108 November 21, 2002
THE INFLATIONARY UNIVERSE: ALAN GUTH
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 CYCLIC UNIVERSE: PAUL STEINHARDT
...in the last year I've been involved in the development of an alternative theory that turns the cosmic history topsy-turvy. All the events that created the important features of our universe occur in a different order, by different physics, at different times, over different time scalesand yet this model seems capable of reproducing all of the successful predictions of the consensus picture with the same exquisite detail.
A BIOLOGICAL UNDERSTANDING OF HUMAN NATURE: A TALK WITH STEVEN PINKER
Bak died on October 16, 2002, at the age of 54. Per was one of the
founders and most influential contributors to the study of complex
systems. Per made many contributions to science, but the best known
was a general theory of self-organization, which he called, "self-organized
criticality". His ideas and discoveries have had an influence
over how people think about a broad range of phenomena, from physics
to biology, neurosciences, cosmology, earth sciences, economics and
beyond. As a scientist and as a person he was an inspiration and a
challenge to those of us who knew him. He was, for me that rare scientist
who, though not in my field, could at any moment surprise me by saying
something that would make me realize I had to rethink something I
had thought I understood....
ALAN GUTH: Paul Steinhardt did a very good job of presenting the case for the cyclic universe. I'm going to describe the conventional consensus 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 is 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 only discussed 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 that 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 that 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 which 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 very 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 are allowed to sit for a long time, the early universe evolved so quickly that there was not enough time for this to happen. To explain, for example, how the universe could have smoothed itself out to achieve the uniformity of temperature that 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 backwards in time towards 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 to 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 backwards 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 15 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 there 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 to be able to start out a factor of 105 or 1010 away from being flat. 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 that 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 non-uniformities. I'd like to say a few words about each of them, one at a time. Let me begin with the question of flatness.
The mechanism that inflation provides that drives the universe towards flatness will in almost all cases overshoot, not giving us a universe that is just nearly flat today, but a universe that's almost exactly flat today. This can be avoided, and people have at times tried to design versions of inflation that avoided it, but these versions of inflation never looked very plausible. You have to arrange for inflation to end at just the right point, where it's almost made the universe flat but not quite. It requires a lot of delicate fine-tuning, but in the days when it looked like the universe was open some people tried to design such models. But they always looked very contrived, and never really caught on.
The generic inflationary model drives the universe to be completely flat, which means that one of the predictions is that today the mass density of the universe should be at the critical value which makes the universe geometrically flat. Until three or four years ago no astronomers believed that. They told us that if you looked at just the visible matter, you would see only about one percent of what you needed to make the universe flat. But they also said that they could offer more than that there's also dark matter. Dark matter is matter that's inferred to exist because of the gravitational effect that it has on visible matter. It's seen, for example, in the rotation curves of galaxies. When astronomers first measured how fast galaxies rotate, they found they were spinning so fast that if the only matter present was what you saw, galaxies would just fly apart.
To understand the stability of galaxies it was necessary to assume that there was a large amount of dark matter in the galaxy about five or ten times the amount of visible matter which was needed just to hold the galaxy together. This problem repeats itself when one talks about the motion of galaxies within clusters of galaxies. The motion of galaxies in clusters is much more random and chaotic than the spiral galaxy, but the same issues arise. You can ask how much mass is needed to hold those clusters of galaxies together, and the answer is that you still need significantly more matter than what you assumed was in the galaxies. Adding all of that together, astronomers came up only to about a third of the critical density. They were pretty well able to guarantee that there wasn't any more than that out there; that was all they could detect. That was bad for the inflationary model, but many of us still had faith that inflation had to be right and that sooner or later the astronomers would come up with something.
And they did, although what they came up with was something very different from the kind of matter that we were talking about previously. Starting in 1998, astronomers have been gathering evidence for the remarkable fact that the universe today appears to be accelerating, not slowing down. As I said at the beginning of this talk, the theory of general relativity allows for that. What's needed is a material with a negative pressure. We are now therefore convinced that our universe must be permeated with a material with negative pressure, which is causing the acceleration that we're now seeing. We don't know what this material is, but we're referring to it as "dark energy." Even without knowing what it is, general relativity by itself allows us to calculate how much mass has to be out there to cause the observed acceleration, and it turns out to be almost exactly equal to two-thirds of the critical density. This is exactly what was missing from the previous calculations! So, if we assume that this dark energy is real, we now have complete agreement between what the astronomers are telling us about the mass density of the universe and what inflation predicts.
