We will use Newtonian versions of solutions to the Einstein field equations to describe a series of model universes that provide a framework within which we can better understand how our Universe works. Newton's theory of gravitation has been replaced by Einstein's, but in many respects Newton's theory is a pretty good approximation: good enough that we depend on it in our everyday lives. The Newtonian view is certainly easier for us to relate to and exploit, but we must understand the inherent limitations.

Here, we highlight the fundamental differences between the Newtonian and Einsteinian theories: Newton with his absolute space and universal time, and Einstein with his geometrisation of gravity. Fortunately, there are some relevant solutions of the Einstein equations that have direct Newtonian analogues. Those Newtonian analogues are lacking some important features, notably a lack of a description of how light propagates. Fortunately, we can graft the information from some of the Einstein models onto the Newtonian models to produce what we might call Newtonian surrogates of the Einsteinian models.

In this chapter we introduce the simplest of a series of homogeneous and isotropic cosmological models formulated within the limited framework of Newtonian gravity. These models contains only ‘dust’: pressure free matter made up of particles that are neither created nor destroyed, and that do not interact with one another. The Universe evolves under the mutual gravitational interaction of those particles.

While this model is not realistic it nevertheless allows us to develop a full cosmological model that is the template for the more complex models that follow. We develop these models in considerable detail since much of what is done will be repeated for the other, more realistic, models.

It is worth remarking that these models are fundamental to numerical N-body simulations of the Universe in which the constituent particles are ‘dust’. Such dust models can also be used to study the growth of the structure in the Universe.