Constraining primordial magnetic fields with CMB polarization experiments

We calculate the effect that a primordial homogeneous magnetic field, ${\text{B}}_0$, will have on the different CMB power spectra due to Faraday rotation. Concentrating on the $TB$, $EB$ and $BB$ correlations, we forecast the ability for future CMB polarization experiments to constrain ${\text{B}}_0$. Our results depend on how well the foregrounds can be subtracted from the CMB maps, but we find a predicted error between ${\sigma }_{{\text{B}}_0}=4\times {10}^{-11}$Gauss (for the QUIET experiment with foregrounds perfectly subtracted) and $3\times {10}^{-10}$Gauss (with the Clover experiment with no foreground subtraction). These constraints are two orders of magnitudes better than the present limits on ${\text{B}}_0$.