Many Worlds in One: The Search for Other Universes

by Vilenkin, Alex

  The wacky monument was a source of embarrassment for the Tufts administration and inspired numerous pranks by the students. It would occasionally disappear, only to reappear where it was least expected. Once it was found blocking the entrance of the trustees and the president at the commencement. At one time it looked as if the stone had disappeared for good, but then it miraculously resurfaced ten years later. It turned out that a group of students had buried it somewhere on campus and then dug it out when they returned to Tufts for their class reunion. Gravity alone was clearly not enough to keep the stone in place, so it was finally cemented to the ground.

  Since few scientists could claim they had an active program of research in antigravity, the Babson money proved rather difficult to get. It’s not that nobody tried: the university president, Jean Mayer, who was a nutritionist, argued unsuccessfully that weight loss was antigravity. After years of discussions and legal arguments, the money was eventually used to establish the Tufts Institute of Cosmology.

  Figure 7.1. A triumphant Dr. Vitaly Vanchurin after his Ph.D. inauguration, surrounded by members of the Institute of Cosmology. Standing, from left to right: Larry Ford, Ken Olum, and the author. (Courtesy of Delia Schwartz-Perlov)

  Like any self-respecting academic institution, our institute has its own unique ritual—an “inauguration” ceremony for cosmology Ph.D. recipients. After defending the dissertation, a new Ph.D. gets an apple dropped on his head while kneeling in front of the antigravity stone. The apple comes from the hand of the thesis advisor and may then be eaten by the “inauguree.”

  By the time the Institute of Cosmology was established, Babson was long since dead and his Gravity Research Foundation had evolved into a respectable institution giving research grants on gravitation. Nobody really expected that Tufts cosmologists would work on antigravity, but strangely enough—they do. Much of the research at the institute is focused on false vacuum and its repulsive gravity, which certainly qualifies as antigravity. So I think Mr. Babson could not have found a better use for the money. We have not succeeded in reducing the number of airplane accidents though.

  8

  Runaway Inflation

  In my opinion, the most plausible answer to what happened before inflation is—more inflation.

  —ALAN GUTH

  UNIVERSE BEYOND THE HORIZON

  What lies beyond our present horizon? That was the question that intrigued me from the early days of inflation. If we can see only a minuscule part of the universe, then what is the big picture—like the view of our planet that is revealed to space travelers as their spaceship leaves the Earth?

  The theory of density perturbations provided some clues. According to this theory, the pattern of how galaxies are distributed in space is determined by quantum kicks experienced by the scalar field during inflation. This is a random process; so some regions of the same size as ours have more galaxies, and others have less. The reason we have the Milky Way galaxy right here, where we are, is that the scalar field at this location had a tiny kick backward, away from the true vacuum, so that it ended its roll down the energy hill a bit later than it did in the neighboring locales. This produced a small density enhancement, which later evolved into our galaxy. Similar little humps on the smooth density background gave rise to our neighbor Andromeda and to countless other galaxies within our horizon and beyond. This description of structure formation suggests that the remotest parts of the universe look more or less the same as what we see around here. But I was beginning to suspect that something was missing from this picture.

  The effect of quantum kicks is very small because they are much weaker than the force due to the slope of the energy hill that drives the scalar field down. This explains why the field reaches the bottom everywhere at about the same time and only small density perturbations are produced. The question I was asking myself was, What happens when the field is near the top of the hill, where the slope is very small? There, it should be at the mercy of quantum kicks, which shove it at random one way and then the other. The universe resulting from inflation might then be far less orderly, and more erratic, than it first appeared.

  Figure 8.1. Mr. Field walks randomly on the flat portion of the hill and slides down when he gets to the steeper slope.

  To picture the behavior of the scalar field near the top of the hill, we shall use a politically incorrect but pertinent analogy. Let me introduce a gentleman, named Mr. Field, who had too much to drink and is now trying to maintain his vertical position. He has little control of his feet and no idea where he is heading, so he steps to the right or to the left completely at random. Mr. Field starts his promenade at the top of the hill, as in Figure 8.1. Since on average he steps to the right as frequently as he does to the left, he is not getting anywhere very fast. But after a large number of steps he will gradually drift away from the hilltop. Eventually, he will get to the steeper part of the hill, where he will inevitably slip and finish the rest of the journey sliding downhill on his rear.

  The scalar field behavior during inflation is very similar. The field wanders aimlessly near the top of the energy hill, until it reaches a steeper slope; then it “rolls” down toward the end of inflation. On the flat portion near the top of the hill, the field variation is induced by quantum kicks and is totally random, while the roll down the slope is orderly and predictable, with quantum kicks introducing only a small disturbance. The time interval between successive quantum kicks is roughly equal to the doubling time of inflation. This means that Mr. Field takes about one step per doubling time. And since he makes many steps wandering around the flat hilltop, it follows that the false vacuum takes many doubling times to decay.

