The Friedman World Models

Abstract

Einstein realised that, in GeneralRelativity, he had discovered a theory which enabled fully self-consistent models for the Universe as a whole to be constructed. The standard models contain three essential ingredients:

– The cosmological principle, which, combined with the observations that the Universe is isotropic, homogeneous and uniformly expanding on a large scale, leads to the Robertson–Walker metric (5.33).

– Weyl’s postulate, according to which theworld lines of particlesmeet at a singular point in the finite or infinite past. This means that there is a unique world line passing through every point in space–time. The fluid moves along streamlines in the universal expansion and so behaves like a perfect fluid for which the energy–momentum tensor is given by the T^αβ of (6.33).

– General Relativity, which enables us to relate the energy–momentum tensor to the geometrical properties of space–time through (6.47) or (6.48).