Cosmological Alfv\'en waves in the recent CMB data, and the observational bound on the primordial vector perturbation

In the presence of the primordial magnetic field, initial vector (vorticity) perturbations produce cosmological Alfven waves and leave imprints on cosmic microwave background (CMB) temperature and polarization anisotropy. We have investigated imprints of cosmological Alfven waves in CMB anisotropy. For data constraints, we have used the power spectrum of the recent CMB observations, and correlations estimated from WMAP Internal Linear Combination (ILC) maps. Our analysis shows 3 sigma evidence of cosmological Alfven waves. Using the 3 sigma limit from our analysis and the Alfven velocity limit from the total energy density constraint, we impose a lower bound on the amplitude of primordial vector perturbation: 4*10^-12 at k_0=0.002/Mpc.