From Eternity to Here: The Quest for the Ultimate Theory of Time

by Sean M. Carroll

  Figure 79: A potential energy curve appropriate for “new inflation.” The field is never stuck in a valley, but rolls very slowly down an elevated plateau, before ultimately crashing down to the minimum. The energy density during that phase is not precisely constant, but is nearly so.

  But that’s not all. Besides offering a solution to the horizon, flatness, and monopole problems, inflation comes with a completely unanticipated bonus: It can explain the origin of the small fluctuations in the density of the early universe, which later grew into stars and galaxies.

  The mechanism is simple, and inevitable: quantum fluctuations. Inflation does its best to make the universe as smooth as possible, but there is a fundamental limit imposed by quantum mechanics. Things can’t become too smooth, or we would violate the Heisenberg Uncertainty Principle by pinpointing the state of the universe too precisely. The inevitable quantum fuzziness in the energy density from place to place during inflation gets imprinted on the amount of matter and radiation the inflaton converts into, and that translates into a very specific prediction for what kinds of perturbations in density we should see in the early universe. It’s those primordial perturbations that imprint temperature fluctuations in the cosmic microwave background, and eventually grow into stars, galaxies, and clusters. So far, the kinds of perturbations predicted by inflation match the observations very well.262 It’s breathtaking to look into the sky at the distribution of galaxies through space, and imagine that they originated in quantum fluctuations when the universe was a fraction of a second old.

  ETERNAL INFLATION

  After inflation was originally proposed, cosmologists eagerly started investigating its properties in a variety of different models. In the course of these studies, Russian-American physicists Alexander Vilenkin and Andrei Linde noticed something interesting: Once inflation starts, it tends to never stop.263

  To understand this, it’s actually easiest to go back to the idea of old inflation, although the phenomenon also occurs in new inflation. In old inflation, the inflaton field is stuck in a false vacuum, rather than rolling slowly down a hill; since space is otherwise empty, the universe during inflation takes the form of de Sitter space with a very high energy density. The trick is, how do you get out of that phase—how do you get inflation to stop, and have the de Sitter space turn into the hot expanding universe of the conventional Big Bang model? Somehow we have to convert the energy stored in the false-vacuum state of the inflaton field into ordinary matter and radiation.

  When a field is stuck in a false vacuum, it wants to decay to the lower-energy true vacuum. But it doesn’t do so all at once; the false vacuum decays via the formation of bubbles, just like liquid water boils when it turns into water vapor. At random intervals, small bubbles of true vacuum pop into existence within the false vacuum, through the process of quantum fluctuations. Each bubble grows, and the space inside expands. But the space outside the bubble expands even faster, since it’s still dominated by the high-energy false vacuum.

  So there is a competition: Bubbles of true vacuum appear and grow, but the space in between them is also growing, pushing the bubbles apart. Which one wins? That depends on how quickly the bubbles are created. If they form fast enough, all the bubbles collide, and the energy in the false vacuum gets converted into matter and radiation. But we don’t want bubbles to form too fast—otherwise we don’t get enough inflation to address the cosmological puzzles we want to solve.

  Unfortunately for the old-inflation scenario, there is no happy compromise. If we insist that we get enough inflation to solve our cosmological puzzles, it turns out that bubbles must form so infrequently that they never fill up the whole space. Individual bubbles might collide, just by chance; but the total set of bubbles doesn’t expand and run into each other fast enough to convert all of the false vacuum into true vacuum. There is always some space in between the bubbles, stuck in the false vacuum, expanding at a terrific rate. Even though bubbles continue to form, the total amount of false vacuum just keeps getting bigger, since space is expanding faster than bubbles are created.

  What we’re left with is a mess—a chaotic, fractal distribution of bubbles of true vacuum surrounded by regions of false vacuum expanding at a terrific rate. That doesn’t seem to look like the smooth, dense early universe with which we are familiar, so old inflation was set aside once new inflation came along.

  But there is a loophole: What if our observable universe is contained inside a single bubble? Then it wouldn’t matter that the space outside was wildly inhomogeneous, with patches of false vacuum and patches of true vacuum—within our single bubble, everything would appear smooth, and we’re not able to observe what goes on outside, simply because the early universe is opaque.

  There’s a good reason why this possibility wasn’t considered by Guth when he originally invented old inflation. If you start with the simplest examples of a bubble of true vacuum appearing inside a false vacuum, the interior of that bubble isn’t full of matter and radiation—it’s completely empty. So you don’t go from de Sitter space with a high vacuum energy to a conventional Big Bang cosmology; you go right to empty space, in the form of de Sitter space with a lower value of the vacuum energy (if the energy of the true vacuum is positive). That’s not the universe in which we live.

