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Constraints on Primordial Magnetic Fields from Planck combined with the South Pole Telescope CMB B-mode polarization measurements
Alex Zucca, Yun Li, Levon Pogosian
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A primordial magnetic field (PMF) present before recombination can leave specific signatures on the cosmic microwave background (CMB) fluctuations. Of particular importance is its contribution to the B-mode polarization power spectrum. Indeed, vortical modes sourced by the PMF can dominate the B-mode power spectrum on small scales, as they survive damping up to a small fraction of the Silk length. Therefore, measurements of the B-mode polarization at high-ℓ , such as the one recently performed by the South Pole Telescope (SPT), have the potential to provide stringent constraints on the PMF. We use the publicly released SPT B-mode polarization spectrum, along with the temperature and polarization data from the Planck satellite, to derive constraints on the magnitude, the spectral index and the energy scale at which the PMF was generated. We find that, while Planck data constrains the magnetic amplitude to B_(1 Mpc) < 3.3 nG at 95\% confidence level (CL), the SPT measurement improves the constraint to B_(1 Mpc) < 1.5 nG. The magnetic spectral index, n_B, and the time of the generation of the PMF are unconstrained. For a nearly scale-invariant PMF, predicted by simplest inflationary magnetogenesis models, the bound from Planck+SPT is B_(1 Mpc) < 1.2 nG at 95% CL. For PMF with n_B=2, expected for fields generated in post-inflationary phase transitions, the 95% CL bound is B_(1 Mpc) < 0.002 nG, corresponding to the magnetic fraction of the radiation density Ω_(Bγ) < 10⁻³ or the effective field B_(eff) < 100 nG. The patches for the Boltzmann code CAMB and the Markov Chain Monte Carlo engine CosmoMC, incorporating the PMF effects on CMB, are made publicly available.
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