What is a cosmological model?

A cosmological model is a model of our universe which, taking into account and using all known physical laws, predicts (approximately) correctly the observed properties of the universe, and in particular explains in detail the phenomena in the early universe. Such a model must also explain inter alia why the universe was so homogeneous and isotropic at the epoch of last scattering of the cosmic microwave background, and how and when inhomogeneities (galaxies and stars) arose.

In a more restricted sense cosmological models are exact solutions of the Einstein field equations for a perfect fluid that reproduce the important features of our universe. Because there is only one actual universe the large number of known or possible cosmological models may at first seem surprising. There are, however, two reasons for this multiplicity.

Firstly, only a section of our universe is known, both in space and in time. All cosmological models which differ only near the origin of the universe must be accepted for competition. In fact solutions are known which are initially inhomogeneous or anisotropic to a high degree, and which then increasingly come to approximate a Friedmann universe. All cosmological models which yield a redshift and a cosmic background radiation can hardly be refuted. The possibility cannot be excluded that our universe is not homogeneous and isotropic, but has those properties only approximately in our neighbourhood. An expanding ‘dust star’, that is, a section of a Friedmann universe which is surrounded externally by a static Schwarzschild metric (the model of a collapsing star discussed in Section 36.3), may also perhaps be an excellent model of the universe.