  It wasn’t until much later that cosmologists realized that this argument was a bit too quick. In fact, there is a way to “reheat” the interior of the true-vacuum bubble, to create the conditions of the Big Bang model: an episode of new inflation inside the bubble. We imagine that the inflaton field inside the bubble doesn’t land directly at the bottom of its potential, corresponding to the true vacuum; instead, it lands on an intermediate plateau, from which the field slowly rolls toward that minimum. In this way, there can be a phase of new inflation within each bubble; the energy density from the inflaton potential while it’s on the plateau can later be converted into matter and radiation, and we end up with a perfectly plausible universe.264

  Figure 80: The decay of false-vacuum de Sitter space into bubbles of true vacuum in old inflation. The bubbles never completely collide, and the amount of space in the false-vacuum phase grows forever; inflation never really ends.

  So old inflation, once it starts, never ends. You can make bubbles of true vacuum that look like our universe, but the region of false vacuum outside always keeps growing. More bubbles keep appearing, and the process never terminates. That’s the idea of “eternal inflation.” It doesn’t happen in every model of inflation; whether or not it occurs depends on details of the inflaton and its potential.265 But you don’t have to delicately tune the theory too badly to allow for eternal inflation; it happens in a healthy fraction of inflationary models.

  THE MULTIVERSE

  There is a lot to say about eternal inflation, but let’s just focus on one consequence: While the universe we see looks very smooth on large scales, on even larger (unobservable) scales the universe would be very far from smooth. The large-scale uniformity of our observed universe sometimes tempts cosmologists into assuming that it must keep going like that infinitely far in every direction. But that was always an assumption that made our lives easier, not a conclusion from any rigorous chain of reasoning. The scenario of eternal inflation predicts that the universe does not continue on smoothly as far as it goes; far beyond our observable horizon, things eventually begin to look very different. Indeed, somewhere out there, inflation is still going on. This scenario is obviously very speculative at this point, but it’s important to keep in mind that the universe on ultra-large scales is, if anything, likely to be very different than the tiny patch of universe to which we have direct access.

  This situation has led to the introduction of some new vocabulary and the abuse of some old vocabulary. Each bubble of true vacuum, if we set things up correctly, resembles our observable universe in rough outline: The energy that used to be in the false vacuum gets converted into ordinary matter and radiation, and we find a hot, dense, smooth, expand
ing space. Someone living inside one bubble wouldn’t be able to see any of the other bubbles (unless they collided)—they would just see the Big-Bang-like conditions at the beginning of their bubble. This picture actually represents the simplest example of a multiverse—each bubble, evolving separately from all the rest, evolves as a universe unto itself.

  Obviously we’re taking some liberties with the word universe here. If we were being more careful, it might be better to use the word universe to refer to the totality of everything there is, whether we could see it or not. (And sometimes we do use it that way, just to add to the confusion.) But most cosmologists have been abusing the nomenclature for some time now, and if we want to communicate with other scientists it will be useful to speak the same language. We have heard sentences like “our universe is 14 billion years old” so often that we don’t want to go back and correct them all by adding “at least, the observable part of our universe.” So instead people often attach the word universe to a region of spacetime that resembles our observable universe, starting from a hot, dense state and expanding from there. Alan Guth has suggested the phrase pocket universes, which conveys the idea a bit more precisely.

  The multiverse, therefore, is just this collection of pocket universes—regions of true vacuum, expanding and cooling after a dramatic beginning—and the background inflating spacetime in which they are embedded. When you think about it, this is a rather mundane conception of the idea of a “multiverse.” It’s really just a collection of different regions of space, all of which evolve in similar ways to the universe we observe.

  An interesting feature of this kind of multiverse has attracted a great deal of attention recently: Local laws of physics can be very different in each of those pocket universes. When we drew the potential energy plot for the inflaton in Figure 78, we illustrated three different vacuum states (A, B, C). But there is nothing to stop there from being many more than that. As we alluded to briefly in Chapter Twelve, string theory seems to predict a huge number of vacuum states—as many as 10500, if not more. Each such state is a different phase in which spacetime can find itself. That means different kinds of particles, with different masses and interactions—basically, completely new laws of physics in each universe. Again, that’s a bit of an abuse of language, because the underlying laws (string theory, or whatever) are still the same; but they manifest themselves in different ways, just like water can be solid, liquid, or gas. String theorists these days refer to the “landscape” of possible vacuum states.266

  But it’s one thing for your theory to permit many different vacuum states, each with its own laws of physics; it’s something else to claim that all the different states actually exist somewhere out there in the multiverse. That’s where eternal inflation comes in. We told a story in which inflation occurs in a false vacuum state, and ends (within each pocket universe) by evolving into a true vacuum, either by bubble formation or by slowly rolling. But if inflation continues forever, there’s nothing to stop it from evolving into different vacuum states in different pocket universes; indeed, that’s just what you would expect it should do. So eternal inflation offers a way to take all those possible universes and make them real.