The other important prediction that comes out of inflation is becoming even more persuasive than the issue of flatness: namely, the issue of density perturbations. Inflation has what in some ways is a wonderful characteristic that by stretching everything out (and Paul's model takes advantage of the same effect) you can smooth out any non-uniformities that were present prior to this expansion. Inflation does not depend sensitively on what you assume existed before inflation; everything there just gets washed away by the enormous expansion. For a while, in the early days of developing the inflationary model, we were all very worried that this would lead to a universe that would be absolutely, completely smooth. After a while several physicists began to explore the idea that quantum fluctuations could save us. The universe is fundamentally a quantum mechanical system, so perhaps quantum theory was necessary not just to understand atoms, but also to understand galaxies. It is a rather remarkable idea that an aspect of fundamental physics like quantum theory could have such a broad sweep. The point is that a classical version of inflationary theory would predict a completely uniform density of matter at the end of inflation. According to quantum mechanics, however, everything is probabilistic. There are quantum fluctuations everywhere, which means that in some places the mass density would be slightly higher than average, and in other places it would be slightly lower than average. That's exactly the sort of thing you want to explain the structure of the universe. You can even go ahead and calculate the spectrum of these non-uniformities, which is something that Paul and I both worked on in the early days and had great fun with. The answer that we both came up with was that, in fact, quantum mechanics produces just the right spectrum of non-uniformities.
We really can't predict the overall amplitude that is, the intensity of these ripples unless we know more about the fundamental theory. At the present time, we have to take the overall factor that multiplies the predicted intensity of these ripples from observation. But we can predict the spectrum that is, the complicated pattern of ripples can be viewed as ripples of many different wavelengths lying on top of each other, and we can calculate how the intensity of the ripples varies with their wavelengths. We knew how to do this back in 1982, but recently it has actually become possible for astronomers to see these non-uniformities imprinted on the cosmic background radiation. These were first observed back in 1992 by the COBE (Cosmic Background Explorer) satellite, but back then they could only see very broad features, since the angular resolution of the satellite was only about seven degrees. Now, they've gotten down to angular resolutions of about a tenth of a degree. These observations of the cosmic background radiation can be used to produce plots of the spectrum of non-uniformities, which are becoming more and more detailed.
The most recent data set was made by an experiment called the Cosmic Background Imager, which released a new set of data in May that is rather spectacular. This graph of the spectrum is rather complicated because these fluctuations are produced during the inflationary era, but then oscillate as the early universe evolves. Thus, what you see is a picture that includes the original spectrum plus all of the oscillations which depend on various properties of the universe. A remarkable thing is that these curves now show five separate peaks, and all five of the peaks show good agreement between theory and observation. You can see that the peaks are in about the right place and have about the right heights, without any ambiguity, and the leading peak is rather well-mapped-out. It's a rather remarkable fit between actual measurements made by astronomers, and a theory based on wild ideas about quantum fluctuations at 10-35 seconds. The data is so far in beautiful agreement with the theory.
At the present time the inflationary theory, which a few years ago was in significant conflict with observation, now agrees very well with our measurements of the mass density and the non-uniformities of the cosmic background radiation. The evidence for either inflation, or something very close to it, is very, very strong.
I'd just like to close by saying that although I've been using the word "theory" in the singular to talk about inflation, I really shouldn't. It's very important to remember that inflation is really a class of theories. If inflation is right it is by no means the end of our study of the origin of the universe, but it's really still closer to the beginning. There are many different versions of inflation, and in fact the cyclic model that Paul described could be considered one version. It's a rather novel version since it puts the inflation at a completely different era of the history of the universe, but inflation is still doing many of the same things that it does in other theories. There are also many versions of inflation of the more traditional type. There's a great deal of flexibility within the inflationary picture, so there is still a lot to be learned. The continuation of this work will involve both the study of cosmology and the study of the underlying particle physics, which is essential to these models. The intersection between cosmology and particle physics us likely to remain an exciting area of science for many years to come.
