Figure 8.4. Scalar field rolls down the slope of a “topless” energy hill.
Here I should stop to clarify the terminological confusion that bedevils this subject. “Eternal inflation” is often confused with “chaotic inflation,” although the two are very different. “Chaotic” refers to a chaotic initial state and has nothing to do with the eternal character of inflation. Linde showed that chaotic inflation can also be eternal, but that’s where the connection ends. For clarity, in the rest of this book I will limit the discussion to the original inflation model with a flattened energy hill. Eternal inflation on a topless hill is similar.
Linde’s paper on eternal inflation was published three years after mine and was met with as much enthusiasm.4 But his reaction was different. He stuck to his guns, continued this line of research, and gave numerous talks on the subject. Still, the physics community was not swayed by his efforts. It took nearly two decades before the fortunes of eternal inflation started to turn.
9
The Sky Has Spoken
What is now proved was once only imagined.
—WILLIAM BLAKE
The theory of inflation was little more than a speculative hypothesis when Alan Guth proposed it in 1980. But by the end of the 1990s it was well on its way to becoming one of the cornerstones of modern cosmology. New observational data were coming in, confirming the predictions of the theory, at times in a rather unexpected way.
RETURN OF THE COSMOLOGICAL CONSTANT
The most straightforward prediction of inflation is that the observable region of the universe should have a flat, Euclidean geometry. The universe as a whole may well be spherical, or have a more complicated shape, but our horizon encompasses only a tiny part of it, so we cannot distinguish it from flat. As we discussed in Chapter 4, this statement is equivalent to saying that the average density of the universe should be equal to the critical density with a very high accuracy.
In the early days of inflation, astronomers viewed this prediction with a high degree of skepticism. Ordinary matter, consisting of protons, neutrons, and electrons, adds up to only a few percent of the critical density. There is also a much larger amount of what is called dark matter, made up of some unknown particles. As its name suggests, the dark matter cannot be seen directly, but its presence is manifested by the gravitational pull it exerts on visible objects. Observations of how stars and galaxies move indicate that the mass in dark matter is about ten times greater than that in ordinary matter. Still, putting it all together, the total mass density of the universe comes out to be about 30 percent of the critical density, 70 percent short of the target.
This is where things stood until 1998, when two independent teams announced a startling discovery.1 They measured the brightness of supernova explosions in distant galaxies and used the data to figure out the history of cosmic expansion.t To their great surprise, they found that instead of being slowed down by gravity, the speed of expansion is actually accelerating. This finding suggests that the universe is filled with some gravitationally repulsive stuff. The simplest possibility is that the true vacuum, which we now inhabit, has a nonzero mass density.u As we know, vacuum is gravitationally repulsive, and if its density is greater than half the average density of matter, the net result is repulsion.
The mass density of the true vacuum is what Einstein called the cosmological constant—the idea he denounced as his greatest blunder. It lay buried for nearly seventy years, but now it looks as though it was not such a bad idea after all. As we shall see later in this book, the sudden return of the cosmological constant led to a deep crisis in elementary particle physics. But for the theory of inflation it was a very welcome development. The mass density of the vacuum, evaluated from the rate of cosmic acceleration, amounts to about 70 percent of the critical density—precisely what is needed to make the universe flat!
This conclusion was later independently confirmed by observations of the cosmic microwave radiation. Rather than relying on Friedmann’s link between the geometry of the universe and its density, the microwave observations probe the geometry directly—in essence, by measuring the sum of the angles in a huge narrow triangle with one vertex on Earth and the other two at the points of emission of microwaves arriving to us from two nearby directions in the sky. (The longer sides of this triangle have lengths of about 40 billion light-years.) In flat space, the angles should add up to 180 degrees, as you might remember from your geometry class at school. A greater value of the sum of three angles would indicate a closed universe of spherical geometry (see Figure 9.1), and a smaller value would point to an open universe with the geometry of a saddle. The microwave observations showed that the sum of the angles is in fact very close to the flat-space answer. These results can be re-expressed in terms of the densities, using Friedmann’s geometry-density relation. The most recent measurements then imply that the density of the universe is equal to the critical density with an accuracy of better than 2 percent—a spectacular success for inflationary cosmology.
Figure 9.1. In a spherical universe, the sum of the angles in a triangle is greater than 180 degrees. The triangle in this figure has three right angles, which add up to 270 degrees.
IMAGES OF THE BLAZING PAST
Another triumph of inflation has been the explanation of small-density perturbations, the tiny ripples that later evolved into galaxies. The theory of inflation makes a sharp prediction—that the magnitude of perturbations should be nearly the same on all astrophysical distance scales, from the typical interstellar distance (a few light-years) all the way to the entire visible universe. By the early 1990s the observers were ready to put this prediction to a test.
