Theories of the Universe: The Alpha and the Omega

The Alpha and the Omega

Now that we know that gravity, entropy, and the second law of thermodynamics all play a role in defining the fate of the universe in big bang theory, let's put it all together and look at the three possible fates of the universe. I've already mentioned two—the big chill and the big crunch—but there is a third alternative as well. Let's get a little more into the role of the scientist and view this whole process and all three possible scenarios in ideas and concepts that cosmologists use.

When discussing the gravitational energy of the universe as a whole, there is a direct correlation to the mass density of the universe: the higher the mass density of the universe or an object, the greater the gravitational energy. For example, a neutron star is a very compact star that is created when the core of a very massive star collapses. A neutron star can have a mass similar to that of the sun, but a radius that is seventy thousand times smaller. Consequently, gravity near the surface of the neutron star is about five billion times stronger than near the surface of the Sun.

The gravitational energy of the universe is precisely equal to its kinetic energy (the energy an object possesses by virtue of its motion) for a particular value of the mass density in the universe. This value, which separates eternal expansion from eventual contraction, is called the critical density. If the density in the universe is higher than the critical density, gravity will prevail; the expansion will stop and contraction will occur. If the density is lower than the critical density, the universe will continue to expand forever. The third scenario is a borderline state between the big crunch and the big chill. In this case, when the kinetic energy exactly equals the gravitational energy (in other words, when the mass density is exactly equal to the critical density) the expansion still proceeds forever, but the speed at which the universe is expanding approaches zero as time progresses.

In physics, as you've seen before, a Greek letter is used to denote this ratio of the actual density to the critical density. The letter used is omega, Ω. Omega is the twenty-fourth and final letter of the Greek alphabet, an appropriate symbol in this case. So using this letter as cosmologists do when they talk about how the universe will end, eventual contraction and the big crunch correspond to a value of omega larger than one. Or in other words, the ratio of the mass density to the critical density is greater than one. If the universe expands forever for eternity, the value of omega will be less than one. This means that the ratio of the mass density to the critical density will be less than one. And in a universe that expands forever, but has a speed that slowly approaches zero, omega will be exactly equal to one. In this case, the ratio of the mass density to the critical density is equal.

The Need for Dark Matter

Therefore, in order to answer the question about the ultimate fate of the universe, we need to determine the present value of omega, or in other words, determine whether the density of the mass in our universe is higher than, lower than, or equal to the critical value. It sounds simple, doesn't it? Well this is where support for the concept of dark matter comes in. It seems that without this hypothetical mass there just isn't enough matter in the universe to account for the gravitational forces that are holding the galaxies and superclusters together, so the universe would go on expanding forever. Without the presence of dark matter, the overall density of the universe (mass density) is 100 times smaller than the critical density, which would give us a value of omega less than 0.01. That figure is too small and doesn't agree with other values for omega that have been estimated.

There are several methods that have been employed by astronomers to determine omega. I'll give you an idea of how one of them works. From the speeds of gaseous clouds around the center of individual galaxies and the speeds of galaxies in clusters and superclusters, astronomers have established that the dark matter overweighs the luminous matter by a factor of 10 or more. So, the value of omega inferred from the gravitational dynamics in clusters and superclusters is about 0.2 to 0.3. This is not the official estimate however. As it turns out, omega has been inferred to be equal to one, and the lower values, it is thought, only represent an inability in the methods used to uncover all the dark matter that exists. The theory that was developed in support of an omega value of one is rather complicated and beyond the introductory scope, but it's important to note that even before the theory was developed, physicists expressed a strong prejudice favoring omega equals one, simply on the basis of aesthetics.

Living in the Flatlands

Gravity, the force that is the key ingredient in big bang cosmology is, as you've learned, also used to define the value of omega. Gravity is also employed to define the shape of the universe. As you'll see in a moment, there is a direct correlation between the shape of the universe and the value assigned to omega. In a universe that is closed, the value of omega is larger than one. In this model, the mass density is sufficiently high that gravity would stop the expansion and the universe will collapse back into itself. Geometrically, this corresponds to space-time with a spherical shape, in other words a big round ball. The mass density causes the space to curve back on itself. In such a universe, if you travel along a straight line, (which would really be a great circle) you would eventually return to the point from which you started. There are other strange features of this shape for a universe: Parallel lines eventually cross each other, the shortest distance between two points is not a straight line but a curve, and the sum of the three angles in a triangle is always more than 180 degrees. (There are always only 180 degrees in a triangle on a flat surface. And when airplanes fly great distances on the Earth, they never fly in a straight line; it's shorter to follow the upward or downward curve of the Earth.)

The second possibility is a universe that's open. This corresponds to a value of omega that is smaller than one. In this case the gravitational field is too weak to stop the expansion and the universe will expand forever. The geometrical shape of this type of universe is the opposite of the previous model. Instead of space-time curving back on itself and creating a finite volume, space curves away from itself in an open universe, which produces an infinite space. The shape can best be described as looking like a saddle. And of course, it would also have the opposite features of the sphere. Parallel lines would eventually diverge, the sum of the angles of a triangle would always be less than 180 degrees, and the shortest distance between two points is a hyperbola.

Our third possibility is that of a universe in which omega is precisely equal to 1. This, as you know, puts the universe on the borderline between eternal expansion and eventual collapse. It expands forever, but the speed at which it expands becomes closer and closer to 0. The geometric shape of this universe is flat. Yes, flat, just like a tabletop or wall. And in this case we have our familiar features: parallel lines stay parallel, there are always 180 degrees in the sum of the angles in a triangle, and the shortest distance between two points is a straight line. Does the fact that our everyday world reflects the geometry of flat space have anything to do with it being flat? Not really, it just makes it easier to understand.