  A particular sequence of steps that brings Mr. Field from the top of the hill to the bottom represents one possible history of the scalar field. But quantum kicks experienced by the field differ from one place to another, so the scalar field histories will also be different. Each quantum kick affects a small region of space. Its size is, roughly, the distance traveled by light during one doubling time of inflation; we shall call it a “kickspan.”p We can imagine a party of gentlemen in the same condition as Mr. Field, each representing the scalar field at some point in space. When two points are within a kickspan of one another, they experience the same quantum kicks; so the corresponding two gentlemen do all the steps in sync, like a pair of tap dancers. But the points are rapidly driven apart by the inflationary expansion of the universe, and when they get separated by more than a kickspan, the two gentlemen part company and start walking independently. Once this happens, the scalar field values at the two points start gradually drifting apart, while the distance between the points continues to be rapidly stretched by inflation.

  The smallness of density perturbations in our observable region tells us that all points in this region were still within a kickspan of one another when the scalar field was well on its way down the hill. That is why the effect of quantum kicks was very minor, and the field reached the bottom everywhere at about the same time. But if we could go to very large distances, far beyond our horizon, we would see regions that parted our company when the field was still wandering near the hilltop. The scalar field histories in such regions could be very different from ours, and I wanted to know what the universe looks like on such superlarge scales.

  Imagine a large party of jolly walkers starting off from the top of the hill. Each walker represents a remote region of the universe, so they all walk independently. If the flat portion of the hill is N steps long, then a typical random walker will cross it in about N2 steps. Roughly half of the walkers will do it faster and another half slower. For example, if the distance is 10 steps, it will take, on average, 100 steps for a random walker to cross it. So, after the first 100 steps, about half of the company will have reached their destination at the bottom, while the other half will still be enjoying the promenade. In another 100 steps, the number of remaining walkers will again be cut in half, and so on, until the last fellow finally slides downhill
.

  But now, there is a crucial difference between the walkers and the inflating regions they represent. While a walker is wandering near the hilltop, the corresponding region undergoes exponential inflationary expansion. So the number of independently evolving regions rapidly multiplies. This is as if the walkers were to multiply as well. As I continued to think about this, the picture was gradually taking shape.

  ETERNAL INFLATION

  In a way, inflation is similar to the reproduction of bacteria. There are two competing processes: bacteria reproduce by division, and they are occasionally destroyed by antibodies. The outcome depends on which process is more efficient. If the bacteria are destroyed faster than they reproduce, they will quickly die out. Alternatively, if the reproduction is faster, bacteria will rapidly multiply (Figure 8.2).

  In the case of inflation, the two rival processes are the false-vacuum decay and its “reproduction” due to the rapid expansion of inflating regions. The efficiency of decay can be characterized by a half-lifeq—the time during which half of the false vacuum would decay if it were not expanding. (In our random-walk analogy, this is the time it takes for the number of walkers to be reduced by half.) On the other hand, the efficiency of reproduction is characterized by the doubling time, during which the volume of inflating false-vacuum doubles. The false-vacuum volume will shrink if the half-life is shorter than the doubling time and will grow otherwise.

  Figure 8.2. The number of bacteria will rapidly grow if the bacteria reproduce faster than they are destroyed.

  But it follows from the discussion in the preceding section that the false-vacuum half-life is long compared with the doubling time. The reason is that in models of inflation the energy hill is rather flat and it takes many steps to cross it. Since each step of a random walker corresponds to one doubling time of inflation, it follows that the half-life must be much longer than the doubling time. Hence, false-vacuum regions multiply much faster than they decay. This means that inflation never ends in the entire universe and the volume of inflating regions keeps growing without bound!

  At this very moment, some distant parts of the universe are filled with false vacuum and are undergoing exponential inflationary expansion. Regions like ours, where inflation has ended, are also constantly being produced. They form “island universes” in the inflating sea.r Because of inflation, the space between these islands rapidly expands, making room for more island universes to form. Thus, inflation is a runaway process, which stopped in our neighborhood, but still continues in other parts of the universe, causing them to expand at a furious rate and constantly spawning new island universes like ours.

  The energy of the decaying false vacuum ignites a hot fireball of elementary particles and triggers the formation of helium and all the subsequent events of the standard big bang cosmology. Thus, the end of inflation plays the role of the big bang in this scenario. If we make this identification, then we should not think of the big bang as a one-time event in our past. Multiple bangs went off before it in remote parts of the universe, and countless others will erupt elsewhere in the future.s

  Once this new worldview was clear in my mind, I could not wait to share it with other cosmologists. And who better could I choose as my first confidant but Mr. Inflation himself—Alan Guth, whose office at MIT was only a 20-minute drive away from Tufts. So I did just that—I drove to the famous institute for a meeting with Alan.

  MIT occupies a monstrous conglomeration of buildings, where I have gotten hopelessly lost on many occasions. You may walk on the third floor of building 6 and suddenly discover that you are already on the fourth floor of building 16. I decided to play it safe and took the simplest, although the longest, way to my destination: through the main entrance (marked by a row of Corinthian columns and crowned with a green dome). I had to march all the way along what locals call the Infinite Corridor, then climb a few flights of stairs, and finally I was in Alan Guth’s office.