PAUL STEINHARDT: I am theoretical cosmologist, so I am addressing the issue from that point of view. If you were to ask most cosmologists to give a summary of where we stand right now in the field, they would tell you that we live in a very special period in human history where, thanks to a whole host of advances in technology, we can suddenly view the very distant and very early universe in ways that we haven't been able to do ever before. For example, we can get a snapshot of what the universe looked like in its infancy, when the first atoms were forming. We can get a snapshot of what the universe looked like in its adolescence, when the first stars and galaxies were forming. And we are now getting a full detail, three-dimensional image of what the local universe looks like today. When you put together this different information, which we're getting for the first time in human history, you obtain a very tight series of constraints on any model of cosmic evolution. If you go back to the different theories of cosmic evolution in the early 1990's, the data we've gathered in the last decade has eliminated all of themsave one, a model that you might think of today as the consensus model. This model involves a combination of the Big Bang model as developed in the 1920s, '30s, and '40s; the Inflationary Theory, which Alan Guth proposed in the 1980s; and a recent amendment that I will discuss shortly. This consensus theory matches the observations we have of the universe today in exquisite detail. For this reason, many cosmologists conclude that we have finally determined the basic cosmic history of the universe.
But I have a rather different point of view, a view that has been stimulated by two events. The first is the recent amendment to which I referred earlier. I want to argue that the recent amendment is not simply an amendment, but a real shock to our whole notion of time and cosmic history. And secondly, in the last year I've been involved in the development of an alternative theory that turns the cosmic history topsy-turvy. All the events that created the important features of our universe occur in a different order, by different physics, at different times, over different time scalesand yet this model seems capable of reproducing all of the successful predictions of the consensus picture with the same exquisite detail.
The key difference between this picture and the consensus picture comes down to the nature of time. The standard model, or consensus model, assumes that time has a beginning that we normally refer to as the Big Bang. According to this model, for reasons we don't quite understand, the universe sprang from nothingness into somethingness, full of matter and energy, and has been expanding and cooling for the past 15 billion years. In the alternative model the universe is endless. Time is endless in the sense that it goes on forever in the past and forever in the future, and, in some sense, space is endless. Indeed, our three spatial dimensions remain infinite throughout the evolution of the universe.
More specifically, this model proposes a universe in which the evolution of the universe is cyclic. That is to say, the universe goes through periods of evolution from hot to cold, from dense to under-dense, from hot radiation to the structure we see today, and eventually to an empty universe. Then, a sequence of events occurs that cause the cycle to begin again. The empty universe is reinjected with energy, creating a new period of expansion and cooling. This process repeats periodically forever. What we're witnessing now is simply the latest cycle.
The notion of a cyclic universe is not new. People have considered this idea as far back as recorded history. The ancient Hindus, for example, had a very elaborate and detailed cosmology based on a cyclic universe. They predicted the duration of each cycle to be 8.64 billion yearsa prediction with three-digit accuracy. This is very impressive, especially since they had no quantum mechanics and no string theory! It disagrees with the number that I'm going suggest, which is trillions of years rather than billions.
The cyclic notion has also been a recurrent theme in Western thought. Edgar Allan Poe and Friedrich Nietzsche, for example, each had cyclic models of the universe, and in the early days of relativistic cosmology, Albert Einstein, Alexandr Friedman, Georges Lemaître, and Richard Tolman were interested in the cyclic idea. I think it is clear why so many have found the cyclic idea to be appealing: If you have a universe with a beginning, you have the challenge of explaining why it began and the conditions under which it began. If you have a universe, which is cyclic, it is eternal, so you don't have to explain the beginning.
During the attempts to try to bring cyclic ideas into modern cosmology, it was discovered in the '20s and '30s that there are various technical problems. The idea at that time was a cycle in which our three-dimensional universe goes through periods of expansion beginning from the Big Bang and then reversal to contraction and a big crunch. The universe bounces and expansion begins again. One problem is that, every time the universe contracts to a crunch, the density and temperature of the universe rises to an infinite value, and it is not clear if the usual laws of physics can be applied. Second, every cycle of expansion and contraction creates entropy through natural thermodynamic processes, which adds to the entropy from earlier cycles. So, at the beginning of a new cycle, there is higher entropy density than the cycle before. It turns out that the duration of a cycle is sensitive to the entropy density. If the entropy increases, the duration of the cycle increases as well. So, going forward in time, each cycle becomes longer than the one before. The problem is that, extrapolating back in time, the cycles become shorter until, after a finite time, they shrink to zero duration. The problem of avoiding a beginning has not been solved. It has simply been pushed back a finite number of cycles. If we're going to reintroduce the idea of a truly cyclic universe, these two problems must be overcome. The cyclic model that I will describe uses new ideas to do just that.
