From Eternity to Here: The Quest for the Ultimate Theory of Time - Sean Carroll (2010)
Part IV. FROM THE KITCHEN TO THE MULTIVERSE
Chapter 14. INFLATION AND THE MULTIVERSE
Those who think of metaphysics as the most unconstrained or speculative of disciplines are misinformed; compared with cosmology, metaphysics is pedestrian and unimaginative.
On a cool Palo Alto morning in December 1979, Alan Guth pedaled his bike as fast as he could to his office in the theoretical physics group at SLAC, the Stanford Linear Accelerator Center. Upon reaching his desk, he opened his notebook to a new page and wrote:
SPECTACULAR REALIZATION: this kind of supercooling can explain why the universe today is so incredibly flat—and therefore resolve the fine-tuning paradox pointed out by Bob Dicke in his Einstein Day lectures.
He carefully drew a rectangular box around the words. Then he drew another one.255
As a scientist, you live for the day when you hit upon a result—a theoretical insight, or an experimental discovery—so marvelous that it deserves a box around it. The rare double-box-worthy results tend to change one’s life, as well as the course of science; as Guth notes, he doesn’t have any other double-boxed results anywhere in his notebooks. The one from his days at SLAC is now on display at the Adler Planetarium in Chicago, open to the page with the words above.
Guth had hit on the scenario now known as inflation—the idea that the early universe was suffused with a temporary form of dark energy at an ultra-high density, which caused space to accelerate at an incredible rate (the “supercooling” mentioned above). That simple suggestion can explain more or less everything there is to explain about the conditions we observe in our early universe, from the geometry of space to the pattern of density perturbations observed in the cosmic microwave background. Although we do not yet have definitive proof that inflation occurred, it has been arguably the most influential idea in cosmology over the last several decades.
Figure 73: Alan Guth, whose inflationary universe scenario may help explain why our observed universe is close to smooth and flat.
Which doesn’t mean inflation is right, of course. If the early universe was temporarily dominated by dark energy at an ultra-high scale, then we can understand why the universe would evolve into just the state it was apparently in at early times. But there is a danger of begging the important question—why was it ever dominated by dark energy in that way? Inflation doesn’t provide any sort of answer by itself to the riddle of why entropy was low in the early universe, other than to assume that it started even lower (which is arguably a bit of a cheat).
Nevertheless, inflation is an extraordinarily compelling idea, which really does seem to match well with the observed features of our early universe. And it leads to some surprising consequences that Guth himself never foresaw when he first suggested the scenario—including, as we’ll see, a way to make the idea of a “multiverse” become realistic. It seems likely, in the judgment of most working cosmologists, that some version of inflation is correct—the question is, why did inflation ever happen?
THE CURVATURE OF SPACE
Imagine you take a pencil and balance it vertically on its tip. Obviously its natural tendency will be to fall over. But you could imagine that if you had an extremely stable surface, and you were a real expert at balancing, you could arrange things so that the pencil remained vertical for a very long time. Like, more than 14 billion years.
The universe is somewhat like that, where the pencil represents the curvature of space. This can be a more confusing concept than it really should be, because cosmologists sometimes speak about the “curvature of spacetime,” and other times about the “curvature of space,” and those things are different; you’re supposed to figure out from context which one is meant. Just as spacetime can have curvature, space all by itself can as well—and the question of whether space is curved is completely independent of whether spacetime is curved.256
One potential problem in discussing the curvature of space by itself is that general relativity gives us the freedom to slice spacetime into three-dimensional copies of space evolving through time in a multitude of ways; the definition of “space” is not unique. Fortunately, in our observed universe there is a natural way to do the slicing: We define “time” such that the density of matter is approximately constant through space on large scales, but diminishing as the universe expands. The distribution of matter, in other words, defines a natural rest frame for the universe. This doesn’t violate the precepts of relativity in any way, because it’s a feature of a particular configuration of matter, not of the underlying laws of physics.
In general, space could curve in arbitrary ways from place to place, and the discipline of differential geometry was developed to handle the mathematics of curvature. But in cosmology we’re lucky in that space is uniform over large distances, and looks the same in every direction. In that case, all you have to do is specify a single number—the “curvature of space”—to tell me everything there is to know about the geometry of three-dimensional space.
