Distinguishing Primordial Magnetic Fields from Inflationary Tensor Perturbations in the Cosmic Microwave Background

A claimed detection of cosmological tensor perturbations from inflation via B-mode polarization of the cosmic microwave background requires distinguishing other possible B-mode sources. One such potential source of confusion is primordial magnetic fields. For sufficiently low-amplitude B-mode signals, the microwave background temperature and polarization power spectra from power-law tensor perturbations and from a power-law primordial magnetic field are indistinguishable. However, we show that such a magnetic field will induce a small-scale Faraday rotation which is detectable using four-point statistics analogous to gravitational lensing of the microwave background. The Faraday rotation signal will distinguish a magnetic-field induced B-mode polarization signal from tensor perturbations for effective tensor-scalar ratios larger than 0.001, detectable in upcoming polarization experiments.