To appreciate why an alternative model is worth pursuing, its important to get a more detailed impression of what the consensus picture is like. Certainly some aspects are appealing. But, what I want to argue is that, overall, the consensus model is not so simple. In particular, recent observations have forced us to amend the consensus model and make it more complicated. So, let me begin with an overview of the consensus model.
The consensus theory begins with the Big Bang: the universe has a beginning. It's a standard assumption that people have made over the last 50 years, but it's not something we can prove at present from any fundamental laws of physics. Furthermore, you have to assume that the universe began with an energy density less than the critical value. Otherwise, the universe would stop expanding and recollapse before the next stage of evolution, the inflationary epoch. In addition, to reach this inflationary stage, there must be some sort of energy to drive the inflation. Typically this is assumed to be due to an inflation field. You have to assume that in those patches of the universe that began at less than the critical density, a significant fraction of the energy is stored in inflation energy so that it can eventually overtake the universe and start the period of accelerated expansion. All of these are reasonable assumption, but assumptions nevertheless. It's important that to count these assumptions and ingredients, because they are helpful in comparing the consensus model to the challenger.
Assuming these conditions are met, the inflation energy overtakes the matter and radiation after a few instants. The inflationary epoch commences and the expansion of the universe accelerates at a furious pace. The inflation does a number of miraculous things: it makes the universe homogeneous, it makes the universe flat, and it leaves behind certain inhomogeneities, which are supposed to be the seeds for the formation of galaxies. Now the universe is prepared to enter the next stage of evolution with the right conditions. According to the inflationary model, the inflation energy decays into a hot gas of matter and radiation. After a second or so, there form the first light nuclei. After a few tens of thousands of years, the slowly moving matter dominates the universe. It's during these stages that the first atoms form, the universe becomes transparent, and the structure in the universe begins to formthe first stars and galaxies. Up to this point the story is relatively simple.
But, there is the recent discovery that we've entered a new stage in the evolution of the universe. After the stars and galaxies have formed, something strange has happened to cause the expansion of the universe to speed up again. During the 15 billion years when matter and radiation dominated the universe and structure was forming, the expansion of the universe was slowing down because the matter and radiation within it is gravitationally self-attractive and resists the expansion of the universe. Until very recently, it had been presumed that matter would continue to be the dominant form of energy in the universe, and this deceleration would continue forever.
But we've discovered instead, due to recent observations that the expansion of the universe is speeding up. This means that most of the energy of the universe is neither matter nor radiation. Rather, another form of energy has overtaken the matter and radiation. For lack of a better term, this new energy form is called "dark energy." Dark energy, unlike the matter and radiation that we're familiar with, is gravitationally self-repulsive. That's why it causes the expansion to speed up rather than slow down. In Newton's theory gravity, all mass is gravitationally attractive, but Einstein's theory allows the possibility of forms of energy that are gravitationally self-repulsive.
I don't think either the physics or cosmology communities, or even the general public, have fully absorbed the full implications of this discovery. This is a revolution in the grand historic sensein the Copernican sense. In fact, if you think about Copernicusfrom whom we derive the word revolutionhis importance was that he changed our notion of space and of our position in the universe. By showing that the earth revolves around the sun, he triggered a chain of ideas that led us to the notion that we live in no particular place in the universe; there's nothing special about where we are. Now we've discovered something very strange about the nature of time: that we may live in no special place, but we do live at a special time, a time of recent transition from deceleration to acceleration; from one in which matter and radiation dominate the universe to one in which they are rapidly becoming insignificant components; from one in which structure is forming in ever-larger scales to one in which now, because of this accelerated expansion, structure formation stops. We are in the midst of the transition between these two stages of evolution. And just as Copernicus's proposal that the earth is no longer the center of the universe led to a chain of ideas that changed our whole outlook on the structure of the solar system and eventually to the structure of the universe, it shouldn't be too surprising that perhaps this new discovery of cosmic acceleration could lead to a whole change in our view of cosmic history. That's a big part of the motivation for thinking about our alternative proposal.