The curvature of space can be a positive number, or a negative number, or zero. If the curvature is zero, we naturally say that space is “flat,” and it has all the characteristics of geometry as we usually understand it. These characteristics were first set out by Euclid, and include properties like “initially parallel lines stay parallel forever,” and “the angles inside a triangle add up to precisely 180 degrees.” If the curvature is positive, space is like the surface of a sphere—except that it’s three-dimensional. Initially parallel lines do eventually intersect, and angles inside a triangle add up to greater than 180 degrees. If the curvature is negative, space is like the surface of a saddle, or of a potato chip. Initially parallel lines grow apart, and angles inside a triangle—well, you can probably guess.257
According to the rules of general relativity, if the universe starts flat, it stays flat. If it starts curved, the curvature gradually diminishes away as the universe expands. However, as we know, the density of matter and radiation also dilutes away. (For right now, forget you’ve ever heard about dark energy, which changes everything.) When you plug in the equations, the density of matter or radiation decreases faster than the amount of curvature. Relative to matter and radiation, curvature becomes more relevant to the evolution of the universe as space expands.
Therefore: If there is any noticeable amount of curvature whatsoever in the early universe, the universe today should be very obviously curved. A flat universe is like a pencil balanced exactly on its tip; if there were any deviation to the left or right, the pencil would tend to fall pretty quickly onto its side. Similarly, any tiny deviation from perfect flatness at early times should have become progressively more noticeable as time went on. But as a matter of observational fact, the universe looks very flat. As far as anyone can tell, there is no measurable curvature in the universe today at all.258
Figure 74: Ways that space can have a uniform curvature. From top to bottom: positive curvature, as on a sphere; negative curvature, as on a saddle; zero curvature, as on a flat plane.
This state of affairs is known as the flatness problem. Because the universe is so flat today, it had to be incredibly flat in the past. But why?
The flatness problem bears a family resemblance to the entropy problem we discussed in the last chapter. In both cases, it’s not that there is some blatant disagreement between theory and observation—all we have to do is posit that the early universe had some particular form, and everything follows nicely from there. The problem is that the “particular form” seems to be incredibly unnatural and finely tuned, for no obvious reason. We could say that both the entropy and the spatial curvature of the early universe just were small, and there’s no explanation beyond that. But these apparently unnatural features of the universe might be a clue to something important, so it behooves us to take them seriously.
Alan Guth wasn’t trying to solve the flatness problem when he hit upon the idea of inflation. He was interested in a very different puzzle, known as the monopole problem.
Guth, for that matter, wasn’t especially interested in cosmology. In 1979, he was in his ninth year of being a postdoctoral researcher—the phase of a scientist’s career in between graduate school and becoming a faculty member, when they concentrate on research without having to worry about teaching duties or other academic responsibilities. (And without the benefit of any job security whatsoever; most postdocs never succeed in getting a faculty job, and eventually leave the field.) Nine years is past the time when a talented postdoc would normally have moved on to become an assistant professor somewhere, but Guth’s publication record at this point in his career didn’t really reflect the ability that others saw in him. He had labored for a while on a theory of quarks that had fallen out of favor, and was now trying to understand an obscure prediction of the newly popular “Grand Unified Theories”: the prediction of magnetic monopoles.
Grand Unified Theories, or GUTs for short, attempt to provide a unified account of all the forces of nature other than gravity. They became very popular in the 1970s, both for their inherent simplicity, and because they made an intriguing prediction: that the proton, the stalwart elementary particle that (along with the electron and the neutron) forms the basis for all the matter around us, would ultimately decay into lighter particles. Giant laboratories were built to search for proton decay, but it hasn’t yet been discovered. That doesn’t mean that GUTs aren’t right; they are still quite popular, but the failure to detect proton decay has left physicists at a loss over how these theories should be tested.
GUTs also predicted the existence of a new kind of particle, the magnetic monopole. Ordinary charged particles are electric monopoles—that is, they have either a positive charge or a negative charge, and that’s all there is to it. No one has ever discovered an isolated “magnetic charge” in Nature. Magnets as we know them are always dipoles—they come with a north pole and a south pole. Cut a magnet in half between the poles, and two new poles pop into existence where you made the cut. As far as experimenters can tell, looking for an isolated magnetic pole—a monopole—is a lot like looking for a piece of string with only one end.
