Conrad Hewitt - Three dimensional symmetry groups in cosmology

We consider spacetimes which admit a two-dimensional Abelian group of isometries together with an additional symmetry. These models may be classified according to the action of this Abelian subgroup, and the causal nature of the element of transitivity surface.

There are two cases of particular interest in cosmology. The first case arises when the additional symmetry is also an isometry and the resulting group orbits are spatially homogeneous. The simplest subclass is formed by the orthogonal spatially homogeneous models, in which the cosmological fluid lies orthogonal to the group orbits. In the second case, the additional symmetry is a homothety and the resulting group orbits are timelike. The simplest subclass arises when the cosmological fluid flow is tangential to the group orbits.

The Einstein field equations for all of these models may be written as an autonomous system of ordinary differential equations. A qualitative description of their properties can be given using the theory of dynamical systems.