The Universe_Leading Scientists Explore the Origin, Mysteries, and Future of the Cosmos

by John Brockman

  Exactly how this works in detail can be described in various ways. I will choose to present a very nice geometrical picture that’s motivated by superstring theory. We use only a few basic elements from superstring theory, so you don’t really have to know anything about superstring theory to understand what I’m going to talk about, except to understand that some of the strange things I’m going to introduce I am not introducing for the first time. They’re already sitting there in superstring theory waiting to be put to good purpose.

  One of the ideas in superstring theory is that there are extra dimensions; it’s an essential element to that theory, which is necessary to make it mathematically consistent. In one particular formulation of that theory, the universe has a total of eleven dimensions. Six of them are curled up into a little ball so tiny that, for my purposes, I’m just going to pretend they’re not there. However, there are three spatial dimensions, one time dimension, and one additional dimension that I do want to consider. In this picture, our three dimensions with which we’re familiar and through which we move lie along a hypersurface, or membrane. This membrane is a boundary of the extra dimension. There is another boundary, or membrane, on the other side. In between, there’s an extra dimension that, if you like, only exists over a certain interval. It’s like we are one end of a sandwich, in between which there is a so-called bulk volume of space. These surfaces are referred to as orbifolds or branes—the latter referring to the word “membrane.” The branes have physical properties. They have energy and momentum, and when you excite them you can produce things like quarks and electrons. We are composed of the quarks and electrons on one of these branes. And, since quarks and leptons can only move along branes, we are restricted to moving along and seeing only the three dimensions of our brane. We cannot see directly the bulk or any matter on the other brane.

  In the cyclic universe, at regular intervals of trillions of years, these two branes smash together. This creates all kinds of excitations—particles and radiation. The collision thereby heats up the branes, and then they bounce apart again. The branes are attracted to each other through a force that acts just like a spring, causing the branes to come together at regular intervals. To describe it more completely, what’s happening is that the universe goes through two kinds of stages of motion. When the universe has matter and radiation in it, or when the branes are far enough apart, the main motion is the branes stretching, or, equivalently, our three dimensions expanding. During this period, the branes more or less remain a fixed distance apart. That’s what’s been happening, for example, in the last 15 billion years. During these stages, our three dimensions are stretching just as they normally would. At a microscopic distance away, there is another brane sitting and expanding, but since we can’t touch, feel, or see across the bulk, we can’t sense it directly. If there is a clump of matter over there, we can feel the gravitational effect, but we can’t see any light or anything else it emits, because anything it emits is going to move along that brane. We only see things that move along our own brane.

  Next, the energy associated with the force between these branes takes over the universe. From our vantage point on one of the branes, this acts just like the dark energy we observe today. It causes the branes to accelerate in their stretching, to the point where all the matter and radiation produced since the last collision is spread out and the branes become essentially smooth, flat, empty surfaces. If you like, you can think of them as being wrinkled and full of matter up to this point, and then stretching by a fantastic amount over the next trillion years. The stretching causes the mass and energy on the brane to thin out and the wrinkles to be smoothed out. After trillions of years, the branes are, for all intents and purposes, smooth, flat, parallel, and empty.

  Then the force between these two branes slowly brings the branes together. As it brings them together, the force grows stronger and the branes speed toward one another. When they collide, there’s a walloping impact—enough to create a high density of matter and radiation with a very high, albeit finite, temperature. The two branes go flying apart, more or less back to where they are, and then the new matter and radiation, through the action of gravity, causes the branes to begin a new period of stretching.

  In this picture, it’s clear that the universe is going through periods of expansion and a funny kind of contraction. Where the two branes come together, it’s not a contraction of our dimensions but a contraction of the extra dimension. Before the contraction, all matter and radiation has been spread out, but, unlike the old cyclic models of the 1920s and ’30s, it doesn’t come back together again during the contraction, because our three dimensions—that is, the branes—remain stretched out. Only the extra dimension contracts. This process repeats itself cycle after cycle.

  If you compare the cyclic model to the consensus picture, two of the functions of inflation—namely, flattening and homogenizing the universe—are accomplished by the period of accelerated expansion that we’ve now just begun. Of course, I really mean the analogous expansion that occurred one cycle ago, before the most recent Bang. The third function of inflation—producing fluctuations in the density—occurs as these two branes come together. As they approach, quantum fluctuations cause the branes to begin to wrinkle. And because they’re wrinkled, they don’t collide everywhere at the same time. Rather, some regions collide a bit earlier than others. This means that some regions reheat to a finite temperature and begin to cool a little bit before other regions. When the branes come apart again, the temperature of the universe is not perfectly homogeneous but has spatial variations left over from the quantum wrinkles.

