Inference of $B$-mode polarization in the presence of non-Gaussian foregrounds

TL;DR

This work tackles the challenge of extracting primordial $B$-mode signals in CMB polarization when confronted with non-Gaussian foregrounds arising from spatially varying SEDs and PMF-induced B-modes. It develops and validates two complementary inference pipelines: a map-space constrained MILC ($\text{cMILC}$) that suppresses spatial SED fluctuations, and a power-spectrum-based moment-expansion framework that models foregrounds up to second order in SED perturbations. Through extensive end-to-end simulations and mock datasets, the study demonstrates that cMILC07 can nearly remove foreground residuals in map space, while the multifrequency power-spectrum approach can jointly constrain $r$, the lensing amplitude, and PMF strength with mitigated degeneracy when including PMF vector modes and extending $\ell_{ m max}$. The results also show that the $EB$ cross-spectrum is robust to foreground non-Gaussianity, and cross-validation with PySM and PICO/LiteBIRD mocks supports the reliability of both methods for future high-sensitivity, multifrequency CMB polarization experiments. Overall, the paper provides practical, rigorous strategies for separating cosmological $B$-modes from complex Galactic foregrounds and PMF signals, informing the design and analysis of next-generation CMB missions.

Abstract

The inflationary $B$-mode signals encode invaluable information about the origin of our Universe and searching for potential signatures of primordial gravitational waves (PGWs) is one of the major science goals for future precision observations of cosmic microwave background (CMB) polarization. However, dominant $B$-mode signals of both Galactic foreground contamination and gravitational lensing effects prevent direct measurements of the PGW $B$-mode signals. There are existing proposals which can effectively eliminate these two contaminants but issues remain for future high-sensitivity and multifrequency CMB polarization observations, such as spatially-varying spectral energy distribution (SED) of polarized foreground and cosmological $B$-mode signals due to primordial magnetic fields (PMFs). In this work, we investigate inference of PGW $B$-mode signals in the presence of both complexities. We employ a constrained moment internal linear combination (cMILC) method to remove polarization signals arising from spatially varying SEDs. Also, we employ a power-spectrum-based approach to extracting both the Galactic and cosmological $B$-mode components. Two methods have been validated by mock data and different consistency tests have been performed. We apply these two methods to end-to-end simulations for future high-sensitivity and multifrequency polarization observations and investigate the detectability of different $B$-mode signals in the presence of non-Gaussian polarized foregrounds under different scenarios. This study will be important for new physics studies with $B$-mode signatures.

Figures (14)

• Figure 1: A representative plot for different $B$-mode components as described in Eq. (\ref{['fghigherALL']}). Power spectra of the polarized foregrounds are calculated at 150 GHz. The $B$-mode power spectra of the primordial gravitational waves (PGWs) and the primordial magnetic fields (PMFs) have similar power-spectrum shapes at large angular scales at $\ell<200$. Moreover, the spatial variations of the spectral energy distribution (SED) can also generate higher-order $B$-mode signals with similar descending features. The $y$-axis denotes $D_{\ell}=\ell(\ell+1)/(2\pi)C_{\ell}$.
• Figure 2: Posterior distribution functions of CMB and foreground parameters. The mock power spectra (mock data 2 in Table \ref{['simtype']})) are used for the Bayesian analysis described in Eq. (\ref{['bayesian']}). The two component CMB model $r+A_{\rm lens}$ is inferred in the presence of polarized foreground using the power-spectrum-based method.
• Figure 3: Posterior distributions functions of foreground and cosmological parameters. This test shows the impact of different multipole ranges.
• Figure 4: Power-spectrum components described in Eq. (\ref{['fghigherALL']}). The power spectra are calculated at seven frequencies, i.e., $\nu$={20, 50, 100, 150, 250, 300, 350} GHz. The components labeled with "total" refer to all the power-spectrum components defined in Eq. (\ref{['fghigherALL']}).
• Figure 5: Different $E$-mode and $B$-mode components at 150 GHz. Maps are filtered by a top-hat window at $2\leq l\leq 300$ in Fourier space to visualize the large-scale modes.