But according to GUTs, monopoles should be able to exist. In fact, in the late 1970s people realized that you could sit down and calculate the number of monopoles that should be created in the aftermath of the Big Bang. And the answer is: way too many. The total amount of mass in monopoles, according to these calculations, should be much higher than the total mass in ordinary protons, neutrons, and electrons. Magnetic monopoles should be passing through your body all the time.
There is an easy way out of this, of course: GUTs might not be right. And that still might be the correct solution. But Guth, while thinking about the problem, hit on a more interesting one: inflation.
Dark energy—a source of energy density that is approximately (or exactly) constant throughout space and time, not diluting away as the universe expands—makes the universe accelerate, by imparting a perpetual impulse to the expansion. We believe that most of the energy in the universe, between 70 percent and 75 percent of the total, is currently in the form of dark energy. But in the past, when matter and radiation were denser, dark energy presumably had about the same density it has today, so it would have been relatively unimportant.
Now imagine that, at some other time in the very early universe, there was dark energy with an extraordinarily larger energy density—call it “dark super-energy.”259 It dominated the universe and caused space to accelerate at a terrific rate. Then—for reasons to be specified later—this dark super-energy suddenly decayed into matter and radiation, which formed the hot plasma making up the early universe we usually think about. The decay was almost complete, but not quite, leaving behind the relatively minuscule amount of dark energy that has just recently become important to the dynamics of the universe.
That’s the scenario of inflation. Basically, inflation takes a tiny region of space and blows it up to an enormous size. You might wonder what the big deal is—who cares about a temporary phase of dark super-energy, if it just decays into matter and radiation? The reason why inflation is so popular is because it’s like confession—it wipes away prior sins.
Figure 75: Inflation takes a tiny patch of space and expands it rapidly to a tremendous size. This figure is not at all to scale; inflation occurs in a tiny fraction of a second, and expands space by more than a factor of 1026.
Consider the monopole problem. Monopoles are (if GUTs are correct) produced in copious amounts in the extremely early universe. So imagine that inflation happens pretty early, but later than the production of monopoles. In that case, as long as inflation lasts long enough, space expands by such a tremendous amount that all the monopoles are diluted away practically to nothing. As long as the decay of the dark super-energy into matter and radiation doesn’t make any more monopoles (which it won’t, if it’s not too energetic), voilà—no more monopole problem.
Likewise with spatial curvature. The problem there was that curvature dilutes away more gradually than matter or radiation, so if there were any curvature at all early on it should be extremely noticeable today. But dark energy dilutes away even more gradually than curvature—indeed, it hardly dilutes away at all. So again, if inflation goes on long enough, curvature can get diluted to practically nothing, before matter and radiation are re-created in the decay of the dark super-energy. No more flatness problem.
You can see why Guth was excited about the idea of inflation. He had been thinking about the monopole problem, but from the other side—not trying to solve it, but using it as an argument against GUTs. In his original work on the problem, with Cornell physicist Henry Tye, they had ignored the possible role of dark energy and established that the monopole problem was very hard to solve. But once Guth sat down to study the effects that an early period of dark energy could have, a solution to the monopole problem dropped right into his lap—that’s worth at least a single box, right there.
The double-box-worthiness came when Guth understood that his idea would also solve the flatness problem, which he hadn’t even been thinking about. Completely coincidentally, Guth had gone to a lecture some time earlier by Princeton physicist Robert Dicke, one of the first people to study the cosmic microwave background. Dicke’s lecture, held at a Cornell event called “Einstein Day,” pointed out several loose ends in the conventional cosmological model. One of them was the flatness problem, which stuck with Guth, even though his research at the time wasn’t especially oriented toward cosmology.
So when he realized that inflation solved not only the monopole problem but also the flatness problem, Guth knew he was onto something big. And indeed he was; almost overnight, he went from being a struggling postdoc to being a hot property on the faculty job market. He chose to return to MIT, where he had been a graduate student, and he’s still teaching there today.
THE HORIZON PROBLEM
In working out the consequences of inflation, Guth realized that the scenario offered a solution to yet another cosmological fine-tuning puzzle: the horizon problem. Indeed, the horizon problem is arguably the most insistent and perplexing issue in standard Big Bang cosmology.