With these thoughts about the consensus model in mind, let me turn to the cyclic proposal. Since it's cyclic, I'm allowed to begin the discussion of the cycle at any point I choose. To make the discussion parallel, I'll begin at a point analogous to the Big Bang; I'll call it The Bang. This is a point in the cycle where the universe reaches its highest temperature and density. In this scenario, though, unlike the Big Bang model, the temperature and density don't diverge. There is a maximal, finite temperature. It's a very high temperature, around 10 (ten to the 20) degrees Kelvinhot enough to evaporate atoms and nuclei into their fundamental constituentsbut it's not infinite. In fact, it's well below the so-called Planck energy scale, where quantum gravity effects dominate. The theory begins with a bang and then proceeds directly to a phase dominated by radiation. In this scenario you do not have the inflation one has in the standard scenario. You still have to explain why the universe is flat, you still have to explain why the universe is homogeneous, and you still have to explain where the fluctuations came from that led to the formation of galaxies, but that's not going to be explained by an early stage of inflation. It's going to be explained by yet a different stage in the cyclic universe, which I'll get to.
In this new model, you go directly to a radiation-dominated universe and form the usual nuclear abundances; then go directly to a matter-dominated universe in which the atoms and galaxies and larger scale structure form; and then proceed to a phase of the universe dominated by dark energy. In the standard case, the dark energy comes as a surprise, since it is something you have to add into the theory to make it consistent with what we observe. In the cyclic model, the dark energy moves to center stage as the key ingredient that is going to drive the universe, and in fact drives the universe into the cyclic evolution. The first thing the dark energy does when it dominates the universe is what we observe today: it causes the expansion of the universe to begin to accelerate. Why is that important? Although this acceleration rate is a hundred orders of magnitude smaller than the acceleration than one gets in inflation, if you give the universe enough time, it actually accomplishes the same feat that inflation does. Over time it thins out the distribution of matter and radiation in the universe, making the universe more and more homogeneous and isotropicin fact, making it perfectly sodriving it into what is essentially a vacuum state.
Seth Lloyd said there were 10 (ten to the 80) or 10 (ten to the 90) bits inside the horizon, but if you were to look around the universe in a trillion years, you would find on average no bits inside your horizon, or less than one bit inside your horizon. In fact, when you count these bits, it's important to realize that now that the universe is accelerating our computer is actually losing bits from inside our horizon. This is something that we observe.
At the same time that the universe is made homogeneous and isotropic, it is also being made flat. If the universe had any warp or curvature to it, or if you think about the universe stretching over this long period of time, although it's a slow process it makes the space extremely flat. If it continued forever, of course, that would be the end of the story. But in this scenario, just like inflation, the dark energy only survives for a finite period, and triggers a series of events that eventually lead to a transformation of energy from gravity into new energy and radiation that will then start a new period of expansion of the universe. From a local observer's point of view, it looks like the universe goes through exact cycles; that is to say, it looks like the universe empties out each round, and a new matter and radiation is created, leading a new period of expansion. In this sense it's a cyclic universe. If you were a global observer and could see the entire universe, you'd discover that our three dimensions are forever infinite in this story. What's happened is that at each stage, when we create matter and radiation, it gets thinned out. It's out there somewhere, but it's getting thinned out. Locally, it looks like the universe is cyclic, but globally the universe has a steady evolution, a well-defined era in which, over time and throughout our three dimensions, entropy increases from cycle to cycle.
Exactly how this works in detail can be described in various ways. I will choose to present a very nice geometrical picture that is 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 that I'm going to introduce I am not introducing for the first time. They are 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 that is necessary to make it mathematically consistent. In one particular formulation of that theory the universe has a total of 11 dimensions. Six of them are curled up into a little ball so tiny that, for my purposes, I'm just going to pretend that 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, lies 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 branesthe 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 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 branes. 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 excitationsparticles 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 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 that 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 towards one another. When they collide, there's a walloping impactenough to bring 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 20's and 30's, it doesn't come back together again during the contraction because our three dimensionsthat is, the branesremain 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 inflationnamely, flattening and homogenizing the universeare 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 inflationproducing fluctuations in the densityoccurs as these two branes come together. As they approach, quantum fluctuations cause the branes to begin to wrinkle. And because they are wrinkled, they do not 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 differentthis is taking billions of years, instead of 10[-30] (ten to the -30) secondsit 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 truealthough 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 that 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 created 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 that are 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 be a combination of observationsfor example, the search for cosmic gravitational wavesand theorybecause 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, which we prefer, and how we can best distinguish between them.
