by Adam Frank
As the last decade of the twentieth century ended, ideas once considered the domain of science fiction were put on sure mathematical footing. Multiple universes became the stuff of foundational physics. Stranger still, some scientists began to ask if the very existence of life might somehow play a role in selecting the nature of the cosmos we see. Another solution to the question of “before” the Big Bang, very different from cyclic models, appeared in the form of a theory called eternal inflation. Looking over the consequences of the new theory, however, many scientists saw it demanding a redefinition of scientific cosmology’s fundamental purpose. Was it a solution with too high a price?
To understand eternal inflation and its universe of universes, the story must begin with inflation’s beginnings—its mechanisms for making cosmic mountains out of infinitesimal molehills.
DEVILS AND DETAILS: MAKING INFLATION
Beginning with Alan Guth, cosmologists invoked inflation as a mechanism for taking a small piece of the infant universe and blowing it up to become the entire universe we can see. By stretching a sliver of reality by the gigantic factor of 1040, all the paradoxes of classic Big Bang theory were resolved: space-time was stretched to flatness, regions that appear unconnected today shared an initial harmony at the beginning of time, unwanted magnetic monopoles were so diluted as to be unobservable.2
Inflation accomplished all this paradox-busting by filling the early universe with what cosmologist Sean Carroll calls “dark superenergy”.3 Inflation’s titanic push, stretching space apart, worked in any region of the universe where this dark superenergy was active, hyperexpanding a speck of creation into everything we can see today. The trick to making inflation theory work, however, was getting the superenergy to start and stop at just the right moment.
Originally, Guth and others hoped to power inflation by using energy locked up in a quantum field associated with grand unification. In physics, a field is a physical entity that extends across space. This is the opposite of a particle, like an electron, that is localized in just one place at just one time. Fields became actors in physics as far back as the 1850s. The electromagnetic field reaching out across space from magnets and electrical charges is the archetype of a physical field. Learning how to describe fields in terms of quantum mechanics took some time, but by the 1940s and 1950s the main principles had been worked out. When the smoke cleared, scientists realized that quantum field theory even blurred the distinction between localized particles and extended fields. In this theory, all the particles we know of—the electron, the neutrino, and so on—are simply localized oscillations of an extended quantum field.
Guth and others hoped to tap the vast energies in the primordial GUTs quantum fields that must have filled the early cosmos and use them for inflation. One of these fields, they argued, could power inflation if it extended across post–Big Bang space in just the right way. This inflation quantum field (associated with some form of quantum particle) would fill space by creating an all-pervading energetic background. If the energy of this background—the false vacuum—could be transformed at just the right moment and in just the right way, then a small region of space could be driven into a fantastically rapid expansion. In the language of physics, a phase transition would occur. Like cold water turning into ice, the false vacuum of the inflation quantum field would transform into the true vacuum of empty space, releasing tremendous energies in the process. After the phase transition was complete, the residual energy of inflation would fill our newly expanded piece of the universe with matter and light particles, continuing on with the usual history of the hot Big Bang.
Making inflation work, however, demanded a description of the potential energy that was locked up in the false vacuum quantum field. We all have experience with potential energy in the context of gravity. A heavy ball, like a bowling ball, placed on a high shelf has more potential energy than the same ball lying on the floor. Knocking the ball off the shelf and letting it plunge to the floor converts the gravitational field’s potential energy into the bowling ball’s kinetic energy.4 The urgency you’d muster to pull your foot away from a ball speeding down towards you is stark testimony to the reality of potential energy. Getting cosmic inflation to work meant finding a quantum field with the right form of potential energy. The field would have to drop from its false-vacuum latent-energy state to its true-vacuum low-energy state in just the right way, and at just the right time, to hyperexpand a small speck of post–Big Bang space-time.
The details depend on what physics calls the quantum field’s potential energy curve, which describes how the potential energy changes when the field itself changes. Any bumps and wiggles in the potential energy curve will change the evolution of the field, in the same way that a ball rolling down a lumpy hill will speed up or slow down as it traverses small depressions. For inflation, the “depressions”, called local minima, were critical, as they shaped the transition from the false vacuum to the true vacuum.
The success of inflation depends greatly on the shape of the quantum field’s potential energy curve. Guth’s original proposal for inflation was almost stillborn because the potential energy curve he used was taken from grand unified field theory and seemed to stop short of making the universe we see today. In Guth’s first proposal, now called “old” inflation, the dark superenergy field began resting in a local depression somewhere high up on the potential energy curve. This was the false vacuum state. Any piece of the universe caught in this state would be inflating, growing and stretching.
FIGURE 10.2. The potential energy curves for inflationary cosmology. These plots show different models for how the energy in the quantum field generating inflation change as the field itself changes. The potential curves determine how an inflating universe evolves. Some curves lead to a cosmos like ours and others don’t.
