Many Worlds in One: The Search for Other Universes

by Vilenkin, Alex

  Shortly before the meeting, Hawking wrote a paper with a very interesting idea. According to the quantum theory, the evolution of all physical systems is not entirely deterministic, but is subject to unpredictable quantum jerks. So, as the scalar field rolls downhill, it experiences random kicks back and forth. The directions of the kicks are not the same in different regions of the universe, and as a result, the scalar field arrives at the bottom of the hill at slightly different times in different places. In regions where inflation lasted a little longer, the matter density would be slightly higher.l Hawking’s idea was that the resulting small inhomogeneities led to the formation of galaxies and galaxy clusters. If he was right, then quantum effects, which are normally important on tiny, subatomic scales, were responsible for the existence of the largest structures in the universe!

  Naturally, Guth was very excited by this development. Not only did it resolve the difficulty of the theory, but also it opened the tantalizing possibility of testing inflation observationally. Density perturbations can be observed through cosmic microwaves and then compared with the predictions of the theory. This was tremendously important!

  The calculation of density inhomogeneities produced during inflation is a very challenging technical problem. Hawking’s paper gave very few details and was difficult to follow. So Guth joined forces with a Korean-born physicist, So-Young Pi, to work out the perturbations using a method that they could both understand. They were not quite done when Guth had to leave for the Nuffield Workshop, and he finished the calculation during his first days in Cambridge. To his great surprise, the result was very different from Hawking’s. They both found that the perturbations depended on the form of the scalar field energy landscape. But the dependence was different, and Guth’s answer gave a much larger magnitude for the perturbations.

  Guth discussed the matter with Hawking, but the difference remained unresolved. Hawking insisted on his result. When Guth told me about their conversation over lunch, he looked puzzled. He was not sure his answer was correct and said he would have to recheck several points in the calculation.

  To add to the confusion, there was yet another group working on the same problem. Paul Steinhardt had calculated the inhomogeneities in collaboration with two other American cosmologists, Jim Bardeen and Michael Turner. They also disagreed with Hawking, but their answer was much smaller! Finally, there was a Russian physicist, Alexei Starobinsky, who was also scheduled to talk on the subject of density perturbations. But he kept to himself, and nobody knew what result he was going to announce.

  Starobinsky was not a novice to cosmology. Among other things, he was known for inventing a version of inflation about a year earlier than Guth. The rub was that he invented it for the wrong reason. He thought his model could remove the initial singularity—which it could not. But he did not realize that it could solve the horizon and flatness problems. Without this crucial insight, the model did not get much notice at the time, but now it is regarded as a viable alternative to the scalar field models of Linde, Albrecht, and Steinhardt.2

  Starobinsky was scheduled to speak first. His style of presentation was typical of the Russian school of physics and could be traced back to one of its originators, the Nobel Prize laureate Lev Landau. At Landau’s famous weekly seminar, the speaker was presumed to be an idiot and had a narrow window of opportunity to prove otherwise at the beginning of the talk. So the seminars were given mainly “for Landau,” to convince him that the speaker knew what he was talking about, and without undue concern that the talk might go above the heads of almost everybody else. Now, add to this a Russian accent and a strong stutter, and you will not be surprised that Starobinsky’s talk was not easy to follow. Yet, by the time he was finished, one thing was clear: he had found the inhomogeneities to be large, pretty close to Guth’s result.

  The next day it was Hawking’s turn to speak. The legendary physicist suffers from Lou Gehrig’s disease and has been wheelchair-bound since the early 1970s. He now communicates through a voice synthesizer, selecting words one by one from a menu on a computer screen. At the time of the meeting he could still speak, but barely. Most people could not understand him, and one of his students served as an interpreter during the talk. Hawking’s lecture followed the line of argument in his paper, but at the end there was a surprise. The last step of the calculation was now different, and the result was the same as found by Guth and Starobinsky! After talking to Guth and hearing Starobinsky’s lecture, Hawking must have spotted an error in his calculation. He never mentioned, though, that he was correcting an error in his paper, or that his new result was also derived by Starobinsky and Guth.

  The majority of the talks at the Nuffield Workshop were on the subject of inflation, and despite much excitement about the new theory, it was a bit of an overdose. The talks on other early-universe topics provided a welcome relief—the sentiment I tried to express in the opening slide of my lecture on cosmic strings (Figure 6.6). Strings are line-like relics of the hot, high-energy epoch in the early universe. They are thin tubes of false vacuum, which are predicted in some particle physics models. In my talk I discussed the formation of strings and their possible astrophysical effects. The talk was well received, and I could now sit back, relax, and watch the final stretch of the race to figure out the density perturbations.

  Figure 6.6. Inflation overdose—the opening slide of my talk on cosmic strings.

  Steinhardt and his friends were still holding out. They were concerned about some subtle points in their calculation and kept working furiously to clear them up. The answer they were getting was still much smaller than Hawking’s original result.

