The Covariant Perturbative Approach to Cosmic Microwave Background Anisotropies

The Ehlers-Ellis 1+3 formulation of covariant hydrodynamics, when supplemented with covariant radiative transport theory, gives an exact, physically transparent description of the physics of the cosmic microwave background radiation (CMB). Linearisation around a Friedmann-Robertson-Walker (FRW) universe provides a very direct and seamless route through to the linear, gaugeinvariant perturbation equations for scalar, vector and tensor modes in an almost-FRW model. In this contribution we review covariant radiative transport theory and its application to the perturbative method for calculating and understanding the anisotropy of the CMB. Particular emphasis is placed on the inclusion of polarization in a fully covariant manner. With this inclusion, the covariant perturbative approach offers a complete description of linearised CMB physics in an almost-FRW universe.