Limits on Cosmological Magnetic Fields and Other Anisotropic Stresses

We discuss the cosmological evolution of matter sources with small anisotropic pressures. This includes electric and magnetic fields, collisionless relativistic particles, gravitons, antisymmetric axion fields in low-energy string cosmologies, spatial curvature anisotropies, and stresses arising from simple topological defects. In many interesting cases the evolution displays a special critical behaviour created by the non-linear evolution of the pressure and expansion anisotropies. The COBE microwave sky maps are used to place strong limits of order Ωa0 ≤ 5 × 10∆ (1 + zrec) on the possible contribution of these matter sources to the total density of the universe, where 1 ≤ ∆ ≤ 3 characterises the anisotropic stress. In the case of cosmological magnetic fields this translates into a present-day bound of B0 < 3.4 × 10 (Ω0h250) 1 2Gauss. We explain why the limits obtained from primordial nucleosynthesis are generally weaker than those imposed by the microwave background isotropy. The effect of inflation on all these stresses is also calculated.