Per Bak died on October 16, 2002, at the age of 54. Per was one of the founders and most influential contributors to the study of complex systems. Per made many contributions to science, but the best known was a general theory of self-organization, which he called, "self-organized criticality". His ideas and discoveries have had an influence over how people think about a broad range of phenomena, from physics to biology, neurosciences, cosmology, earth sciences, economics and beyond. As a scientist and as a person he was an inspiration and a challenge to those of us who knew him. He was, for me that rare scientist who, though not in my field, could at any moment surprise me by saying something that would make me realize I had to rethink something I had thought I understood.
Per's theory of self-organized criticality was formulated in a paper he wrote in 1987 with two younger colleagues, Chao Tang and Kurt Wiesenfeld. This was one of the most highly cited and influential physics papers of the last two decades. It presented a general mechanism by which systems which are out of thermal equilibrium may evolve to a fractal, or scale invariant, distribution. These distributions are characteristic of many non-equilibrium systems, but before their paper no one had understood why. This idea, and the methodology it spawned, has been applied to understand the patterns that form spontaneously in many different systems, including earthquakes, forest fires, traffic jams, economic markets, and biological phenomena ranging from natural selection to the distribution of species of trees in a forest. It has also been applied to astrophysical phenomena ranging from x ray busts to the distribution of galaxies in the universe. Many of these applications were pioneered by Per himself, in collaboration with specialists in these fields.
Per's career proves that a scientist can indeed be a public intellectual, for the influence of his work extends far beyond science. Al Gore mentioned self-organized criticality in his book, "Earth in the Balance". I've heard executives of powerful software companies say they did not understand why their business strategies succeeded until they read Per's popular book, How Nature Works. At a meeting in Santa Fe I heard Lt. General (Retired) Paul Van Riper, one of the planners of the Gulf War, say that he learned so much from that book that could be applied to military strategy that he made it required reading for all U.S. Marine officers in training.
There was no one better than Per at grasping the heart of a complicated phenomena, and then realizing his insight by the invention of a simple model. Per's models were so elegant in their elimination of extraneous features that some experts were unable to understand why they applied at all to their subject. You could explain any of his models to a child, but to understand how they worked you had to be able to be able to strip everything away from a phenomena but the mechanisms by which a pattern forms and propagates. A tree on fire is like a person with the flu, is like a galaxy forming stars, is like a gene turning on, is like a trader making a bid...and each is represented by a single bit: all that matters is how many neighbors have to be on for it to light up. I remember him telling me once how excited he had been when he had accidentally run into Stephen J Gould. He introduced himself and very excitedly said that he had invented a theory that could explain Gould and Eldridges notion of evolution by punctuated equilibrium. Gould replied that he wasnt interested because "punctuated equilibrium is already a theory". Per was very disappointed. Several years later I was fortunate myself to meet Gould and I was glad to be able to report back to Per that I had spent a dinner explaining his theory to Gould and he had finally got it.
Spending time with Per was an exhilarating but sometimes daunting experience. Per's energy exceeded that of most people, he was full of ideas, and completely direct in expressing his opinions. If he liked an idea he was childlike in his enthusiasm; he praised it unreasonably, no matter whether it was his or someone elses. But if he thought something was stupid, he said so bluntly, no matter his relation with the speaker, or the consequences.
Per was perhaps the most fearless scientist I ever met. He more than once began a talk at a conference of neuroscientists or cosmologists with the statement that after six months of thinking about their field, he realized that everything done in the last 20 years was wrong. Having said that he would explain where he saw the mistake and propose a simple theory that reversed it, which he illustrated by a simple computer model. One such talk I heard, about how the brain works, was titled, "Learning from mistakes." Certainly some people went away unhappy, but I am convinced this was more childlike simplicity than arrogance. It would not have occurred to him that there was any other way to be: science is hard and we have to say what we think.
What Per understood better than any other scientist Ive known is that doing good science takes courage, stubbornness and a willingness to take big risks in the hope of making big advances. He argued stubbornly when he felt that someone did not understand one of his ideas, but he did not seem to mind if one of his theories was shown wrong or improved upon.
What Per certainly had no patience for was anything that smacked of insincerity or hypocrisy. If there was not a good reason to do something, he didnt waste his time, nor did he see why anyone else should. He was the kind of professor that university administrators most fear: a renowned scientist who simply said no when asked to take time and energy away from science in order to do something that interested him less at that moment.
The philosopher Roberto Mangabeira Unger explains some of the problems faced by contemporary scientists by saying that "we are something relatively infinite caught within finite realities: the body, society and culture." Certainly this is how I remember Per.