In this chapter we develop some models of the universe. As a first approximation, consider the analogy of the Newtonian ball of self-gravitating particles.
Gravity acts to try to pull the ball together.
If the ball is expanding with sufficient velocity it can resist this collapse. We obtain a simple equation to describe the evolution of this Newtonian ball. Remarkably, the fully general relativistic solution for a universe consisting of smoothly distributed matter has the same form as the Newtonian solution. The equations that describe the evolution of the universe under the influence of its self-gravity are called the Friedmann equations. The three possible fates of the universe were seen to correspond to the three basic geometry types studied in Chapter 8.