Guth then imagined that small regions of space, whose fields were trapped in a local minimum, would spontaneously decay, like a radioactive nucleus, to a lower position on the curve, corresponding to the true vacuum of the universe. This would be a phase transition similar to what happens when bubbles of steam pop into existence within a pot of boiling water. Different parts of inflating space would make the transition at different times, leading to bubbles of true vacuum. Guth hoped that eventually all the bubbles of true vacuum would collide and merge to form one spatially expanded true-vacuum universe. But the timing didn’t work out. Space in the false-vacuum state was still inflating so fast that new bubbles of true vacuum would be swept apart too quickly to interact. Trying to tweak the theory so bubbles of true vacuum could form faster and collide only forced inflation to stop before it could work its full magic.5
The problems with Guth’s idea were fixed a few years later when theorists began abandoning explicit grand unified theories and realized that other kinds of quantum fields could be used as inflation fuel. These quantum fields were not associated with any known GUT’s field (or particle). They were inventions, obeying the basic rules of quantum field theory. Relinquishing the GUT’s framework was not considered a loss. No one knew what kinds of quantum fields might exist in the early, early universe because no complete theory for that era existed. Most physicists felt free to construct models of possible inflation quantum fields with associated particles they called “inflatons”. These alternative models did not begin with the inflaton field stuck in a false-vacuum local minimum; instead they allowed it to begin at the top of a potential-energy hill and slowly roll down to the true-vacuum state. A ball rolling down from the crest of a hill after a random nudge was the analogy physicists were using to construct their new versions of inflation. By assuming that the initial high point in the curve was unstable, physicists realized, a small nudge would be all that was needed to start the inflaton rolling down its potential curve. The extended roll was important for the theory because it kept space in the false vacuum state long enough to form a local bubble of true vacuum.
This “new” inflation overcame the timing issue plaguing Guth
’s original model and allowed it to yield the observable universe with all the properties we now see. New inflation was a spectacular theoretical success and soon won over many converts. Different versions of the basic theory rapidly multiplied as scientists explored various potential energy curves for the inflaton and their consequences for cosmic evolution. But it was not long before people started thinking about the rest of the universe—the part that did not make the transition from false vacuum to true vacuum. What about these other regions of cosmic space-time that remained in the false vacuum state?
In the late 1980s physicists began exploring inflation’s consequences for the entire post–Big Bang universe, and not just the little speck that grew into our cosmic home. Their conclusions expanded the meaning of inflationary cosmology and the very definition of the universe it was meant to explain.
INFLATION BECOMES ETERNAL: MAKING THE MULTIVERSE
Inflation, in its way, is an elegant solution to the paradoxes haunting Big Bang cosmology and particle physics. Fill the early universe with dark superenergy to hyperexpand space just when needed, then sit back and watch all the problems with monopoles, causality and so on wash away. But the cost of inflation’s solution to the paradox was a recognition that the Big Bang created more universe than what we see. Just as important was the realization that the other regions of creation existed in an entirely different state than our slice of the pie did. Once that genie—the rest of the universe—was let out of the bottle, physicists found it difficult to force it back in.
Alexander Vilenkin and Andrei Linde were two of the first physicists to begin thinking about the rest of the universe under the auspices of inflation.6 Both scientists began exploring the relationship between the parts of the post–Big Bang universe that had decayed to true vacuum and the parts that continued to inflate in the dark-superenergy-sodden false-vacuum state.7
If a ball is resting exactly at the top of a hill, all that is needed is a gentle breeze or the tremor from a passing lorry to send it rolling down. With inflation, it is quantum mechanics that determines when a transition up to false vacuum occurs and when the fall back to true vacuum follows. Inflationary cosmology uses the random fluctuations associated with quantum physics to kick a small region of space up to its false-vacuum perch and then back down to the true-vacuum state lower on the potential energy curve. The random quantum kicks come about once every 10–33 of a second. In some regions of space, the random kicks will build up enough to push the inflation field out of its false-vacuum state and send it “rolling” downhill to the true vacuum. Exploring this process in more detail, Vilenkin realized that inflating space always won out over noninflating space in terms of sheer volume. Once inflation began, there would always be some parts of the universe left in the false vacuum. Inflation, in other words, just kept going. It was eternal.
Together Vilenkin, Linde and others began working out the consequences of this eternal inflation idea. Through their work, a new vision of cosmic history and cosmic cartography was formed. If inflation continued even after our observable universe had formed, then what was to stop other small regions of space that were still inflating from making their own transitions to the true vacuum in their own sweet time? The answer was nothing. Under eternal inflation, different regions of space make their own phase transition from false vacuum to true vacuum, each creating a “pocket universe” like our own in the process. Each pocket universe is, in general, cut off from the others because the inflating space in between carries them apart at such tremendous speeds. It is worth noting that while nothing travelling through space can exceed the speed of light, this speed limit does not apply to how fast space itself can expand. Thus, the different pocket universes are carried out of causal contact with each other even though they are all part of the same grand, infinite space-time fabric.
By allowing different regions to drop into the true vacuum on their own, eternal inflation makes a radical prediction about the universe—that there is no longer just one.