  Remarkably, although the physical processes are completely different and the time scale is completely different—this is taking billions of years, instead of 10-30 seconds—it turns out that the spectrum of fluctuations you get in the distribution of energy and temperature is essentially the same as what you get in inflation. Hence, the cyclic model is also in exquisite agreement with all of the measurements of the temperature and mass distribution of the universe that we have today.

  Because the physics in these two models is quite different, there is an important distinction in what we would observe if one or the other were actually true—although this effect has not been detected yet. In inflation when you create fluctuations, you don’t just create fluctuations in energy and temperature but you also create fluctuations in spacetime itself, so-called gravitational waves. That’s a feature we hope to look for in experiments in the coming decades as a verification of the consensus model. In our model, you don’t get those gravitational waves. The essential difference is that inflationary fluctuations are created in a hyperrapid, violent process that is strong enough to create gravitational waves, whereas cyclic fluctuations are created in an ultraslow, gentle process that is too weak to produce gravitational waves. That’s an example where the two models give an observational prediction that is dramatically different. It’s just difficult to observe at the present time.

  What’s fascinating at the moment is that we have two paradigms now available to us. On the one hand, they are poles apart in terms of what they tell us about the nature of time, about our cosmic history, about the order in which events occur, and about the time scale on which they occur. On the other hand, they are remarkably similar in terms of what they predict about the universe today. Ultimately what will decide between the two is a combination of observations—for example, the search for cosmic gravitational waves—and theory, because a key aspect to this scenario entails assumptions about what happens at the collision between branes that might be checked or refuted in superstring theory. In the meantime, for the next few years, we can all have great fun speculating about the implications of each of these ideas and how we can best distinguish between them.

  3

  The Inflationary Universe

  Alan Guth

  Paul Steinhardt did a very good job of presenting the case for the cyclic universe. I’m going to describe the conventional con
sensus model upon which he was trying to say that the cyclic model is an improvement. I agree with what Paul said at the end of his talk about comparing these two models; it’s yet to be seen which one works. But there are two grounds for comparing them. One is that in both cases the theory needs to be better developed. This is more true for the cyclic model, where one has the issue of what happens when branes collide. The cyclic theory could die when that problem finally gets solved definitively. Secondly, there is, of course, the observational comparison of the gravitational-wave predictions of the two models.

  A brane is short for “membrane,” a term that comes out of string theories. String theories began purely as theories of strings, but when people began to study their dynamics more carefully, they discovered that for consistency it was not possible to have a theory which discussed only strings. Whereas a string is a one-dimensional object, the theory also had to include the possibility of membranes of various dimensions to make it consistent, which led to the notion of branes in general. The theory that Paul described in particular involves a four-dimensional space plus one time dimension, which he called the bulk. That four-dimensional space was sandwiched between two branes.

  That’s not what I’m going to talk about. I want to talk about the conventional inflationary picture, and in particular the great boost that this picture has attained over the past few years by the somewhat shocking revelation of a new form of energy that exists in the universe. This energy, for lack of a better name, is typically called dark energy.

  But let me start the story further back. Inflationary theory itself is a twist on the conventional Big Bang theory. The shortcoming that inflation is intended to overcome is the basic fact that although the Big Bang theory is called the Big Bang, it is in fact not really a theory of a bang at all; it never was. The conventional Big Bang theory, without inflation, was really only a theory of the aftermath of the Bang. It started with all of the matter in the universe already in place, already undergoing rapid expansion, already incredibly hot. There was no explanation of how it got that way. Inflation is an attempt to answer that question, to say what “banged,” and what drove the universe into this period of enormous expansion. Inflation does that very wonderfully. It explains not only what caused the universe to expand but also the origin of essentially all the matter in the universe at the same time. I qualify that with the word “essentially” because, in a typical version of the theory, inflation needs about a gram’s worth of matter to start. So inflation is not quite a theory of the ultimate beginning, but it is a theory of evolution that explains essentially everything we see around us, starting from almost nothing.

  The basic idea behind inflation is that a repulsive form of gravity caused the universe to expand. General relativity, from its inception, predicted the possibility of repulsive gravity; in the context of general relativity, you basically need a material with a negative pressure to create repulsive gravity. According to general relativity, it’s not just matter densities or energy densities that create gravitational fields, it’s also pressures. A positive pressure creates a normal attractive gravitational field, of the kind we’re accustomed to, but a negative pressure would create a repulsive kind of gravity. It also turns out that according to modern particle theories, materials with a negative pressure are easy to construct out of fields that exist according to these theories. By putting together these two ideas—the fact that particle physics gives us states with negative pressures, and that general relativity tells us that those states cause a gravitational repulsion—we reach the origin of the inflationary theory.

