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. There is even hope that planned CMB anisotropy experiments may revolutionize cosmology. Together with determinations of the CMB spectrum, they represent the first precise cosmological measurements. The value of CMB anisotropies lies in large part in the simplicity of the theoretical analysis. Fluctuations in the CMB can be determined almost fully within linear cosmological perturbation theory and are not severely influenced by complicated nonlinear physics. In this contribution the different physical processes causing 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 field, the so-called Sachs-Wolfe contribution, is described in a very general form using the Weyl tensor of the perturbed geometry.