ANISOTROPIES IN THE COSMIC MICROWAVE BACKGROUND - THEORETICAL FOUNDATIONS

The analysis of anisotropies in the cosmic microwave background (CMB) has become an extremely valuable tool for cosmology. We even have hope s that planned CMB anisotropy experiments may revolutionise cosmology. Together with determinations of the CMB spectrum, they represent the first cosmological precision, measurements. This is illustrated in the talk by Anthony Lasenby. The value of CMB anisotropies lies to a big part in the simplicity of the theoretical analysis. Fluctuations in th e CMB can be determined almost fully within linear cosmological pertur bations theory and are not severely influenced by complicated nonlinea r physics. In this contribution the different physical processes causi ng or influencing anisotropies in the CMB are discussed. The geometry perturbations at and after last scattering, the acoustic oscillations in the baryon-photon-plasma prior to recombination, and the diffusion damping during the process of recombination. The perturbations due to the fluctuating gravitational held, the so called Sachs-Wolfe contribu tion, is described in a very general form using the Weyl tensor of the perturbed geometry.