  That scenario—if it’s right—comes with profound consequences. Most obviously, if you had entertained some hope of uniquely predicting features of physics we observe (the mass of the neutrino, the charge of the electron, and so forth) on the basis of a Theory of Everything, those hopes are now out the window. The local manifestations of the laws of physics will vary from universe to universe. You might hope to make some statistical predictions, on the basis of the anthropic principle; “sixty-three percent of observers in the multiverse will find three families of fermions,” or something to that effect. And many people are trying hard to do just that. But it’s not clear whether it’s even possible, especially since the number of observers experiencing certain features will often end up being infinitely big, in a universe that keeps inflating forever.

  For the purposes of this book, we are very interested in the multiverse, but not so much in the details of the landscape of many different vacua, or attempts to wrestle the anthropic principle into a useful set of predictions. Our problem—the small entropy of the observable universe at early times—is so very blatant and dramatic that there’s no hope of addressing it via recourse to the anthropic principle; life could certainly exist in a universe with a much higher entropy. We need to do better, but the idea of a multiverse might very well be a step in the right direction. At the very least, it suggests that what we see might not be nearly all there is, as far as the universe is concerned.

  WHAT GOOD IS INFLATION?

  Let’s put it all together. The story that cosmologists like to tell themselves about inflation267 goes something like this:

  We don’t know what conditions in the extremely early universe were really like. Let’s assume it was dense and crowded, but not necessarily smooth; there may have been wild fluctuations from place to place. These may have included black holes, oscillating fields, and even somewhat empty patches. Now imagine that at least one small region of space within this mess is relatively quiet, with its energy density consisting mostly of dark super-energy from the inflaton field. While the rest of space goes on its chaotic way, this particular patch begins to inflate; its volume increases by an enormous amount, while any preexisting perturbations get wiped clean by the inflationary stretching. At the end of the day, that particular patch evolves into a region of space that looks like our universe as described by the standard Big Bang model, regardless of what happens to the rest of the initially fluctuating primordial soup. Therefore, it doesn’t require any delicate, unnatural fine-tuning of initial conditions to get a universe that is spatially flat and uniform over large distances; it arises robustly from generic, randomly fluctuating initial conditions.

  Note that the goal is to explain why a universe like the one we find ourselves in today would arise naturally as the result of dynamical processes in the early universe. Inflation is concerned solely with providing an explanation for some apparently finely tuned features of our universe at early times; if you choose to take the attitude that the early universe is what it is, and it makes no sense to “explain” it, then inflation has nothing to offer to you.

  Does it work? Does inflation really explain why our seemingly unnatural initial conditions are actually quite likely? I want to argue that inflation by itself doesn’t answer these questions at all; it might be part of the final story, but it needs to be supplemented by some ideas about what happened before inflation if the idea is to have any force whatsoever. This puts us (that is to say, me) squarely in the minority of contemporary cosmologists, although not completely alone268; most workers in the field are confident that inflation operates as advertised to remove the fine-tuning problems that plague the standard Big Bang model. You should be able to make your own judgments, keeping in mind that ultimately it’s Nature who decides.

  In the last chapter, in order to discuss the evolution of the entropy within our universe, we introduced the idea of our “comoving patch”—the part of the universe that is currently observable to us, considered as a physical system evolving through time. It’s reasonable to approximate our patch as a closed system—even though it is not strictly isolated, we don’t think that the rest of the universe is influencing what goes on within our patch in any important way. That remains true in the inflationary scenario. Our patch finds itself in a configuration where it is very small, and dominated by dark super-energy; other parts of the universe might look dramatically different, but who cares?

  We previously presented the puzzle of the early universe in terms of entropy: Our comoving patch has an entropy today of about 10101, but at earlier times it was approximately 1088, and it could be as large as 10120. So the early universe had a much, much smaller entropy than the current universe. Why? If the state of the universe were chosen randomly among all possible states, it would be extraordinarily unlikely to b
e in such a low-entropy configuration, so clearly there is more to the story.

  Inflation purports to provide the rest of the story. From wildly oscillating initial conditions—which, implicitly or explicitly, are sometimes misleadingly described as “high entropy”—a small patch can naturally evolve into a region with an entropy of 1088 that looks like our universe. Having gone through this book, we all know that a truly high-entropy configuration is not a wildly oscillating high-energy mess; it’s exactly the opposite, a vast and quiet empty space. The conditions necessary for inflation to start are, just like the early universe in the conventional Big Bang story, not at all what we would get if we were picking states randomly from a hat.

  In fact it’s worse than that. Let’s focus in on the tiny patch of space, dominated by dark super-energy, in which inflation starts. What is its entropy? That’s a hard question to answer, for the standard reason that we don’t know enough about entropy in the presence of gravity, especially not in the high-energy regime relevant for inflation. But we can make a reasonable guess. In the last chapter we discussed how there are only so many possible states that can “fit” into a given region of an expanding universe, at least if they are described by the ordinary assumptions of quantum field theory (which inflation assumes). The states look like vibrating quantum fields, and the vibrations must have wavelengths smaller than the size of the region we are considering, and larger than the Planck length. This means there is a maximum number of possible states that can look like the small patch that is ready to inflate.