From Eternity to Here (62 page)

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 inflation
²⁶⁷
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 alone
²⁶⁸
; 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 10
¹⁰¹
, but at earlier times it was approximately 10
⁸⁸
, and it could be as large as 10
¹²⁰
. 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 10
⁸⁸
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:

S
_inflation
≈ 10
¹²
.

That’s an incredibly small value, compared either to the 10
¹²⁰
it could have been or even the 10
⁸⁸
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.
²⁷⁰
Indeed, 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.