  Guth was scheduled to speak during the third week of the meeting. He worried that Steinhardt and company might give him a hard time and used every opportunity to retreat into his room and check various parts of his calculation. He later realized that he had even missed the conference banquet while preparing for his talk.

  Despite mounting tension, the battle was not to happen. A few days before the talk, Steinhardt and his collaborators conceded defeat. They found some errors in the approximations that they had used, and now their result was in agreement with the other contestants’. Guth’s talk went very smoothly: he reiterated the original result that he had obtained earlier. Thus, by the end of the workshop, all four participating teams had reached a full consensus.

  The final surprise of this remarkable race came long after the workshop was over. Much to their dismay, the former contestants discovered that the problem of quantum-induced density perturbations that they worked so hard to untangle had already been solved—a full year before they crossed swords in Cambridge. The solution was published by two Russian physicists, Slava Mukhanovm and Gennady Chibisov, from the Lebedev Institute in Moscow.3 They worked out perturbations for the Starobinsky version of inflation, but the calculation was essentially the same as for the scalar field models. You can often find something interesting by reading Russian physics journals!

  The end point of the calculations was a formula for the magnitude of density perturbations produced by quantum jitters of the scalar field as it rolls downhill during inflation. This magnitude depends on the shape of the energy landscape and also on the size of the region where the perturbation occurs. Cosmic structures span a wide range of distance scales. The scale of stars is much smaller than that of galaxies, which is in turn smaller than the scale of galaxy clusters. The magnitude of perturbations on these vastly different scales could well be very different. But the formula says that all perturbations are created very nearly equal. From the smallest cosmic structures to the largest, their magnitude changes by no more than 30 percent.

  This property of scale-independence of the inflationary perturbations is not difficult to understand. The quantum kicks initially affect the scalar field in a tiny region of space, but then the perturbation is stretched to a much greater size by the exponential expansion of the universe. Perturbations produced earlier during inflation are stretched for a
longer time and encompass a larger region. But the magnitude of the perturbation is set by the initial quantum kick, which is pretty much the same for all relevant scales.n

  Scale-independence of the density perturbations can be used to derive predictions for variations in the intensity of cosmic microwaves over the sky and, ultimately, to test inflation. A speculative hypothesis about the early moments of the universe has thus been transformed into a testable physical theory. But it took another decade before the theory of inflation was put to the test.

  A RECIPE FOR OVERNIGHT SUCCESS

  It usually takes years, if not decades, for a new theory to be widely accepted. Physicists may appreciate a beautiful idea, but they will only be convinced when predictions of the theory are confirmed by experiments or by astronomical observations. This is particularly true in cosmology, where observers have always had a hard time keeping up with the imagination of the theorists, and the big bang theory is as good an example as any. The papers by Alexander Friedmann remained unnoticed until after his death, and the work of George Gamow was all but ignored for more than a decade. What a contrast to how inflation was received!

  Nearly forty papers were published on the new theory in the first year after Guth’s original paper. In a couple of years, this number climbed to two hundred and remained more or less steady at about two hundred papers a year for the following decade. It looked as if people dropped whatever they were doing and started working on the theory of inflation.

  Why was inflation such an instant success? In part, this was due to sociological reasons. Particle physicists had just finished developing theories of strong and electroweak interactions. There was a small army of them, and suddenly they found themselves with little to do. New ideas in particle physics were all related to extremely high energies. There was no way to test these theories in the existing particle accelerators, so progress had stalled. The only accelerator that could boost particles to the required energies appeared to be the big bang, and particle physicists were increasingly turning their sights to cosmology as a testing ground for new ideas. By the early 1980s, a mass conversion was under way from particle physics to cosmology. The converts were new to the field and were looking for interesting problems to solve.

  It was on this background that Guth suggested his idea of inflation. He gave physicists exactly what they were looking for. It really helped that Guth’s theory was incomplete. If you fully solve an important problem, your work may be admired, but you do not create an industry. Inflation, on the other hand, was just an outline of a theory, with many blanks to be filled. It offered plenty of problems to work on and to give to your graduate students.

  But, apart from sociology, the long-term popularity of inflation is due to the appeal and the power of the idea itself. In some ways, inflation is similar to Darwin’s theory of evolution. Both theories proposed an explanation for something that was previously believed to be impossible to explain. The realm of scientific inquiry was thus substantially expanded. In both cases, the explanation was very compelling, and no plausible alternatives have ever been suggested.

  Another parallel with Darwin is that the idea of inflation was already in the air at the time when Guth proposed it.o Guth’s key contribution was that he clearly realized what inflation was good for, providing the motivation to solve the graceful exit and other problems of inflation.

  UNIVERSE AS A FREE LUNCH

  We have assumed so far that the starting point for inflation was a small closed universe with a scalar field in the false vacuum, at the top of its energy hill. But these assumptions are not necessary. We could instead have started with a small chunk of false vacuum in an infinite universe. Such a beginning would also lead to inflation, but in a somewhat unexpected way.

