Searching for primordial magnetism with multifrequency cosmic microwave background experiments

Bounds on the amplitude of a scale-invariant stochastic primordial magnetic field (PMF) can be significantly improved by measurements of the Faraday rotation (FR) of cosmic microwave background polarization. The mode-coupling correlations induced by FR make it possible to extract it from cross-correlations of the B-mode polarization with the E-mode and the temperature anisotropy. In this paper, we construct an estimator of the rotation measure that appropriately combines measurements of the FR from multiple frequency channels. We study the dependence of the signal-to-noise ratio in the PMF detection on the resolution and the noise of the detectors, as well as the removal of the weak lensing contribution and the Galactic FR. We show that a recently proposed space-based experiment Polarized Radiation Imaging and Spectroscopy Mission can detect magnetic fields of 0.1 nG strength at a 2 Sigma level. Higher detection levels can be achieved by reducing the detector noise and improving the resolution or increasing the number of channels in the 30-70 GHz frequency range.