  By answering the question of what drove the universe into expansion, the inflationary theory can also answer some questions about that expansion that would otherwise be mysterious. There are two very important properties of our observed universe that were never really explained by the Big Bang theory; they were just part of one’s assumptions about the initial conditions. One of them is the uniformity of the universe—the fact that it looks the same everywhere, no matter which way you look, as long as you average over large enough volumes. It’s both isotropic, meaning the same in all directions, and homogeneous, meaning the same in all places. The conventional Big Bang theory never really had an explanation for that; it just had to be assumed from the start. The problem is that although we know that any set of objects will approach a uniform temperature if they’re allowed to sit for a long time, the early universe evolved so quickly that there wasn’t enough time for this to happen. To explain, for example, how the universe could have smoothed itself out to achieve the uniformity of temperature we observe today in the cosmic background radiation, one finds that in the context of the standard Big Bang theory it would be necessary for energy and information to be transmitted across the universe at about a hundred times the speed of light.

  In the inflationary theory, this problem goes away completely, because, in contrast to the conventional theory, it postulates a period of accelerated expansion while this repulsive gravity is taking place. That means that if we follow our universe backward in time toward the beginning using inflationary theory, we see that it started from something much smaller than you ever could have imagined in the context of conventional cosmology without inflation. While the region that would evolve to become our universe was incredibly small, there was plenty of time for it to reach a uniform temperature, just like a cup of coffee sitting on the table cools down to room temperature. Once this uniformity is established on this tiny scale by normal thermal-equilibrium processes—and I’m talking now about something that’s about a billion times smaller than the size of a single proton—inflation can take over and cause this tiny region to expand rapidly and become large enough to encompass the entire visible universe. The inflationary theory not only allows the possibility for the universe to be uniform but also tells us why it’s uniform: It’s uniform because it came from something that had time to become uniform and was then stretched by the process of inflation.

  The second peculiar feature of our universe that inflation does a wonderful job of explaining, and for which there never was a prior explanation, is the flatness of the universe—the fact that the geometry of the universe is so close to Euclidean. In the context of relativity, Euclidean geometry is not the norm, it’s an oddity. With general relativity, curved space is the generic case. In the case of the universe as a whole, once we assume that the universe is homogeneous and isotropic, then this issue of flatness becomes directly related to the relationship between the mass density and the expansion rate of the universe. A large mass density would cause space to curve into a closed universe in the shape of a ball; if the mass density dominated, the universe would be a closed space with a finite volume and no edge. If a spaceship traveled in what it thought was a straight line for a long enough distance, it would end up back where it started from. In the alternative case, if the expansion dominated, the universe would be geometrically open. Geometrically open spaces have the opposite geometric properties from closed spaces. They’re infinite. In a closed space, two lines which are parallel will start to converge; in an open space, two lines which are parallel will start to diverge. In either case, what you see is very different from Euclidean geometry. However, if the mass density is right at the borderline of these two cases, then the geometry is Euclidean, just like we all learned about in high school.

  In terms of the evolution of the universe, the fact that the universe is at least approximately flat today requires that the early universe was extraordinarily flat. The universe tends to evolve away from flatness, so even given what we knew ten or twenty years ago—we know much better, now, that the universe is extraordinarily close to flat—we could have extrapolated backward and discovered that, for example, at one second after the Big Bang the mass density of the universe must have been equal, to an accuracy of fifteen decimal places, to the critical density where it counterbalanced the expansion rate to produce a flat universe. The conventional Big Bang theory gave us no reason to believe that th
ere was any mechanism to require that, but it has to have been that way, to explain why the universe looks the way it does today. The conventional Big Bang theory without inflation really only worked if you fed into it initial conditions which were highly finely tuned to make it just right to produce a universe like the one we see. Inflationary theory gets around this flatness problem, because inflation changes the way the geometry of the universe evolves with time. Even though the universe always evolves away from flatness at all other periods in the history of the universe, during the inflationary period the universe is actually driven towards flatness incredibly quickly. If you had approximately 10-34 seconds or so of inflation at the beginning of the universe, that’s all you need. Inflation would then have driven the universe to be flat closely enough to explain what we see today.

  There are two primary predictions that come out of inflationary models, which appear to be testable today. They have to do (1) with the mass density of the universe, and (2) with the properties of the density nonuniformities. I’d like to say a few words about each of them, one at a time. Let me begin with the question of flatness.