B polarization of the CMB from Faraday rotation

C. SCOCCOLA; D. HARARI; S. MOLLERACH

PHYSICAL REVIEW D - PARTICLE AND FILDS

American Physical Society

Año: 2004 vol. 70 p. 1 - 9

0556-2821

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 $u=30$ GHz. The strength of B-modes produced by Faraday rotation scales as $B_0/u^2$. We evaluate also the depolarizing effect of Faraday rotation upon the cross correlation between temperature anisotropy and E-type polarization.