15-6 The shape of the universe indicates its matter and energy content

Go to Video 15-4

We have seen that by following the mass densities of radiation and matter, we can learn about the evolution of the universe. But it is equally important to know the combined mass density of all forms of matter and energy. (In an analogous way, an accountant needs to know the overall financial status of a company, not just individual profits or losses.) Remarkably, we can do this by investigating the overall shape of the universe.

The Curvature of the Universe

Einstein’s general theory of relativity explains that gravity curves the fabric of space. Furthermore, the equivalence between matter and energy, expressed by Einstein’s equation E = mc2, tells that either matter or energy produces gravity. Thus, the matter and energy scattered across space should give the universe an overall curvature. The degree of curvature depends on the combined average mass density of all forms of matter and energy. Thus, by measuring the curvature of space, we should be able to learn about the content of the universe as a whole.

To see what astronomers mean by the curvature of the universe, imagine shining two powerful laser beams out into space so that they are perfectly parallel as they leave Earth. Furthermore, suppose that nothing gets in the way of these two beams, so that we can follow them for billions of light-years as they travel across the universe and across the space whose curvature we wish to detect. There are only three possibilities:

Figure 15-17 illustrates the three cases of flat, closed, and open. Real space is three-dimensional, but we have drawn the three cases as analogous, more easily visualized two-dimensional surfaces. Therefore, as you examine the drawings in Figure 15-17, remember that the real universe has one more dimension. For example, if the universe is in fact open, then the geometry of space must be the (difficult-to-visualize) three-dimensional analog of the two-dimensional surface of a saddle.

Figure 15-17: The Geometry of the Universe The shape of the universe is either (a) closed, (b) flat, or (c) open. The curvature depends on whether the combined density of all mass and energy is greater than, equal to, or less than a critical value that is “just right.” In theory, such a curvature could be determined by seeing whether two laser beams initially parallel to each other would converge, remain parallel, or spread apart.

Note that in accordance with the cosmological principle, none of these models of the universe has an “edge” or a “center.” This is clearly the case for both the flat and open universes, because they are infinite and extend forever in all directions. Alternatively, a closed universe is finite, but it also lacks a center and an edge. You could walk forever around the surface of a closed spherical shape (like the surface of Earth if you could walk on the oceans) without ever finding a center or an edge.

The shape of the universe is determined by the value of a combined density of mass and energy for the universe. If this value is large, then the universe is closed. Alternatively, if it is small, then the universe is open. In the special case that the combined density of mass in the universe is “just right,” then the universe is flat. To help you get a sense for what would be “just right,” a sample of hydrogen gas with this perfect density would contain just 6 hydrogen atoms per cubic meter—that’s not much!

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A way to determine the curvature of the universe that is both practical and precise is to see if light rays bend toward or away from each other, as shown in Figure 15-17. The greater the distance a pair of light rays has traveled, and, hence, the longer the time the light has been in flight, the more pronounced any such bending should be. Therefore, astronomers test for the presence of such bending by examining the oldest radiation in the universe: the cosmic microwave background.

When carefully observing the cosmic microwave background, astronomers have discovered that there are localized “hot spots” due to density variations in the early universe. The apparent size of these hot spots depends on the curvature of the universe (Figure 15-18). If the universe is closed, the bending of light rays from a hot spot will make the spot appear larger (Figure 15-18a); if the universe is open, the light rays will bend the other way and the hot spots will appear smaller (Figure 15-18c). Only in a flat universe will the light rays travel along straight lines, so that the hot spots appear with their true size (Figure 15-18b).

Figure 15-18: RIVUXG The Cosmic Microwave Background and the Curvature of Space Temperature variations in the early universe appear as “hot spots” in the cosmic microwave background. The apparent size of these spots depends on the curvature of space.

By calculating what conditions were like in the early universe, astrophysicists find that in a flat universe, the dominant “hot spots” in the cosmic background radiation should have an angular size of about 1°. This is just what the BOOMERANG and MAXIMA experiments observed, and what the WMAP observations have confirmed (see Figure 15-13). Hence, the curvature of the universe must be very close to zero, and it appears that our universe must either be flat or very nearly so.

This brings us to a curious problem. If we add the total amount of known energy and matter in the universe, including dark matter, together they account for only 24% of the total amount in the observed universe! The dilemma is this: What could account for the rest? The source of the missing amount must be some unexpected form of energy that we cannot detect from its gravitational effects (the technique astronomers use to detect dark matter). It must also not emit detectable light of any kind. We refer to this mysterious energy as dark energy. We do not know what it is, but whatever dark energy is, it accounts for 76% of the contents of the universe!

The concept of dark energy is actually due to Einstein. When he proposed the existence of a cosmological constant, he was suggesting that the universe is filled with a form of energy that by itself tends to make the universe expand. Unlike gravity, which tends to make objects attract, the energy associated with a cosmological constant would provide a form of “antigravity.” Hence, it would not be detected in the same way as matter. These ideas concerning dark energy are extraordinary, and extraordinary claims require extraordinary evidence to confirm them. As we will see in the next section, a crucial test is to examine how the rate of expansion of the universe has evolved over the eons.

Question

ConceptCheck 15-13: If you could start walking in a straight line around planet Earth and return to your exact starting point, would you categorize Earth as a flat, closed, or open world?

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