Many Worlds in One: The Search for Other Universes

by Vilenkin, Alex

If this was not bad enough, things got considerably worse in the mid-1990s as a result of some unexpected new developments. As the mathematics of string theory was better understood, it became clear that in addition to one-dimensional strings, the theory must include two-dimensional membranes, as well as their higher-dimensional analogues. All these new arrivals are collectively called branes.be Vibrating little branes would look like particles, but they are too massive to be produced in particle accelerators.7

  The branes have one unpleasant side effect: they dramatically increase the number of ways in which new vacua can be constructed. A brane can be wrapped, like a rubber band, around some of the compact dimensions. Every new stable brane configuration gives a new vacuum. You can wrap one, two, or more branes on each of the handles of the compact space, and with a large number of handles, the number of possibilities is enormous. The equations of the theory have no adjustable constants, but their solutions, describing different vacuum states, are characterized by several hundred parameters—the sizes of compact dimensions, the locations of the branes, and so on.

  If we had just one parameter, it would be very similar to a scalar field in the usual particle theory. As we discussed in earlier chapters, it would then behave as a little ball in the energy landscape and would roll to the nearest minimum of the energy density. With two parameters, the landscape would be two-dimensional, as illustrated in Figure 15.5. It would have maxima (peaks) and minima (valleys), with minima representing the vacuum states. The altitude at each minimum gives the corresponding vacuum energy density (the cosmological constant).

  The actual energy landscape of string theory is much more complicated, since it includes many more parameters. This landscape cannot be drawn on a sheet of paper: to account for all the parameters, we would need a space of several hundred dimensions. But the landscape can still be mathematically analyzed. A rough estimate indicates that it contains about 10500 (google to the fifth power!) different vacua. Some of these vacua are similar to ours; others have very different values for the constants of nature. Still others differ more drastically and have totally different kinds of particles and interactions, or more than three large dimensions.

  As the outlines of the landscape were emerging, the hope of deriving a unique vacuum from string theory was rapidly slipping away. But string theorists were in denial and not ready to accept defeat.

  Figure 15.5. Energy landscape in two dimensions. Each horizontal dimension (not to be confused with the dimensions of ordinary space) represents one of the parameters characterizing string theory vacua. The height represents the energy density.

  THE BUBBLING UNIVERSE

  The first physicists to break from the pack were Raphael Bousso, now at the University of California at Berkeley, and Joseph Polchinski of the Kavli Institute for Theoretical Physics at Santa Barbara. Remember Polchinski? He is the string theorist who could not stand the anthropic principle and pledged to quit physics if the cosmological constant was discovered.bf Luckily, he changed his mind—both about quitting physics and about the anthropic principle.

  Bousso and Polchinski combined the picture of the string theory landscape with the ideas of inflationary cosmology and argued that regions of all possible vacua will be created in the course of eternal inflation. The highest-energy vacuum will inflate the fastest. Bubbles of lower-energy vacua will nucleate and expand in this inflating background (as in Guth’s original inflationary scenario, discussed in Chapters 5 and 6). The interiors of the bubbles will inflate at a smaller rate, and bubbles of still-lower energy will pop out inside them (see Figure 15.6).bg As a result, the entire string theory landscape will be explored—countless bubbles will be formed, filled with every possible kind of vacuum.8

  Figure 15.6. Bubbles filled with lower-energy vacua nucleate in the inflating high-energy background, and still-lower energy bubbles nucleate inside them.

  We live in one of the bubbles, but the theory does not tell us which one. Only a tiny fraction of the bubbles are hospitable to life, and we must find ourselves in one of these rare bubbles. Much to the dismay of many string theorists, this is precisely the kind of picture that is assumed in anthropic arguments. If string theory is indeed the ultimate theory of reality, then it appears that the anthropic worldview is inevitable.

  It needs to be said that the landscape of string theory is far from being fully mapped. In order to yield a realistic cosmology, some of the slopes have to be very gentle, allowing for slow-roll inflation. Recent work indicates that there are indeed such regions in the landscape. We should also search for even gentler slopes, required by Linde’s scalar field model of a variable cosmological “constant” (discussed in Chapter 13). None have been found so far. But Bousso and Polchinski suggest that googles of vacua in the landscape provide a suitable alternative.

  Instead of a continuum of vacuum energy densities in Linde’s model, the landscape gives a discrete set of values. Normally, this would be a problem, because only a tiny fraction of these values (about 1 in 10120) fall in the small anthropically allowed range. If we had less than 10120 vacua, this range would most probably be empty. But with 10500 vacua in the landscape, the set of values is so dense that it is almost continuous, and we expect that googles of vacua will have the cosmological constant in the anthropically allowed interval. The principle of mediocrity can then be applied in the same manner as before, and the successful prediction of the observed cosmological constant is unaffected.

  A PROGRAM FOR THE TWENTY-FIRST CENTURY

  The paper by Bousso and Polchinski, which appeared in 2000, did make a stir, but the landslide began three years later, when they were joined by one of the inventors of string theory, Leonard Susskind of Stanford University. Susskind is a fiercely independent thinker and is also a man of great charm and charisma. His power of persuasion is phenomenal; this is the man you want to have on your side.