The problem arises from the simple fact that the early universe looks more or less the same at widely separated points. In the last chapter, we noted that a “typical” state of the early universe, even if we insisted that it be highly dense and rapidly expanding, would tend to be wildly fluctuating and inhomogeneous—it should resemble the time-reverse of a collapsing universe. So the fact that the universe was so smooth is a feature that seems to warrant an explanation. Indeed, it’s fair to say that the horizon problem is really a reflection of the entropy problem as we’ve presented it, although it’s usually justified in a different way.
We think of horizons in the context of black holes—the horizon is the place past which, once we get there, we can never return to the outside world. Or, more precisely, we would have to be able to travel faster than light to escape. But in the standard Big Bang model, there’s a completely separate notion of “horizon,” stemming from the fact that the Big Bang happened a finite time ago. This is a “cosmological horizon,” as opposed to the “event horizon” around a black hole. If we draw a light cone from our present location in spacetime into the past, it will intersect the beginning of the universe. And if we now consider the world line of a particle that emerges from the Big Bang outside our light cone, no signal from that world line can ever reach our current event (without going faster than light). We therefore say that such a particle is outside our cosmological horizon, as shown in Figure 76.
That’s all well and good, but things start to get interesting when we realize that, unlike an event horizon of a static black hole, our cosmological horizon grows with time as we age along our world line. As we get older, our past light cones encompass more and more of spacetime, and other particle world lines that used to be outside now enter our horizon. (The world lines haven’t moved—our horizon has expanded to include them.)
Therefore, events that are far in the past have cosmological horizons that are correspondingly smaller; they are closer (in time) to the Big Bang, so fewer events lie in their past. Consider different points that we observe when we look at the cosmic microwave background on opposite sides of the sky, as shown in Figure 77. The microwave background shows us an image of the moment when the universe became transparent, when the temperature cooled off sufficiently that electrons and protons got together to form atoms—about 380,000 years after the Big Bang. Depending on the local conditions at these points—the density, expansion rate, and so on—they could appear very different to us here today. But they don’t. From our perspective, all the points on the microwave background sky have very similar temperatures; they differ from place to place by only about one part in a hundred thousand. So the physical conditions at all these different points must have been pretty similar.
Figure 76: The cosmological horizon is defined by the place where our past light cone meets the Big Bang. As we move forward in time, our horizon grows. A world line that was outside our horizon at moment A comes inside the horizon by the time we get to B.
Figure 77: The horizon problem. We look at widely separated points on the cosmic microwave background and see that they are at nearly the same temperature. But those points are far outside each other’s horizons; no signal could have ever passed between them. How do they know to be at the same temperature?
The horizon problem is this: How did those widely separated points know to have almost the same conditions? Even though they are all within our cosmological horizon, their own cosmological horizons are much smaller, since they are much closer to the Big Bang. These days it’s a standard exercise for graduate students studying cosmology to calculate the size of the cosmological horizons for such points, under the assumptions of the standard Big Bang model; the answer is that points separated by more than about one degree on the sky have horizons that don’t overlap at all. In other words, there is no event in spacetime that is in the past of all these different points, and there is no way that any signal could be communicated to each of them.260 Nevertheless, they all share nearly identical physical conditions. How did they know?
It’s as if you asked several thousand different people to pick a random number between 1 and a million, and they all picked numbers between 836,820 and 836,830. You’d be pretty convinced that it wasn’t just an accident—somehow those people were coordinating with one another. But how? That’s the horizon problem. As you can see, it’s closely connected to the entropy problem. Having the entire early universe share very similar conditions is a low-entropy configuration, as there are only a limited number of ways it can happen.
Inflation seems to provide a neat solution to the horizon problem. During the era of inflation, space expands by an enormous amount; points that were initially quite close get pushed very far apart. In particular, points that were widely separated when the microwave background was formed were right next to each other before inflation began—thereby answering the “How did they know to have similar conditions?” question. More important, during inflation the universe is dominated by dark super-energy, which—like any form of dark energy—has essentially the same density everywhere. There might be other forms of energy in the patch of space where inflation begins, but they are quickly diluted away; inflation stretches space flat, like pulling at the edges of a wrinkled bedsheet. The natural outcome of inflation is a universe that is very uniform on large scales.
TRUE AND FALSE VACUA
Inflation is a simple mechanism to explain the features we observe in the early universe: It stretches a small patch of space to make it flat and wrinkle free, solving the flatness and horizon problems, and dilutes away unwanted relics such as magnetic monopoles. So how does it actually work?