If inflation continues forever, then true-vacuum pocket universes are constantly forming from the background of false-vacuum hyperexpanding space. All these universes, together with the inflating space between them, form a new entity: a multiverse. The multiverse is a universe of universes. Once a pocket universe like ours forms, then its history is no different from what occurs in the standard post–Big Bang model. Space expands, matter cools, nuclei form and the CMB eventually fills the observable sky. As Vilenkin stated:
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.8
But there is more to the story. Not only does eternal inflation predict other universes forming in the multiverse, most of them won’t look anything like the one we live in.
FIGURE 10.3. Eternal inflation and the multiverse. Eternal inflation assumes that many different regions of space-time as a whole can make the transition from false vacuum to true vacuum. Thus a multiverse of “pocket universes” arises. Each pocket universe can have its own version of physics.
There are many ways for a small shard of space to make a transition from the false vacuum. Once inflation ends, the energy of the false vacuum is freed up to fill each pocket universe with particles, allowing normal cosmic evolution to proceed. But the exact form of those particles, and the forces they obey, will vary from one pocket universe to the next. This is similar to ice forming in freezing water. Each ice crystal gets its own orientation from the random motions of water molecules in that region. Before freezing, the water looks the same from one region to the other, but in the phase transition that constitutes ice formation that symmetry is broken. Ice crystals forming on one region of a pane of glass will not be aligned with crystals forming on another region.
Drawing on the analogy of freezing water, eternal inflation theory predicts that each pocket universe might form with different physics. The initial symmetry and unified physics of the false vacuum are broken during the transition to the true vacuum state inside a pocket universe. In some pockets there might be no electromagnetism, while in others electromagnetism might be a thousand times stronger than it is in ours. Some pockets have two forms of the strong nuclear force and no weak force. In others it will be reversed. The possibilities are nearly infinite. In fact, the landscape of string theory can be brought into play at this point, providing 10500 different ways to go from false to true vacuum. If string theory is the correct theory of everything, then it will be the foundation for inflation. The 10500 dimples in string theory’s own “energy landscape” of possibilities then becomes 10500 possible laws of physics for the pocket universes. Every possibility is a pocket universe existing within the totality of the multiverse.
From the 1990s onward, eternal inflation gained recognition as an almost inevitable consequence of plain old inflation. While there were ways to construct inflation theory so that all space-time made the transition from false vacuum at once, these types of inflation were not its most general form. Left to its own devices, an inflating cosmos appeared likely to become an eternally inflating cosmos complete with separate pocket universes and different laws of physics. In this way, multiverse was added to the lexicon of cosmology. Entire conferences attended by sober physicists were dedicated to the theoretical exploration of the multiverse’s properties. And while scientists spoke of pocket universes with different laws of physics, the goal was always to find the meta-laws (such as string theory) that would govern the multiverse as a whole. Through it all, recognition of a shift away from the Big Bang was becoming apparent. The eternity implied in eternal inflation seemed to nullify time’s beginning.
Infinity in the past and the future had found its way back into cosmology.
PIERCING THE MULTIVERSE’S ARROW OF TIME
“
The real problem is not the beginning of time but the arrow of time,”9 said Sean Carroll, a theoretical physicist at Caltech in Pasadena. Carroll is a prodigious thinker on cosmological issues both inside and outside academia, and from his point of view, the problem has never been what came before the Big Bang; it’s the very notion of “before” and “after.” “The thing we really have to understand,” he says, “is why cosmic time has a direction at all.”10 For Carroll, the multiverse of eternal inflation offers a new form of the steady-state model writ large.
The arrow of time is one of deepest problems in physics. Big Bang cosmology cannot escape its conundrums. The problem is simple and lives at the interface between the second law of thermodynamics and the rest of physics. Ever since Newton, the equations describing physics have been time-reversible. The laws governing individual objects do not care about time’s direction. Imagine a film of two billiard balls colliding in space. There is really no way to say if the film is being run forward or backwards. The same is true of two atoms colliding. The equations of quantum physics, like Newton’s equations, do not have a direction of time built into them.
If, however, you mix a zillion atoms together into something like a dozen eggs, then everything changes. Suddenly past and future look very different. As everyone knows, you can’t unscramble an omelette made with those eggs. With large collections of atoms, thermodynamics enters the picture and with it comes that all-important quantity, entropy. We have already encountered different ways of thinking about entropy, including as a measure of a system’s disorder. The flip side of this definition is to see how entropy is directly related to the number of ways a system’s parts can be arranged. Together these definitions link the important second law of thermodynamics to a direction of time.
Pop a balloon in a big empty room and the atoms will fill the entire space. Heat up a cup of coffee and it will cool down to the temperature of the room. In both cases, the system slides through changes until an equilibrium is reached. But in physics, equilibrium and maximum entropy mean the same thing, and both are related to the system achieving a state of maximum disorder. What does maximum disorder mean? It’s just another way of saying the maximum number of ways for arranging the system’s parts. There are, for example, only a few ways to get atoms squeezed into a corner of the room. The atoms have to be packed in close and there is not much room between them. There are, on the other hand, a lot of ways to distribute the same atoms across the entire room. So the path from low entropy (all atoms in one corner of the room) to maximum entropy (atoms filling the room) defines the arrow of time. The route to equilibrium discriminates what is before from what is after. Once equilibrium is reached, nothing changes, and the difference between past and future has no meaning.
