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 WMAP experiment .
We place 3 \sigma 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 .