Debiasing cosmological parameters from large-scale foreground contamination in Cosmic Microwave Background data

TL;DR

This work tackles foreground residual contamination as a key source of bias in estimating the primordial tensor-to-scalar ratio $r$ from CMB $B$-mode polarization. It introduces a model-independent pipeline that constructs a cleaned template of foreground residuals using GNILC and propagates it through the component-separation weights, embedding the foreground template spectrum into the cosmological likelihood via an amplitude parameter $A_{f}$. The method yields unbiased $r$ estimates across LiteBIRD-like simulations and multiple component-separation approaches, at the cost of modestly increased uncertainty due to marginalization. By enabling robust debiasing and leveraging larger sky fractions, the approach has practical implications for future CMB polarization experiments and can be integrated with various data-processing pipelines (e.g., BROOM) to improve cosmological inferences from $B$-mode data.

Abstract

Current and future Cosmic Microwave Background (CMB) experiments aim to achieve high-precision reconstruction of the CMB polarization signal, with the most ambitious objective being the detection of primordial $B$ modes sourced by cosmic inflation. Given the expected low amplitude of the signal, its estimate-parametrized by the tensor-to-scalar ratio $r$-is highly susceptible to contamination from Galactic foreground residuals that remain after component separation. In this work, we introduce a model-independent procedure to construct a spectral template of residual foreground contamination in the observed angular power spectrum. Specifically, a cleaned multifrequency set of foreground-emission maps is blindly reconstructed from the observed data using the Generalized Needlet Internal Linear Combination (GNILC) technique. These maps are then combined with the weights adopted for CMB reconstruction, yielding an estimate of the spatial distribution of foreground residuals after component separation. The power spectrum of this estimated residual map is incorporated into the spectral model of the cosmological likelihood. We validate the proposed method using realistic simulations of a LiteBIRD-like experiment processed with two Internal Linear Combination (ILC) component-separation techniques, focusing on constraints on the tensor-to-scalar ratio. When the foreground contribution is not included in the model, the resulting $r$ posteriors are biased, irrespective of its input value, the assumed foreground model, or the adopted masking strategy. Conversely, when the residual template is included in the likelihood, the analysis yields unbiased estimates of $r$ for all considered cases, thereby demonstrating the robustness of the proposed procedure. The pipeline has been made publicly available as part of the BROOM Python package (https://github.com/alecarones/broom).

Figures (6)

• Figure 1: Harmonic needlet filters used in the component separation step (left) and in the GNILC derivation of the multifrequency cleaned foreground maps (right). Both configurations employ mexican-hat needlet bands mexican_needlets.
• Figure 2: Flowchart of the pipeline used to process each simulated data set, leading to the derived average observed and model angular power spectra, which are then used as inputs to the cosmological likelihood in Equation \ref{['eq:like']}.
• Figure 3: Angular power spectra, averaged over $100$ realizations, of the noise residuals (dotted lines), foreground residuals (solid lines) and denoised template of foreground residuals (dashed lines, obtained with Equation \ref{['eq:cl_templ']}). Left and right panels report results for NILC and (MC-)NILC, respectively. Orange and red lines correspond to results obtained when GAL60 and GAL40 masks are used to compute angular power spectra. The reported results refer to the case where input $r=0$. The grey shaded area denotes the range of primordial tensor CMB $B$-mode power spectra corresponding to tensor-to-scalar ratio values $r\in [0.004,0.01]$.
• Figure 4: Posterior distributions of the tensor-to-scalar ratio derived from the average observed angular power spectrum after applying NILC (top) and (MC-)NILC (bottom) to simulated data sets with the d1s1 foreground model and input CMB signals with $r=0$ (left), $r=0.004$ (center), and $r=0.01$ (right). In these cases, no contribution from foreground residuals is included in the spectral model, as defined in Equation \ref{['eq:model_1']}. The vertical black dashed lines indicate the input nonzero values of the tensor-to-scalar ratio.
• Figure 5: Two-dimensional and one-dimensional posteriors ($r$ and $A_{f}$, shown in the top and right sub-panels of each panel, respectively) obtained from sampling the likelihood of Equation \ref{['eq:like']} when the spectral template of foreground residuals is included in the model of Equation \ref{['eq:model_2']}. The top and bottom rows correspond to the application of NILC and (MC-)NILC, respectively, to the simulated d1s1 data set. Different input values of the tensor-to-scalar ratio are shown: $r=0$ (left), $r=0.004$ (center), and $r=0.01$ (right). The vertical black dashed lines indicate the input nonzero values of the tensor-to-scalar ratio.