Clearly, the trick to inflation is to have a temporary form of dark super-energy, which drives the expansion of the universe for a while and then suddenly goes away. That might seem difficult, as the defining feature of dark energy is that it is nearly constant through space and time. For the most part that’s true, but there can be sudden changes in the density—“phase transitions” where the dark energy abruptly goes down in value, like a bubble bursting. A phase transition of that form is the secret to inflation.
You may wonder what it is that actually creates this dark super-energy that drives inflation. The answer is a quantum field, just like the fields whose vibrations show up as the particles around us. Unfortunately, none of the fields we know—the neutrino field, the electromagnetic field, and so on—are right for the job. So cosmologists simply propose that there is a brand new field, imaginatively dubbed the “inflaton,” whose task it is to drive inflation. Inventing new fields out of whole cloth like this is not quite as disreputable as it sounds; the truth is, inflation supposedly takes place at energies far higher than we can directly re-create in laboratories here on Earth. There are undoubtedly any number of new fields that become relevant at such energies, even if we don’t know what they are; the question is whether any of them have the right properties to be the inflaton (i.e., give rise to a temporary phase of dark super-energy that expands the universe by a tremendous amount before decaying away).
In our discussions of quantum fields up to this point, we’ve emphasized that vibrations in such fields give rise to particles. If a field is constant everywhere, so there are no vibrations, you don’t see any particles. If all we cared about were particles, the background value of the field—the average value it takes when we imagine smoothing out all the vibrations—wouldn’t matter, since it’s not directly observable. But the background value of a field can be indirectly observable—in particular, it can carry energy, and therefore affect the curvature of spacetime.
The energy associated with a field can arise in different ways. Usually it comes about because the field is changing from point to point in spacetime; there is energy in the stretching associated with the changing field values, much like there is energy in the twists or vibrations in a sheet of rubber. But in addition to that, fields can carry energy just by sitting there with some fixed value. That kind of energy, associated with the value of the field itself rather than changes in the field from place to place or time to time, is known as “potential energy.” A rubber sheet that is perfectly flat will have more energy if it’s sitting at a high elevation than it will if it’s down on the ground; we know that, because we can extract that energy by picking up the sheet and tossing it down. Potential energy can be converted into other sorts of energy.
With a rubber sheet (or any other object sitting in the Earth’s gravitational field), the way the potential energy behaves is pretty straightforward: The higher the elevation, the more potential energy it has. With fields, things can become much more complicated. If you’re inventing a new theory of particle physics, you have to specify the particular way in which the potential energy depends on the value of each field. There aren’t many underlying rules to guide you; every field simply is associated with a potential energy for each possible value, and that’s part of the specification of the theory. Figure 78 shows an example of the potential energy for some hypothetical field, as a function of different field values.
Figure 78: A plot of how the potential energy changes depending on the background value of some hypothetical field such as the inflaton. Fields tend to roll to a low point in the energy curve; in this plot, points A, B, and C represent different phases the vacuum could be in. Phase B has the lowest energy, so it’s the “true vacuum,” while A and C are “false vacua.”
A field that has potential energy, but nothing else (no vibrations, motions, or twists) just sits there, unchanging. The potential energy per cubic centimeter is therefore constant, even as the universe expands. We know what that means: It’s vacuum energy. (More carefully, it’s one of many possible contributions to the vacuum energy.) You can think of the field like a ball rolling down a hill; it will tend to settle at the bottom of a valley, where the energy is lowest—at least, lower than any other nearby value. There might be other values of the field for which the energy is even lower, but these deeper “valleys” are separated by “hills.” In Figure 78, the field could happily live at any of the values A, B, or C, but only B truly has the lowest energy. The values A and C are known as “false vacua,” as they appear to be states of lowest energy if you only look at nearby values, while B is known as the “true vacuum,” where the energy is truly the lowest. (To a physicist, a “vacuum” is not a machine that cleans your floors, nor does it even necessarily mean “empty space.” It’s simply “the lowest-energy state of a theory.” Looking at the potential energy curve for some field, the bottom of every valley defines a distinct vacuum state.)