  Remember, false vacuum has a large tension, which is responsible for its repulsive gravity. If it fills the entire space, the tension is the same everywhere and has no physical effect other than gravitational. But if it is surrounded by true vacuum, the tension inside is not balanced by any force outside and causes the false vacuum chunk to shrink. You might think that tension would be counteracted by the repulsive gravity, but this is not what actually happens.

  Analysis based on Einstein’s general relativity shows that the gravitational repulsion is purely internal. So, if you had a false-vacuum chunk for your lecture demonstration, objects would not fly away from it as in Figure 1.1. They would be attracted to it instead. Outside the false vacuum, the gravitational force is attractive as usual. So the force of tension causes the chunk to shrink, while its interior “wants” to expand because of the internal gravitational repulsion. The outcome depends on the size of the chunk.

  If it is smaller than a certain critical size, the tension wins, and the chunk shrinks like a piece of stretched rubber. Then, after a few oscillations, it disintegrates into elementary particles.

  If the size is bigger than critical, repulsive gravity wins and the false vacuum begins to swell. As it does so, it warps space, like a blown-up balloon. This effect is illustrated in Figure 6.7 for a spherical false-vacuum region. Only two spatial dimensions are shown, so the spherical boundary of the region is represented by a circle. Tension pulls the boundary inward, toward the center of the sphere, and this has the effect of reducing the volume of false vacuum. But this reduction is totally negligible compared with the exponential expansion of the interior.

  The inflating balloon is connected to the exterior space by a narrow “wormhole.” From outside, the wormhole is seen as a black hole, and observers in the exterior region can neither verify nor disprove that there is a huge inflating universe inside this black hole. Likewise, observers that will evolve in the inflating bubble universe will see only a tiny part of it and will never find out that their universe has a boundary and that there is another big universe beyond it.

  Figure 6.7. An inflating false-vacuum balloon (dark) is connected to the exterior space by a “wormhole” and is seen as a black hole from the exterior region.

  Since the fate of the false-vacuum sphere depends so crucially on whether its radius is greater than critical, it is important to know what the critical radius actually is. The answer depends on the vacuum energy density: the larger the energy density, the smaller the critical radius. For the electroweak vacuum it turns out to be about 1 millimeter, and for the grand-unified vacuum it is 10 trillion times smaller. This is all that is needed to create a universe! Truly, the ultimate free lunch. Almost …

  PART II

  ETERNAL INFLATION

  7

  The Antigravity Stone

  It would be more impressive if it flowed the other way.

  —OSCAR WILDE, on Niagara Falls

  The theory of inflation became a major topic of my research soon after that Wednesday seminar at Harvard in 1980, where I first heard about it. In fact, if I were more mystically inclined, I might have seen the writing on the wall even before Guth’s seminar. There were some clues pointing to repulsive gravity right where I work, at Tufts University.

  Set on a gently sloping hill, amid shady elms, the Tufts campus exudes an air of grace and tranquility. As you climb the stairs up the hill to the heart of the campus, and walk past the ivy-covered Romanesque chapel, you may notice a peculiar monument. It is a sizable slab of granite, rising vertically from the ground, like an old tombstone. The inscription says:

  THIS MONUMENT HAS BEEN

  ERECTED BY THE

  GRAVITY RESEARCH FOUNDATION,

  ROGER W. BABSON FOUNDER.

  IT IS TO REMIND STUDENTS OF

  THE BLESSINGS FORTHCOMING

  WHEN A SEMI-INSULATOR IS

  DISCOVERED IN ORDER TO HARNESS

  GRAVITY AS FREE POWER

  AND REDUCE AIRPLANE ACCIDENTS.

  1961

  This is the notorious antigravity stone, the sign of my destiny.

  Roger Babson, who also founded Babson College, was living proof that shrewd business judgment can peacefully coexist with far-out scientific id
eas. He claimed it was by using Newton’s laws of mechanics that he predicted the stock market crash of 1929 and the Great Depression that followed. With Newton’s help, he managed to amass a great fortune, and in gratitude to Sir Isaac, he bought an entire room from Newton’s last residence in London as well as an apple tree that is a descendant of the famous tree at Newton’s family home in Lincolnshire. Legend has it that the fall of an apple from that tree inspired Newton to discover the law of gravity. And gravity, as you might have guessed, was a paramount theme in Babson’s universe.

  Babson’s obsession with gravity dates back to his childhood, when his sister drowned in a river. He blamed gravity for her death and resolved to free humanity from its fatal pull. In his book Gravity—Our Enemy No. 1, Babson described the benefits to be derived from an insulator against gravity. It would reduce the weight of airplanes and increase their speed; it could even be used in the soles of shoes to lighten weight when walking. Babson’s lifelong friend, the famous inventor Thomas Edison, suggested to him that birds may have some antigravity stuff in their skin, and Babson promptly acquired a collection of some five thousand stuffed birds. It is not clear exactly what he did with them, but apparently this line of research did not result in any breakthrough.

  To his credit, Babson did put his money where his mouth was. He made gifts to several universities, Tufts included, to facilitate antigravity research. The only condition of the grant was that a monument with Babson’s inscription be erected on campus.