[In 1922 as Einstein tried to alter his Theory of Relativity to conform to the preconceived model of a static universe, Russian physicist and mathematician Alexander] Friedmann made two very simple assumptions about the universe: that the universe looks identical in whichever direction we look [meaning that it contains a roughly uniform distribution of stars in every direction] and that this would be true if we were observing the universe from anywhere else. [Based on these two assumptions, Friedman created a model of an expanding universe wherein all galaxies were moving away from each other with no center of expansion.]
Friedmann derived only one model of the universe. But if his assumptions are correct, there are actually three possible types of solutions to Einstein’s equations, that is three different kinds of Friedmann models – and three different ways the universe can behave.
In the first kind of solution (which Friedman found), the universe is expanding sufficiently slowly that the gravitational attraction between the different galaxies causes the expansion to slow down and eventually stop. The galaxies then start to move toward each other, and the universe contracts. In the second kind of solution, the universe is expanding so rapidly that the gravitational attraction can never stop it [and so the universe is in an infinite state of expansion]. Finally there is a third kind of solution, in which the universe is expanding only just fast enough to avoid collapse. The speed at which the galaxies are moving apart gets smaller and smaller, but it never quite reaches zero.
A remarkable feature of the first kind of Friedmann model is that in it the universe is not infinite in space, but neither does space have any boundary. Gravity is so strong that space is bent round itself. This is rather like the surface of the earth, which is finite, but has no boundary. If you keep traveling in a certain direction on the surface of the earth, you never come up against an impassable barrier or fall over the edge, and you eventually come back to where you started. In this model space is just like this, but with three dimensions instead of two for the earth’s surface.
Friedmann derived only one model of the universe. But if his assumptions are correct, there are actually three possible types of solutions to Einstein’s equations, that is three different kinds of Friedmann models – and three different ways the universe can behave.
In the first kind of solution (which Friedman found), the universe is expanding sufficiently slowly that the gravitational attraction between the different galaxies causes the expansion to slow down and eventually stop. The galaxies then start to move toward each other, and the universe contracts. In the second kind of solution, the universe is expanding so rapidly that the gravitational attraction can never stop it [and so the universe is in an infinite state of expansion]. Finally there is a third kind of solution, in which the universe is expanding only just fast enough to avoid collapse. The speed at which the galaxies are moving apart gets smaller and smaller, but it never quite reaches zero.
A remarkable feature of the first kind of Friedmann model is that in it the universe is not infinite in space, but neither does space have any boundary. Gravity is so strong that space is bent round itself. This is rather like the surface of the earth, which is finite, but has no boundary. If you keep traveling in a certain direction on the surface of the earth, you never come up against an impassable barrier or fall over the edge, and you eventually come back to where you started. In this model space is just like this, but with three dimensions instead of two for the earth’s surface.
-From A Brief History of Time, by Stephen Hawking
