Cross-correlation between CMB B-modes and Faraday Rotation as a Novel Probe of Primordial Magnetic Fields
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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BibTeX
@misc{namikawa2026crosscorrelation,
title = {{Cross-correlation between CMB B-modes and Faraday Rotation as a Novel Probe of Primordial Magnetic Fields}},
author = {Toshiya Namikawa and Guanming Liang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32171},
eprint = {2609.32171},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32171},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cross-correlation between CMB B-modes and Faraday Rotation as a Novel Probe of Primordial Magnetic Fields
AU - Toshiya Namikawa
AU - Guanming Liang
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32171
UR - https://arxiv.org/abs/2609.32171
AB - 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.
ER -