B polarization of the CMB from Faraday rotation

CLAUDIA SCÓCCOLA; DIEGO HARARI; SILVIA MOLLERACH

PHYSICAL REVIEW D

AMER PHYSICAL SOC

Lugar: New York; Año: 2004 vol. 70 p. 630031 - 630039

1550-7998

We study the effect of Faraday rotation due to a uniform 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 uniform 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.