  Susskind was still unconvinced when Bousso and Polchinski’s paper first came out. He felt that the existence of a multitude of vacua assumed in the paper relied more on conjecture than on mathematical fact. But the developments of the following few years showed that the conjectures were basically sound, and in 2003 Susskind came out in full force promoting what he called “the anthropic landscape of string theory.” He argued that the diversity of vacua in string theory provided, for the first time, a solid scientific basis for anthropic arguments. String theorists, he said, should therefore embrace the anthropic principle, instead of fighting against it.

  In less than a year, everybody was talking about “the landscape.” The number of papers discussing multiple vacua and other anthropic-related issues grew from four in 2002 to thirty-two in 2004. Of course, not everybody was pleased with this turn of events. “I hate this recent landscape idea,” says Paul Steinhardt, “and I am hopeful it will go away.”9 David Gross, the 2004 Nobel Prize winner, who regards the use of the anthropic principle as giving up the ideal of uniqueness, paraphrased Winston Churchill, saying “Never, never, never, never give up!” When I talked to him at a meeting in Cleveland, he complained that the anthropic principle is like a virus. Once you get it, you are lost to the community. “Ed Wittenbh dislikes this idea intensely,” says Susskind, describing the situation, “but I’m told he’s very nervous that it might be right. He’s not happy about it, but I think he knows that things are going in that direction.”10

  If the landscape ideas are correct, explaining the observed constants of nature is not going to be easy. First, we will need to map the landscape. What kinds of vacua are there, and how many of each kind? We cannot realistically hope to obtain a detailed characterization of all 10500 vacua, so some kind of statistical description will be necessary. We will also need to estimate the probabilities for bubbles of one vacuum to form amidst another vacuum. Then we will have all the ingredients to develop a model of an eternally inflating universe with bubbles inside bubbles inside bubbles, as illustrated in Figure 15.6. Once we have this model, the principle of mediocrity can be used to determi
ne the probability for us to live in one of the vacua or another.

  We are now making our first, tentative steps in this program, and formidable challenges lie ahead. “But,” writes Leonard Susskind, “I would bet that at the turn of the 22nd century, philosophers and physicists will look nostalgically at the present and recall a golden age in which the narrow provincial 20th century concept of the universe gave way to a bigger better megaverse, populating a landscape of mind-boggling proportions.”11

  PART IV

  BEFORE THE BEGINNING

  16

  Did the Universe Have a Beginning?

  Whence all creation had its origin, … he, who surveys it all from highest heaven, he knows or maybe even he does not know.

  —RIG-VEDA

  A PROBLEM WITH THE COSMIC EGG

  Ancient creation myths display wonderful ingenuity, but at the most fundamental level they have to choose one of two basic options: either the universe was created a finite time ago, or it has existed forever.1

  Here is one of several scenarios offered in the sacred Hindu scripture, the Upanishads:

  In the beginning this [world] was nonexistent. It became existent. It turned into an egg. The egg lay for the period of a year. Then it broke open … And what was born of it was yonder Aditya, the Sun. When it was born shouts of “Hurrah” arose, together with all beings and all objects of desire.

  This idea looks simple enough, but unfortunately it has a serious flaw, which it shares with every other story of creation. The ancients were well aware of the problem; the Jain poet Jinasena wrote in the ninth century:

  The doctrine that the world was created is ill-advised, and should be rejected.

  If God created the world, where was he before creation? …

  How could God have made the world without any raw material? If you say he made this first, and then the world, you are faced with an endless regression …

  Thus the doctrine that the world was created by God makes no sense at all …

  Know that the world is uncreated, as time itself is, without beginning and end … Uncreated and indestructible, it endures under the compulsion of its own nature.2

  This critique applies equally well to every scenario of the cosmic origin—be it a creation by God, as in the story of the cosmic egg, or a “natural” creation, such as the big bang model of modern cosmology.3

  According to the big bang theory, all the matter that we see around us came out of a hot cosmic fireball some 14 billion years ago. But where did the fireball come from? The theory of inflation has shown that an expanding fireball could arise out of a tiny false-vacuum nugget. But the question still remains: Where did that initial nugget originate? What happened before inflation?

  For the most part, cosmologists were in no hurry to tackle this thorny issue. In fact, it appeared that a satisfactory answer could never be given. Whatever the answer is, one can always ask “And what happened before that?” This is the “endless regression” that Jinasena is referring to. However, in the 1980s, when the eternal inflation scenario was developed, it appeared to offer an attractive alternative.

  An eternally inflating universe consists of an expanding “sea” of false vacuum, which is constantly spawning “island universes” like ours. Inflation is thus a never-ending process. It has ended in our own island universe, but will continue indefinitely in other remote regions. But if inflation is going to continue forever into the future, then perhaps it might have had no beginning in the past. We would then have an eternally inflating universe without a beginning and without an end; that would eliminate the perplexing problems associated with the cosmic origin. This picture is reminiscent of the steady-state cosmology of the 1940s and ’50s. Some people found it very appealing.

