We now turn to the future. Will the universe last forever? Or will it someday stop expanding and collapse?

As superclusters move apart in the expanding universe, their mutual gravitational attractions act on one another and thereby slow the rate at which they separate. If that were all that mattered in determining the fate of the universe, you could simply locate and add up all of the visible and (presently) dark matter in existence and see if the mutual gravitational force acting between all the components is enough to eventually stop the expansion.

This process is analogous to what engineers do in calculating, for example, how high a cannonball shot upward from the surface of Earth will travel. Earth’s gravitational force slows the ball’s ascent. If the cannonball’s speed upward is less than the escape velocity from Earth’s gravity (about 11 km/s or 7 mi/s straight up), it will fall back to Earth. If the ball’s speed exceeds the escape velocity, it will leave Earth and continue outward forever, despite the relentless pull of Earth’s gravity. On the boundary between these two scenarios is the situation when the cannonball’s speed equals the escape velocity. In that case, the cannonball will just barely escape falling back to Earth, slowing forever, and come to rest an infinite distance away at an infinite time in the future.

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By analogy with the cannonball fired from Earth, it would seem that if the universe is expanding too slowly to overcome the mutual gravitational attraction of its parts, it should stop expanding and someday collapse. If it is expanding at exactly its escape velocity, it should expand until coming to a stop an infinite time in the future. Or if it is expanding fast enough, it should slow down but continue to expand forever. However, none of these options is correct!

The laws of physics pertaining to the evolution of the universe, as spelled out in the theory of general relativity and in recent observations of distant objects, reveal that reality is more complex than this simple analogy. Just when astronomers were getting comfortable with the idea that the gravitational force is always attractive, general relativity once again showed that reality ignores our common sense by demonstrating that either gravity has a repulsive component or, equivalently, that there is a fifth force in nature that is repulsive on very large scales.

To understand the fate of the universe, we must consider two large-scale factors: the effect of matter on the shape of the universe and the presence of a universe-wide repulsive force named dark energy (not to be confused with dark matter). We begin by considering the effect that matter and energy have on the shape of the universe.

During the 1920s, Alexandre Friedmann in Russia, Georges Lemaître in Belgium, Willem de Sitter in the Netherlands, and Einstein himself applied the theory of general relativity to the expanding universe. General relativity predicts that the presence of matter curves the fabric of spacetime, as we saw in Chapters 12 and 13, in the form of gravitational lensing and the distortion of spacetime around black holes. Similarly, the presence of energy also curves spacetime—recall that matter and energy are related by E = mc².

Only three possibilities exist for the overall shape of the universe. These possibilities are determined by the amount of mass and energy the universe contains and how fast it is expanding. For example, imagine shining two powerful laser beams out into space. Suppose that we can align these two beams so that they are perfectly parallel as they leave Earth. Suppose, further, that nothing gets in the way of these two beams. We follow them across the spacetime whose shape we wish to determine. The light beams will begin to diverge due to the expanding universe carrying them apart. This effect happens regardless of any properties of the spacetime, and, because we are not interested in the effect of expansion right now, we compensate for it (that is, we ignore it) in what follows. The three possibilities for the paths of the laser beams, due to the actual curvature of the universe, are the following:

Most astronomers have come to believe that the universe is flat. The reason for this stems from the observations that the universe is homogeneous and isotropic. The only mechanism we have at present to explain these properties of the matter and energy distribution in space is inflation, as discussed earlier. However, the equations predict that if inflation occurred, it stretched the volume of the universe and the matter and energy in it so much that the universe must be very nearly flat.

Telescopic observations strongly support the belief that the universe is flat. This conclusion comes from examining the sizes of the regions of slightly higher and lower temperature in the cosmic microwave background (see Figure 14-15) and comparing them to the sizes predicted for a flat universe. The observations are consistent with the theoretical variations. Furthermore, if the universe had positive curvature, light from the hot regions of the early universe would be curved and thereby focused, creating bigger, brighter images than are observed. Figure 14-21 summarizes the effects of space curvature on observations of the cosmic microwave background.

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Until the past few years, there was a major inconsistency between the distribution of observed matter and energy in the universe and the flatness of space. Just as there is not enough visible matter to account for galaxies and clusters of galaxies that remain as bound systems, there is not enough observed matter and energy to account for a flat universe. Visible matter accounts for only 5% of the required mass. The cosmic microwave background photons add only 0.005% of the required gravitational effects needed for flatness, and calculations of the mass necessary to keep galaxies and clusters bound, combined with gravitational lensing by dark matter of distant galaxies and quasars, reveal that the dark matter known to exist accounts for only about 27% of the required mass. Therefore, the universe has only about 32% of the required mass and energy necessary to make it flat. Allowing for the errors that still exist in all of these observations, the possible range of mass and energy from all matter and photons in the universe is still between only 25% and 30% of that required for flatness. Yet flat it certainly appears to be.

By the mid-1990s, combined evidence of the microwave background and large-scale structure had forced astronomers to the conclusion that in order for the universe to be flat, the remaining energy must be a form of a dark energy with the remarkable feature that it causes the universe to accelerate outward. This energy is considered “dark” because we do not yet know what it is or where it originates.

