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 form—the 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 sense—in the Copernican sense. In fact, if you think about Copernicus—from whom we derive the word revolution—his 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[20] (ten to the 20) degrees Kelvin—hot enough to evaporate atoms and nuclei into their fundamental constituents—but 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 isotropic—in fact, making it perfectly so—driving it into what is essentially a vacuum state.

Seth Lloyd said there were 10[80] (ten to the 80) or 10[90] (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 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 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 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 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.