  A CYCLIC UNIVERSE

  Apart from a steady state, there is another way for the universe to be eternal. And again, the Hindus figured this out a long time ago. The endless cycle of creation and destruction is symbolized by the dance of the god Shiva. “He rises from His rapture and, dancing, sends through inert matter pulsing waves of awakening sound.” The universe comes to life, but then “[i]n the fullness of time, still dancing, He destroys all forms and names by fire and gives new rest.”4

  A parallel idea in scientific cosmology is that of an oscillating universe, which goes through a cycle of expansion and contraction. It was briefly popular in the 1930s, but then fell out of favor, because of apparent conflict with the second law of thermodynamics.

  The second law requires that entropy, which is a measure of disorder, should grow in each cycle of cosmic evolution. If the universe had already gone through an infinite number of cycles, it would have reached the maximum-entropy state of thermal equilibrium. We certainly do not find ourselves in such a state. This is the “heat death” problem that I mentioned earlier.

  The idea of an oscillating universe was abandoned for more than half a century, but in 2002 it was revived in a new guise by Paul Steinhardt and Neil Turok of Cambridge University. As in earlier models, they suggested that the history of the universe consists of an endlessly repeating cycle of expansion and contraction. Each cycle starts with a hot expanding fireball. It expands and cools down, galaxies form, and the vacuum energy comes to dominate the universe soon thereafter. At this point the universe starts expanding exponentially, with its size doubling every 10 billion years or so. After trillions of years of this super-slow inflation, the universe becomes very homogeneous, isotropic, and flat. Eventually the expansion slows down and then turns into contraction. The universe recollapses and immediately bounces back to start a new cycle. Part of the energy generated in the collapse goes to create a hot fireball of matter.5

  Steinhardt and Turok argue that the problem of the beginning does not arise in their scenario. The universe has always been going through the same cycle, so there was no beginning. The problem of the heat death is also avoided, because the amount of expansion in a cycle is greater than the amount of contraction, so the volume of the universe is increased after each cycle. The entropy of our observable region is now the same as the entropy of a similar region in the preceding cycle, but the entropy of the entire universe has increased, simply because the volume of the universe is now greater. As time goes on, both the entropy and the total volume grow without bound. The state of maximum entropy is never reached, because there is no maximum entropy.

  Thus, it appears that we have two possible models for an eternal universe without a beginning: one is based on eternal inflation and the other on cyclic evolution. However, it turns out that neither possibility can yield a complete description of the universe.

  DE SITTER SPACE

  When a physicist wants to understand some phenomenon, the first thing she does is to maximally simplify it, stripping it down to the bare essentials. In the case of eternal inflation, we can strip away island universes, keeping only the inflating sea. In addition, we can assume that the universe is homogeneous and isotropic, as in Friedmann’s models. With these simplifications, Einstein’s equations for the inflating universe can be easily solved.

  The solution has the geometry of a three-dimensional sphere, which contracts from a very large radius in the remote past. The contraction is slowed down by the repulsive gravity of the false vacuum, until the sphere stops for a moment and then starts to re-expand. The force of gravity now works in the direction of motion, so the sphere expands with acceleration. Its radius grows exponentially, with a doubling time determined by the energy density of the false vacuum.bi

  The solution I have just described has been known since the early days of general relativity; it is called de Sitter spacetime—after the Dutch astronomer Willem de Sitter, who discovered it in 1917. This spacetime is illustrated in Figure 16.1. Inflation begins in de Sitter spacetime only after the spherical universe has reached its minimum radius. But once started, the exponential expansion continues forever, so inflation is eternal to the future.

  If we were to allow the formation of island universes, th
ey would collide and merge in the contracting part of spacetime. The islands would then quickly fill the entire space, the false vacuum would be completely eliminated, and the universe would continue collapsing to a big crunch. Thus, inflation cannot be extended into the infinite past. It must have had some sort of beginning.

  We should keep in mind, however, that this conclusion is based on the maximally simplified model of inflation, which assumes a homogeneous and isotropic universe. In reality, the universe may well be very irregular—inhomogeneous and anisotropic—on scales much greater than the present horizon. Could it be, then, that the contracting phase of de Sitter spacetime is an artifact of the simplifying assumptions that we have made? Is it possible to avoid the beginning in a more general spacetime?

  Figure 16.1. De Sitter spacetime, with two of the three spatial dimensions suppressed. Horizontal slices of the spacetime give “snapshots” of the universe at different moments of time. In a four-dimensional spacetime the slices would be three-dimensional spherical spaces.

  BEYOND UNREASONABLE DOUBT

  These doubts were put to rest only recently, in a paper I wrote in collaboration with Arvind Borde of Long Island University and Alan Guth. The theorem we proved in that paper is amazingly simple. Its proof does not go beyond high school mathematics, but its implications for the beginning of the universe are very profound.

  Borde, Guth, and I studied what an expanding universe looks like from the point of view of different observers. We considered imaginary observers moving through the universe under the action of gravity and inertia and recording what they see. If the universe had no beginning, then the histories of all such observers should extend into the infinite past. We showed that this assumption leads to a contradiction.