Small-scale cosmic microwave background polarization anisotropies due to tangled primordial magnetic fields

Tangled, primordial cosmic magnetic fields create small rotational velocity perturbations on the last scattering surface (LSS) of the cosmic microwave background radiation (CMBR). Such perturbations can contribute significantly to the CMBR temperature and polarization anisotropies at large l > 1000 or so, like the excess power detected by the Cosmic Background Imager (CBI) experiment. The magnetic contribution can be distinguished from most conventional signals, as they lead to CMBR polarization dominated by the odd-parity, B-type signal. Experiments like the Degree Angular Scale Interferometer (DASI) and the Wilkinson Microwave Anisotropy Probe (WMAP) have detected evidence for CMBR polarization at low l. Many experiments will also probe the large l regime. Therefore we calculate the polarization signals due to primordial magnetic fields for different spectra and different cosmological parameters. A scale-invariant spectrum of tangled fields which redshifts to a present value of B₀= 3 × 10⁻⁹ G produces B-type polarization anisotropies of ∼0.3–0.4 μK between l∼ 1000 and 5000. Larger signals result if the spectral index of magnetic tangles is steeper, n > −3. The peak of the signal shifts to larger l for a Λ-dominated universe or if the baryon density is larger. The signal will also have non-Gaussian statistics. We also predict the much smaller E-type polarization and T–E cross-correlations for these models.