The cosmological model presented here rests on the postulate that the universe can be described as an interacting attraction (exerted by matter) and repulsion (exerted by the excitation energy of the quantum vacuum) system in virial equilibrium. The basic parameters of the model, the matter density and the excitation energy of the quantum vacuum are determined by observations and are not adjusted to the model. The model requires only a few assumptions that can be deduced from the laws of conventional physics and from the rules of quantum field theory. Existing problems in standard cosmology, such as the flatness and the horizon problems, among others, can be resolved in a straightforward way without inflation and without recourse to dark matter and dark energy.