  I told Alan about the random walk of the scalar field and how it could be described mathematically. But then, when I was in the middle of unveiling my new dazzling picture of the universe, I noticed that Alan was beginning to doze off. Years later, when I got to know Alan better, I learned that he is a very sleepy fellow. We organize a joint seminar for the Boston-area cosmologists, and at every seminar meeting Alan falls peacefully asleep a few minutes after the talk begins. Miraculously, when the speaker is finished, he wakes up and asks the most penetrating questions. Alan denies any supernatural abilities, but not everybody is convinced. So, in retrospect, I should have continued the discussion. But at the time I was not aware of Alan’s magical powers and hastily retreated.

  The response I got from other colleagues was also less than enthusiastic. Physics is an observational science, they said, so we should refrain from making claims that cannot be observationally confirmed. We cannot observe other big bangs, nor can we observe distant inflating regions. They are all beyond our horizon, so how can we verify that they really exist? I was disheartened by such a cool reception and decided to publish this work by embedding it as a section in a paper on a different subject: I came to think that it did not deserve to have a full paper devoted to it.1

  To explain the idea of eternal inflation in the paper, I used the analogy of a drunk wandering near the top of a hill. In a couple of months I got a letter from the editor saying that my paper was accepted, except that the discussion of drunks “was not appropriate for an archival journal like the Physical Review” and I should replace it with a more suitable analogy. I heard of a similar incident that happened earlier to Sidney Coleman. He had a diagram in his paper that looked like a circle with a wiggly tail. Coleman referred to it as a “tadpole diagram.” Predictably, the editor complained that the term was inappropriate. “OK,” replied Coleman, “let us call it sperm diagram.” Following that, the original version of the paper was accepted without further comment. I briefly contemplated using Coleman’s tactic, but then decided against it and removed the drunk analogy altogether: I did not feel like picking a fight.

  I did not return to the theory of eternal inflation for nearly ten years. Except for one episode …

  A GLIMPSE OF ETERNITY

  I went on to work on my other research interests, and at times it even appeared that I was cured of my strange obsession with unobservable worlds. But the truth was that the temptation to get a glimpse of the universe beyond the horizon did not go away. In 1986, when I could not resist it any more, I developed a computer simulation of the eternally inflating universe, together with a graduate student, Mukunda Aryal.

  I am technologically challenged and have never written a single line of computer code. But I have a pretty good understanding of how computers think, and over the years I have supervised several major computational projects by graduate students. Since I cannot check the code (and I suspect that I would not enjoy that even if I could), I am wary of hidden dangers and always view the results with great suspicion. So I made Mukunda go through multiple checks and run the simulation for simple cases, where we knew the answers. Finally, when I was satisfied that everything worked fine, we turned to the real thing.

  We started the simulation with a small region of false vacuum, represented by a light square area on the computer screen. After a while, the first dark islands of true vacuum made their appearance. These island universes grew rapidly in size, as their boundaries advanced into the inflating sea. But the inflating regions expanded even faster, so the gaps separating the island universes widened and new island universes formed in the newly created space.2

  The picture that emerged after we allowed the simulation to run for some time showed large island universes surrounded by smaller ones, which were surrounded by still smaller ones, and so forth, resembling an aerial view of an archipelago—a pattern known as a fractal to mathematicians. Figure 8.3 is the result of a similar, but more sophisticated, simulation that I later developed with my students Vitaly Vanchurin and Serge Winitzki.

  Mukund
a and I published the results of our simulation in the European journal Physics Letters.3 My curiosity about the unobservable universe now satisfied, I moved on to other things. In the meantime, the subject was taken up by Andrei Linde.

  LINDE’S CHAOTIC INFLATION

  Linde is the hero of inflation, the person who saved the theory by inventing a flattened energy hill for the scalar field. Since 1983, he was developing the idea that the universe started in a state of primordial chaos. The scalar field in that state was varying wildly from one place to another. In some regions it happened to be high up on the energy hill, and that’s where inflation took place.

  Figure 8.3. Computer simulation of an eternally inflating universe. Island universes (dark) in the inflating false-vacuum background (light). The larger island universes are the older ones: they had more time to grow.

  Linde realized that it was not necessary for the field to start at the highest point of the energy landscape. It could also roll down from some other point on the slope. In fact, the energy hill might have no highest point and keep rising without limit (see Figure 8.4). Such a “topless” hill has a true vacuum at the bottom, but there is no definite location for the false vacuum. Its role can be played by any point on the slope where the field happens to be in the initial chaos, provided that it is high enough to allow sufficient roll-down time for inflation. Linde described these ideas in a paper called “Chaotic Inflation.”

  A few years later, Linde investigated the effect of quantum kicks on the scalar field in this scenario. Surprisingly, he found that they can also result in eternal inflation, even though the energy hill does not have a flat top. His key observation was that at higher elevations quantum kicks get stronger and can push the field up, against the downward force of the slope. So, if the field starts high up the hill, it pays little attention to the slope and undergoes a random walk, as in the flat hilltop case. When it wanders into the lower terrain, where quantum kicks are weak, it rolls in an orderly way down to the true vacuum. The time it takes for this to happen is much longer than the inflationary doubling time; so inflating regions multiply faster than they decay, which results once again in eternal inflation.