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 fields, can then be potentially important contributors to CMBR temperature and polarization anisotropies at small angular scales, corresponding to multipoles with $ l>1000$ or so. Indeed the recently detected excess power at large $l$ by the CBI experiment, could have a contribution from such magnetic modes. Polarization anisotropies can be used to distinguish the magnetic contribution from more conventional sources. In particular, unlike conventional signals, tangled magnetic fields lead to CMBR polarization dominated by the odd parity, B-type signal. Recently, E-type polarization has been detected by the DASI experiment, and T-E correlations by DASI and WMAP, albeit at smaller $l$. Several experiments are also expected to probe the large $l$ regime. In view of this observational focus, we determine the predicted polarization signals due to primordial tangled 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 $\sim 0.3 - 0.4\mu K$ between $l\sim 1000-5000$. 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