  Einstein's General Theory of Relativity enables cosmologists to understand how the contents of our universe determine what kind of universe we observe, but the theory requires a high level of mathematical sophistication to understand it. Luckily, there is an easier way to comprehend the results of the theory at a much lower level of math by using a fundamental principle of physics, energy conservation: energy cannot be created or destroyed but only converted from one form to another.

We know that the universe contains matter, and we also know that this matter is often in motion. But what prevents a moving ball, a ball that has been tossed upwards, for example, from escaping into space? Gravity, of course, pulls the ball back down to earth before it can escape. The energy of motion is called kinetic energy (KE) and it is always positive. The gravity trap is called gravitational potential energy (GPE); it is always negative and it depends inversely on the ball's distance from the earth's center. These two forms of energy combine to give constant total energy so that the ball's energy is conserved:

`(kinetic energy of ball) + (gravitational potential energy of ball) = (total energy)`

Three possible values for the ball's total energy—positive, negative, or zero—also happen to correspond to three possible values for the total energy of any universe. When the positive KE dominates the negative GPE (positive total energy), the ball escapes the earth's surface. Compare this to the graph for expansion of the zero matter and zero dark energy universe. When the negative GPE dominates the KE (negative total energy), the ball reaches a maximum height then falls to earth, analogous to the behavior of the closed universe graphs. And when the total energy is zero, the ball barely escapes the earth, comparable to expansion of the flat universes, including the one where we live (red curve). But note that if the dark energy were negative, closed universes would be possible. (The CDF player may take a couple of minutes to load.)

#### Requires the Free Wolfram CDF Player dsmith@scsu.edu, South Carolina State University, 06/27/2012