As the universe expands, its parts pull on one another owing to gravitational attraction, and this slows down the expansion. The competition between the outward motion of expansion and the inward pull of gravity leads to three possibilities for the ultimate fate of the universe. The universe may expand forever, with its outward motion always overwhelming the inward pull of gravity, in the way that a rock thrown upward with sufficient speed will escape the gravity of the earth and keep traveling forever. Such a universe is called an open universe. A second possibility is that the inward force of gravity is sufficiently strong to halt and reverse the expansion, just as a rock thrown upward with insufficient speed will reach a maximum height and then fall back to the earth. A universe of this type, called a closed universe, reaches a maximum size and then starts collapsing, toward a reverse big bang. This universe grows smaller and hotter, and has both a beginning and an end in time. The final possibility, called a flat universe, is analogous to a rock thrown upward with precisely the minimum speed needed to escape from the pull of the earth. A flat universe, like an open universe, keeps expanding forever. Meanwhile, stars and galaxies evolve, heavy elements are synthesized, radioactive decay transmutes elements, and the universe grows colder and colder.
The Big Bang model allows all three possibilities. Which one holds for our universe depends on how the cosmic expansion began, in the same way that the path of the rock depends on the rock's initial speed relative to the strength of the earth's gravity. For the rock, the critical initial speed is 7 miles per second. Rocks thrown upward with less than this speed will fall back to the earth; rocks with greater initial speed will never return. Likewise, the fate of the universe was, according to the Big Bang model, determined by its initial rate of expansion relative to its gravity. Even without knowledge of these initial conditions, however, we can infer the fate of our universe by comparing its current rate of expansion to its current average density. If the density is greater than a critical value, which is determined by the current rate of expansion, then gravity dominates; the universe is closed, fated to collapse at some time in the future. If the density is less than the critical value, the universe is open. If it is precisely equal to the critical value, the universe is flat. The ratio of the actual density to the critical density is called omega. Thus the universe is open, flat, or closed depending on whether omega is less than 1, equal to 1, or larger than 1, respectively.
Omega can be measured. According to the best current measurements, the critical density of the universe, as determined by the rate of expansion, is equivalent to a few atoms of hydrogen in a box a meter on a side, roughly the density achieved by spreading the mass of a postage stamp through a sphere about the size of the earth. The average density of all the matter we can detect by its radiation or by its gravitational effect is about one-tenth this critical value.