Corroborating evidence for the existence of such dark energy was found in the recent observations of Type Ia supernovae in extremely distant galaxies (Figure 14-22). The light curves (see Section 12-2) for Type Ia supernovae (explosions of white dwarfs in binary star systems) are very well known. Studies show that these supernovae in nearby galaxies behave similarly to those observed in the Milky Way, regardless of their environment. Because they are so bright, such supernovae are excellent standard candles for determining distances to objects billions of light-years away. Assuming that supernovae in distant galaxies behave similarly to those in our Galaxy (an assumption that is now undergoing careful scrutiny), observations first made in 1998 revealed that the supernovae in distant galaxies appear dimmer than they would if the universe had been continually decelerating or even expanding at a constant speed. In other words, the universe is now expanding faster than it was, so the distant galaxies are farther away than they otherwise would have been if the expansion were slowing or continuing at a constant rate. The universe is accelerating outward. Figure 14-23 summarizes the major stages of cosmic evolution discussed in this chapter.

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There must be some kind of repulsive force acting to increase the rate at which superclusters separate today. Astronomers hypothesize that this is due to some kind of dark energy that has a repulsive gravitational effect, as mentioned earlier. Confirmation that dark energy exists came in 2003, when astronomers observed light from very distant galaxies passing through clusters of galaxies closer to us on its way toward Earth. As the distant light moved toward a cluster on its way to us, that light was gravitationally blueshifted, meaning the light gained energy as it was pulled toward the cluster. If there were no dark energy in a flat universe, then, as that light left the vicinity of the cluster, it would have been redshifted (lost energy) by exactly the same amount and come to us with the same wavelengths it would have had if it had never passed through the cluster.

However, if dark energy exists, then the universe is accelerating outward (expanding outward faster and faster). So the universe would have expanded more during the time that the light was leaving the cluster than when that light was first moving toward the cluster. The universe’s acceleration helps carry the departing photon away from the cluster, so the photon does not have to use as much energy leaving the cluster as it gained traveling toward it. Under those conditions, the light would have gained more energy from the cluster’s gravitational attraction while traveling toward the cluster than the light would have lost to that gravitational attraction as it was moving away from the cluster. In other words, the amount of blueshift that the light underwent falling into the cluster would be greater than the amount of redshift that it underwent leaving the vicinity of the cluster. This was precisely what astronomers discovered: The light from distant galaxies undergoes a net blueshift when it passes through clusters of galaxies on its way to us—the universe is accelerating outward.

Cosmological constantThere are presently two viable theoretical explanations for dark energy. Let us first consider what would happen if the cosmological constant that Einstein introduced and then rejected actually did exist. As Einstein had intended, it would provide a repulsive force to nature. The energy associated with that force would appear in the vacuum of space. The cosmological constant form of vacuum energy has the property of contributing a constant repulsive gravitational force that competes with the normal attractive gravitational force from matter and radiation that slows down the expansion. Which gravitational force wins depends on whether there is more vacuum energy or more matter and radiation.

As the universe expands, the average density of matter and energy decreases. In other words, on average there is less matter and energy in each cubic meter or yard of space every second than there was the second before. However, the density of energy created by the cosmological constant is unchanged—as the universe expands, the amount of vacuum energy in each cubic meter of space remains constant. If the universe is still expanding when the vacuum energy exceeds the matter and energy per unit volume, then the repulsive gravitational force would dominate and force the universe to start accelerating outward, as is observed.

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The concern that some astronomers express about the cosmological constant is that the repulsive force it creates has just the right strength to have allowed the universe to slow down for several billion years and then to slowly cause it to accelerate outward, as seen today. To explain this apparent coincidence would require fine-tuning the ratio of the vacuum energy to the matter and radiation to a remarkably high degree of precision. Scientists do not yet have a good reason why the repulsion created by a cosmological constant is not, say, a hundred times greater, in which case structure throughout the universe, such as stars and galaxies, would not have formed yet, or a billion times less, in which case the repulsive effects of the cosmological constant would be negligible today.

QuintessenceDespite these concerns, observations of distant Type Ia supernovae suggest that the outward force acting on the universe is nearly constant, consistent with the dark energy being created by the physics we characterized with the cosmological constant. However, these observations do not yet rule out the major competing theory of dark energy, called quintessence. Scientists are exploring a variety of mathematical descriptions of quintessence. Quintessence differs from the vacuum energy associated with the cosmological constant in that the energy of quintessence is not constant but changes slowly with the expansion of the universe and can also be changed by the flow of energy and matter through the universe. Because it can change, quintessence need not have been fine-tuned to a strength that makes the universe flat and creates just the slight acceleration we are seeing. Instead, it could have started out with some arbitrary strength and then been adjusted by physical properties of the universe to match the growth of the universe.

As the universe grew, the energy in quintessence would eventually come to dominate the gravitational energy from matter. If this took place a few billion years ago, quintessence would have begun exerting a negative gravitational force and so the universe would have begun accelerating.

The unexpected discovery that the universe is accelerating outward completely alters astronomers’ perspectives about the fate of the cosmos. This discovery tells us that the universe will expand forever. At the same time, it neatly solves the mystery of why the universe is flat, as required by the occurrence of inflation in the early universe. Dark energy provides the remaining 68% of the energy needed to account for the universe being flat. The contributions of all of its major components to the mass and energy in the universe are shown in Figure 14-24, with details listed in Appendix L: Mass and Energy Inventory for the Universe.

We have seen that our present understanding of the laws of nature is incomplete, especially in that our theories do not explain the nature of the universe during the Planck era (or why the universe began in the first place). Driven by these challenges, scientists have begun to develop superstring theories that may resolve these issues. Discovery 14-1: Superstring Theory and M-Theory is intended to give you a brief introduction to them and what they now predict.