Guth put these ideas together to construct the inflationary universe scenario. Imagine that a hypothetical inflaton field found itself at point A, one of the false vacua. The field would be contributing a substantial amount to the vacuum energy, which would cause the universe to rapidly accelerate. Then all we have to do is explain how the field moved from the false vacuum A to the true vacuum B, where we now live—the phase transition that turns the energy locked up in the field into ordinary matter and radiation. Guth’s original suggestion was that it occurred when bubbles of true vacuum would appear amidst the false vacuum, and then grow and collide with other bubbles to fill up all of space. This possibility, now known as “old inflation,” turns out not to work; either the transition happens too quickly, and you don’t get enough inflation, or it happens too slowly, and the universe never stops inflating.
Fortunately, soon after Guth’s original paper, an alternative suggestion was made: Rather than the inflaton being stuck in a false vacuum “valley,” imagine that it starts out on an elevated plateau—a long stretch that is nearly flat. The field then slowly rolls down the plateau, keeping the energy almost constant but not quite, before ultimately falling off a cliff (the phase transition). This is called “new inflation” and is the most popular implementation of the inflationary universe idea among cosmologists today.261
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.
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.
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, expanding 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 be 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.
The numerical answer will depend on the particular way in which inflation happens, and in particular on the vacuum energy during inflation. But the differences between one model and another aren’t that significant, so it suffices to pick an example and stick to it. Let’s say that the energy scale during inflation is 1 percent of the Planck scale; pretty high, but low enough that we’re safely avoiding complications from quantum gravity. In that case, the estimated entropy of our comoving patch at the beginning of inflation is:
Sinflation ≈ 1012.
That’s an incredibly small value, compared either to the 10120 it could have been or even the 1088 it would soon become. It reflects the fact that every single degree of freedom that goes into describing our current universe must have been delicately packed into an extremely smooth, small patch of space, in order for inflation to get going.
The secret of inflation is thereby revealed: It explains why our observable universe was in such an apparently low-entropy, finely tuned early state by assuming that it started in an even lower-entropy state before that. That’s hardly surprising, if we believe the Second Law and expect entropy to grow with time, but it doesn’t seem to address the real issue. Taken at face value, it would seem very surprising indeed that we would find our comoving patch of universe in the kind of lo w-entropy configuration necessary to start inflation. You can’t solve a fine-tuning problem by appealing to an even greater fine-tuning.
OUR COMOVING PATCH REVISITED
Let’s think this through, because we’re deviating from orthodoxy here and it behooves us to be careful.
We have been making two crucial assumptions about the evolution of the observable universe—our comoving patch of space and all of the stuff within it. First, we’re assuming that the observable universe is essentially autonomous—that is, it evolves as a closed system, free from outside influences. Inflation does not violate this assumption; once inflation begins, our comoving patch rapidly turns into a smooth configuration, and that configuration evolves independently of the rest of the universe. This assumption can obviously break down before inflation, and play a role in setting up the initial conditions; but inflation itself does not take advantage of any hypothetical external influences in attempting to explain what we currently see.
The other assumption is that the dynamics of our observable universe are reversible—they conserve information. This seemingly innocuous point implies a great deal. There is a space of states that is fixed once and for all—in particular, it is the same at early times as at late times—and the evolution within that space takes different starting states to different ending states (in the same amount of time). The early universe looks very different from the late universe—it’s smaller, denser, expanding more rapidly, and so on. But (under our assumptions of reversible dynamics) that doesn’t mean the space of states has changed, only that the particular kind of state the universe is in has changed.
The early universe, to belabor the point, is the same physical system as the late universe, just in a very different configuration. And the entropy of any given microstate of that system reflects how many other microstates look similar from a macroscopic point of view. If we were to randomly choose a configuration of the physical system we call the observable universe, it would be overwhelmingly likely to be a state of very high entropy—that is, close to empty space.269
To be honest, however, people tend not to think that way, even among professional cosmologists. We tend to reason that the early universe is a small, dense place, so that when we imagine what states it might be in, we can restrict our attention to small, dense configurations that are sufficiently smooth and well behaved so that the rules of quantum field theory apply. But there is absolutely no justification for doing so, at least within the dynamics itself. When we imagine what possible states the early universe could have been in, we need to include unknown states that are outside the realm of validity of quantum field theory. For that matter, we should include all of the possible states of the current universe, as they are simply different configurations of the same system.
