The vacuum fluctuations of the gauge fields present during the inflationary stage of expansion may be amplified if conformal invariance is broken. It is then plausible that magnetic inhomogeneities are amplified not only at the scale of protogalactic collapse but also at larger length-scales. agnetic fields can be generated over all physical scales compatible Large-scale magnetic fields may then have various interesting implications on the physics of the CMB and of its anisotropies. The following possible effects have been discussed through the years:
distortion of the Planckian spectrum;
shift of the polarization plane (provided the CMB is linearly polarized);
shift in the position of the first Doppler peak;
generic increase of the amount of the (primary) anisotropy.
On top of these effects, magnetic fields can also modify the evolution of the tensor fluctuations of the geometry for typical length scales much smaller than the ones probed by CMB anisotropy experiments.
The possible distortions of the Planckian spectrum of CMB are usually discussed in terms of a chemical potential which is bounded, by experimental data, to me |µ| < 9 × 10-5. Magnetic field dissipation at high red-shift implies the presence of a chemical potential. Hence bounds on the distorsion of the Planckian spectrum of the CMB can be turned into bounds on the magnetic field strength at various scales. In particular [287] the obtained bound are such that B < 3 × 10-8 G for comoving coherence lengths between 0.4 kpc and 500 kpc.
Large scale magnetic fields can also afffect the poosition of the Doppler peak. In [288] this analysis has been performed in a non-relativistic approximation where the scalar perturbations of the geometry obey linearized Newtonian equations of motion. It has been found that, in this approximation, the effect of the presence of the magnetic fields is an effective renormalization of the speed of sound of the baryons.