Current and Future Constraints on Primordial Magnetic Fields

Abstract: We present new limits on the amplitude of potential primordial magnetic fields (PMFs) using temperature and polarization measurements of the cosmic microwave background (CMB) from Planck, BICEP2/Keck Array, POLARBEAR, and SPTpol. We reduce twofold the 95% CL upper limit on the CMB anisotropy power due to a nearly-scale-invariant PMF, with an allowed B-mode power at $\ell=1500$ of $D_{\ell=1500}^{BB} < 0.071 \mu K^2$ for Planck versus $D_{\ell=1500}^{BB} < 0.034 \mu K^2$ for the combined dataset. We also forecast the expected limits from soon-to-deploy CMB experiments (like SPT-3G, Adv. ACTpol, or the Simons Array) and the proposed CMB-S4 experiment. Future CMB experiments should dramatically reduce the current uncertainties, by one order of magnitude for the near-term experiments and two orders of magnitude for the CMB-S4 experiment. The constraints from CMB-S4 have the potential to rule out much of the parameter space for PMFs.