Looking for Cosmological Alfven Waves inWilkinson Microwave Anisotropy ProbeData

A primordial cosmological magnetic field induces and supports vorticity or Alfvén waves, which in turn generate cosmic microwave background (CMB) anisotropies. A homogeneous primordial magnetic field with fixed direction induces correlations between the a l -1, m and a l +1, m multipole coefficients of the CMB temperature anisotropy field. We discuss the constraints that can be placed on the strength of such a primordial magnetic field using CMB anisotropy data from the Wilkinson Microwave Anisotropy Probe experiment. We place 3 σ upper limits on the strength of the magnetic field of B < 15 nG for vector perturbation spectral index n = -5 and B < 1.7 nG for n = -7.