ABSTRACT
General relativity provides the formalism to study the global evolution of the Universe. This problem — in principle extremely complex — is substantially simplified by requiring that the universe is isotropic and homogeneous. These assumptions at the foundation of modern cosmology were theoretically justified by the cosmological principle: in the universe there cannot be privileged positions or directions. These assumptions are supported by an overwhelming number of observations. This chapter presents the basic phenomenology of cosmological models as provided by the field equation of general relativity, extended to the case of a non-vanishing cosmological constant. It discusses radiation-dominated models. For a non-vanishing cosmological constant the space-time is intrinsically curved even in the absence of matter. The cosmological constant can be reinterpreted as the vacuum energy density, the zero-point quantum vacuum fluctuations of a fundamental scalar field. Adiabaticity is a necessary condition to keep the homogeneity and the isotropy required by the cosmological principle.
