Cosmic microwave background anisotropies: Nonlinear dynamics - art. no. 083506

We develop a new approach to local nonlinear effects in cosmic microwave ba ckground anisotropies, and discuss the qualitative features of these effect s. New couplings of the baryonic velocity to radiation multipoles are found , arising from nonlinear Thomson scattering effects. We also find a new non linear shear effect on small angular scales. The full set of evolution and constraint equations is derived, including the nonlinear generalizations of the radiation multipole hierarchy, and of the dynamics of multi-fluids. Th ese equations govern radiation anisotropies in any inhomogeneous spacetime, but their main application is to second-order effects in a universe that i s close to the Friedmann models. Qualitative analysis is given here, and qu antitative calculations are taken up in further papers. [S0556-2821(99)0250 8-4].