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B polarization of the CMB from Faraday rotation

Claudia Scoccola·Diego Harari·Silvia Mollerach
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Abstract

We study the effect of Faraday rotation due to a homogeneous magnetic field on the polarization of the cosmic microwave background (CMB). Scalar fluctuations give rise only to parity-even E-type polarization of the CMB. However in the presence of a magnetic field, a non-vanishing parity-odd B-type polarization component is produced through Faraday rotation. We derive the exact solution for the E and B modes generated by scalar perturbations including the Faraday rotation effect of a uniform magnetic field, and evaluate their cross-correlations with temperature anisotropies. We compute the angular autocorrelation function of the B-modes in the limit that the Faraday rotation is small. We find that primordial magnetic fields of present strength around $B_0=10^{-9}$G rotate E-modes into B-modes with amplitude comparable to those due to the weak gravitational lensing effect at frequencies around $ν=30$ GHz. The strength of B-modes produced by Faraday rotation scales as $B_0/ν^2$. We evaluate also the depolarizing effect of Faraday rotation upon the cross correlation between temperature anisotropy and E-type polarization.

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Claudia Scoccola, Diego Harari, Silvia Mollerach. 2004-10-18. B polarization of the CMB from Faraday rotation. https://doi.org/10.1103/physrevd.70.063003

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