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arXiv · 2609.32171

Cross-correlation between CMB B-modes and Faraday Rotation as a Novel Probe of Primordial Magnetic Fields

Toshiya Namikawa·Guanming Liang
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Abstract

We investigate the cross-bispectrum between the cosmic microwave background (CMB) $B$-mode polarization and two Faraday rotation (FR) angles as a new probe of primordial magnetic fields (PMFs). Assuming Gaussian PMFs with both non-helical and helical components, we derive the $Bαα$ bispectrum and decompose it into parity-even and parity-odd contributions. The mixed non-helical--helical contribution appears in the parity-even sector, whereas the purely non-helical and purely helical contributions contribute to the parity-odd sector. This parity dependence provides sensitivity to PMF helicity that is absent in the FR power spectrum alone. We then forecast the detectability of the cross-bispectrum for SO-like and LiteBIRD-like CMB experiments, and find that future observations can probe PMFs with amplitudes at the sub-nG level. The $Bαα$ bispectrum is dominated by the helicity-sensitive parity-even sector and provides a promising avenue for constraining both the amplitude and helicity of PMFs.

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Toshiya Namikawa, Guanming Liang. 2026-09-26. Cross-correlation between CMB B-modes and Faraday Rotation as a Novel Probe of Primordial Magnetic Fields. https://arxiv.org/abs/2609.32171

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