Cosmological limits on slightly skew stresses

We present an analysis of 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. We calculate their evolution during the radiation and dust eras of an almost isotropic universe. In many interesting cases the evolution displays a special critical behavior created by the nonlinear evolution of the pressure and expansion anisotropies. The isotropy of the microwave background is used to place strong limits of order Omega(a0)less than or equal to 5x10(-6)Delta(1+z(rec))(-Delta) on the possible contribution of these matter sources to the total density of the universe, where 1 less than or equal to Delta less than or equal to 3 characterizes the anisotropic stress. The present abundance of an anisotropic stress which becomes nonrelativistic at a characteristic low-energy scale is also calculated. 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 these stresses is also calculated.