As we discussed in Chapter 4, the primordial ripples leave an imprint on the cosmic background radiation. This afterglow of the big bang was emitted more than 13 billion years ago and now comes to us from all directions in the sky. Ever since its discovery in the mid-1960s, cosmologists were aware that hidden in this radiation was an image of the early universe. However, the primordial non-uniformities are so small, only one part in 100,000, that for many years they were beyond the accuracy of the measurements, and all one could observe was a perfectly uniform background. The breakthrough occurred in 1992, with the launch of the Cosmic Background Explorer (COBE) satellite. COBE produced a full map of the sky, detecting radiation from every direction, and we were, for the first time, able to discern tiny variations in the intensity of the radiation.
The COBE map is like a photograph that is somewhat out of focus: it captures the gross features of the cosmic fireball, but finer details, smaller than about 7 degrees on the sky, are completely blurred. (For comparison, the Moon subtends an angle of about half a degree.) COBE was followed by a series of other experiments, of ever increasing accuracy. The most recent of these was another satellite mission, WMAP.v Its image of the fireball, shown in Figure 4.2, resolves features as small as one-fifth of a degree; it is thirty times sharper than COBE’s original map.
Step by step, as the data accumulated, the pattern of primordial ripples gradually emerged. And amazingly, it was in striking agreement with the predictions of inflation! These records of the hot early epoch were there in the sky for billions of years, waiting to be discovered and deciphered. Now, finally, the sky has spoken.
In the years to come, the theory of inflation will face a succession of new observational tests. A physical theory can be supported by the data, but it can never be proved. On the other hand, a single well-established fact that contradicts the theory would be enough to disprove it. For example, inflation predicts that the density should be equal to the critical density with an accuracy of 1 in 100,000. So, if some future experiment discovers a greater deviation from the critical density, inflation will be in trouble.2
The next-generation microwave background missions include the Planck satellite,w which will further improve the image resolution, and the ground-based Clover and QUIET observatories. Clover and QUIET will accurately measure the orientation of the elec
tric field, or polarization, of the microwaves. The polarization pattern is sensitive to the presence of gravitational waves—tiny vibrations of spacetime geometry. This effect can be used to test yet another prediction of inflation: we should be bathing in gravitational waves with a very wide spectrum of lengths, ranging from less than the size of the solar system up to the largest observable scales.3 The amplitude of the waves is determined by the energy of the false vacuum that drives inflation : the higher the vacuum energy, the larger the waves. Thus, if Clover detects gravitational waves, we should be able to deduce the energy of the false vacuum that drove the inflationary expansion.4 This would be an important step in our understanding of inflation and of its connection with the physics of the microworld.
As the new data were coming in, my thoughts were going back to my neglected brainchild, the theory of eternal inflation. The main objection against it was that it was concerned with the universe beyond our horizon, which is not accessible to observation. But if the theory of inflation is supported by the data in the observable part of the universe, shouldn’t we also believe its conclusions about the parts that we cannot observe?
If I drop a stone into a black hole, I can use general relativity to describe how it falls toward the center and how it is crushed and vaporized by immense gravitational forces. None of this can be observed from the outside, because neither light nor any other signal can escape from the black hole interior. And yet very few physicists would question the accuracy of my description. We have every reason to believe that general relativity applies inside black holes just as much as it does outside. The same case could now be made for the theory of inflation. We should try to extract from this theory as much as it will tell us about the grand design of the universe, its origin, and its ultimate fate.
10
Infinite Islands
I could be bounded in a nutshell, and count myself a king of infinite space …
—SHAKESPEARE, Hamlet
THE FUTURE OF CIVILIZATIONS
The question that started me thinking about eternal inflation again had more to do with science fiction than with physics. It was about the future of intelligent life in the universe. The long-term prospects for any civilization appear to be rather bleak. Even if a civilization avoids natural catastrophes and self-destruction, it will, in the end, run out of energy. The stars will eventually die, and all other sources of energy will also come to an end. But now eternal inflation appeared to offer some hope.
Stars will die in our cosmic neighborhood, but an infinite number of new stars will form in the future big bangs of eternal inflation. Our visible region is but a tiny part of one island universe, lost in the inflating sea of false vacuum (see Figure 8.3). New island universes constantly emerge in the midst of that sea, bringing in myriads of new stars. In fact, star formation will always continue even within our own island universe.
The frontiers of island universes are constantly advancing into the inflating sea. This relentless advance is caused by the decay of false vacuum in the adjacent inflating regions. These frontiers are thus the regions where the big bang is happening right now.x Newly formed island universes are microscopically small, but they grow without limit as they get older. Central parts of large island universes are very old. They are dark and barren: all stars have long since died there, and life has become extinct. But regions at the periphery of the islands are very new and must be teeming with shining stars.