The size of the universe is not conserved—it evolves into something else. When we consider statistical mechanics of gas molecules in a box, it’s okay to keep the number of molecules fixed, because that reflects the reality of the underlying dynamics. But in a theory with gravity, the “size of the universe” isn’t fixed. So it makes no sense—again, just based on the known laws of physics, without recourse to some new principles outside those laws—to assume from the start that the early universe must be small and dense. That’s something we need to explain.
All of which is somewhat problematic for the conventional justification that we put forward for the inflationary universe scenario. According to the previous story, we admit that we don’t know what the early universe was like, but we imagine that it was characterized by wild fluctuations. (The current universe, of course, is not characterized by such fluctuations, so already there is something to be explained.) Among those fluctuations, every once in a while a region will come into existence that is dominated by dark super-energy, and the conventional inflation story follows. After all, how hard can it be to randomly fluctuate into the right conditions to start inflation?
The answer is that it can be incredibly hard. If we truly randomly chose a configuration for the degrees of freedom within that region, we would be overwhelmingly likely to get a high-entropy state: a large, empty universe.270Indeed, simply by comparing entropies, we’d be much more likely to get our current universe, with a hundred billion galaxies and all the rest, than we would be to get a patch ready to inflate. And if we’re not randomly choosing configurations of those degrees of freedom—well, then, what are we doing? That’s beyond the scope of the conventional inflationary story.
These problems are not specific to the idea of inflation. They would plague any possible scenario that claimed to provide a dynamical explanation for the apparent fine-tuning of our early universe, while remaining consistent with our two assumptions (our comoving patch is a closed system, and its dynamics are reversible). The problem is that the early universe has a low entropy, which means that there are a relatively small number of ways for the universe to look like that. And, while information is conserved, there is no possible dynamical mechanism that can take a very large number of states and evolve them into a smaller number of states. If there were, it would be easy to violate the Second Law.
SETTING THE STAGE
This discussion has intentionally emphasized the hidden skeletons in the closet of the inflationary universe scenario—there are plenty of other books that will emphasize the arguments in its favor.271 But let’s be clear: The problem isn’t really with inflation; it’s with how the theory is usually marketed. We often hear that inflation removes the pressing need for a theory of initial conditions, as inflation will begin under fairly generic circumstances, and once it begins all our problems are solved.
The truth is almost the converse: Inflation has a lot going for it, but it makes the need for a theory of initial conditions much more pressing. Hopefully I’ve made the case that neither inflation nor any other mechanism can, by itself, explain our lo w-entropy early universe under the assumptions of reversibility and autonomous evolution. It’s possible, of course, that reversibility should be the thing to go; perhaps the fundamental laws of physics violate reversibility at a fundamental level. Even though that’s intellectually conceivable, I’ll argue that it’s hard to make such an idea match what we actually see in the world.
A less drastic strategy would be to move beyond the assumption of autonomous evolution. We knew all along that treating our comoving patch as a closed system was, at best, an approximation. It seems like an extremely good approximation right now, or even at any time in the history of the universe about which we actually have empirical data. But surely it breaks down at the very beginning. Inflation could play a crucial role in explaining the universe we see, but only if we can discard the idea that “we just randomly fluctuated into it,” and come up with a particular reason why the conditions necessary for inflation ever came to pass.
In other words, it seems like the most straightforward way out of our conundrum is to abandon the goal of explaining the unnatural early universe purely in terms of the autonomous evolution of our comoving patch, and instead try to embed our observable universe into a bigger picture. This brings us back to the idea of the multiverse—a larger structure in which the universe we observe is just a tiny part. If something like that is true, we are at least able to contemplate the idea that the evolution of the multiverse naturally gives rise to conditions under which inflation can begin; after that, the story proceeds as above.
So we want to ask, not what our the physical system making up our observable universe should look like, but what a multiverse should look like, and whether it would naturally give rise to regions that look like the universe we see. Ideally, we’d want it to happen without putting in time asymmetry by hand at any step along the way. We want to explain not only how we can get the right conditions to start inflation, but why it might be natural to have a large swath of spacetime (our observable universe) that features those conditions at one end of time and empty space at the other. This is a program that is far from complete, although we have some ideas. We’re deep into speculative territory by now, but if we keep our wits about us we should be able to take a safe journey without being devoured by dragons.