Small-scale CMB 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 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 DASI and WMAP have detected evidence for CMBR polarization at small l. Many experiments will also probe the large $l$ regime. We therefore 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 B_{0}=3\times 10^{-9} Gauss, produces B-type polarization anisotropies of order 0.3 - 0.4 micro Kelvin between l of 1000-5000. 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 lambda-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.