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.
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
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