Advanced civilizations may wish to send missions to colonize newly formed stellar systems near the boundary of their island. If not, they could at least send messages to new civilizations that will evolve close to the boundary, or in other island universes. Those civilizations could in turn send messages to posterity, and so on. If we follow this path, we could become a branch in an ever-growing “tree” of civilizations and our accumulated wisdom would not be completely lost.
These scenarios were suggested by Andrei Linde in a paper called “Life after Inflation,”1 and I wanted to know if any of them is actually possible, at least in principle. Linde analyzed various aspects of the problem, but did not commit himself to a definite answer. The fact that stars in some part of the universe are formed later than they are formed here does not necessarily mean that we can get from here to there in the available time. Besides, we know from Einstein that the notions of “earlier” and “later” are not absolute and may be observer-dependent. To make any progress with the problem, I had to understand the spacetime structure of the eternally inflating universe.
As we discussed in Chapter 2, space and time in the theory of relativity are united in a four-dimensional entity called spacetime. A point in spacetime is an event, which has a certain location and time. Consider, for example, two events that you may wish to attend. One is your class reunion here on Earth and the other is an interstellar superball game, which is scheduled to take place three years later at the star Alpha Centauri, about four light-years away from here. The question is, Can you get to both of these events?
The answer can be found by calculating the spacetime interval between the two events. The interval between events in spacetime plays the role analogous to the distance between points in space. Its mathematical definition is not important for us here; what is important is that the interval can be of two kinds: it is either spacelike or timelike. The interval is timelike if a material object can get from one event to the other without violating the basic tenet of relativity—that it should not move faster than the speed of light.2 In this case all observers will agree on which of the two events is earlier and which is later. Alternatively, if getting from one event to the other is impossible (that is, if it requires faster-than-light motion), the interval is spacelike. None of these events can then be caused by the other. Einstein showed that the time order of such events is observer-dependent and that there always exists an observer who will find that they occurred simultaneously.
In our example with Alpha Centauri, the interval turns out to be spacelike, so you will have to choose which of the two events you want to attend. In fact, in this example it is easy to figure out the answer without calculating the interval. The distance traveled by light in three years is 3 light-years; so in order to cover the 4-light-year distance to Alpha Centauri, you would have to move faster than light. In the curved spacetime of the eternally inflating universe, the analysis is more complicated, and one does have to calculate the interval.
The spacetime of an island universe is schematically illustrated in Figure 10.1. The vertical direction is time, and the horizontal direction is one of the three spatial dimensions; the other two dimensions are not shown. Each horizontal line gives a snapshot of the universe at a moment of time. You can follow the history of the island universe by starting with a horizontal dotted line marked “before” at the bottom of the figure and gradually moving it upward. (The moment of time represented by this line is in the inflating part of spacetime, where the island universe has not yet formed.) The thick solid line labeled “Big Bang” is the boundary between the island universe and the inflationary part of spacetime. The location marked by a black galaxy is the here and now, and white galaxies mark spacetime regions where the conditions are similar to what we have here today. The horizontal dotted line labeled “now” represents the present time. It shows the island universe with a barren central region and some star-forming regions close to the boundaries.
A simple calculation showed that all big bang events, which are located along the solid line in the figure, are separated by spacelike intervals. That was the key observation; it gave me the answer to my question about the future of civilizations. It also completely changed the way I viewed the island universes.
Figure 10.1. Spacetime diagram of an island universe (global view).
The spacelike character of the intervals means that you cannot get from any one of the big bang events to any other. In other words, you cannot keep up with the expanding boundaries of the island universe: they are expanding faster than the spe
ed of light. Thus, we will never be able to reach the shores of the inflating sea and bask in the light of the new suns that will be born there. We cannot even send any messages to the future civilizations that will thrive around these suns, since no signal can travel faster than light. Regrettably, eternal inflation does not seem to improve the long-term prospects for humanity.
You may be puzzled by faster-than-light expansion of island universes, as it apparently contradicts Einstein’s ban on superluminal velocities. The ban, however, is very specific: it applies only to the motion of material objects (including radiation, such as light or gravitational waves) relative to one another, while the boundary of an island universe is a geometric entity, which does not have any mass or energy.
The faster-than-light expansion of the boundary means that successive big bangs cannot be causally related. They are not like a row of dominoes, where the fall of one domino triggers the fall of the next. The progression of false-vacuum decay is predetermined by the pattern of the scalar field that was produced during inflation. The field variation in space is very gradual, and as a result the false-vacuum decay in nearby regions occurs almost simultaneously. That is why the big bangs happen in such a quick succession and the boundary is advancing so fast.
Many Worlds in One: The Search for Other Universes Page 9