the final cosmological parameters (in this case the tensor-to-scalar ratio $r$). This is particularly relevant for surveys over large fractions of the sky, such as the Simons Observatory (SO), where the spectra should be modeled over a distribution of parameter values. Here we propose a method based on the existing ``moment expansion'' approach to address this issue in a power-spectrum-based analysis that is directly applicable in ground-based multi-frequency data. Additionally, the method uses only a small set of parameters with simple physical interpretation, minimizing the impact of foreground uncertainties on the final $B$-mode constraints. We validate the method using SO-like simulated observations, recovering an unbiased estimate of the tensor-to-scalar ratio $r$ with standard deviation $\sigma(r)\simeq0.003$, compatible with official forecasts. When applying the method to the public BICEP2/Keck data, we find an upper bound $r<0.06$ ($95\%\,{\rm C.L.}$), compatible with the result found by BICEP2/Keck when parametrizing spectral index variations through a scale-independent frequency decorrelation parameter. We also discuss the formal similarities between the power spectrum-based moment expansion and methods used in the analysis of CMB lensing.