THE CYCLIC UNIVERSE
[NEIL TUROK:] For the last ten years I have mainly been working on the question of how the universe began — or didn't begin. What happened at the Big Bang? To me this seems like one of the most fundamental questions in science, because everything we know of emerged from the Big Bang. Whether it's particles or planets or stars or, ultimately, even life itself.
In recent years, the search for the fundamental laws of nature has forced us to think about the Big Bang much more deeply. According to our best theories — string theory and M theory — all of the details of the laws of physics are actually determined by the structure of the universe; specifically, by the arrangement of tiny, curled-up extra dimensions of space. This is a very beautiful picture: particle physics itself is now just another aspect of cosmology. But if you want to understand why the extra dimensions are arranged as they are, you have to understand the Big Bang because that's where everything came from.
Somehow, until quite recently, fundamental physics had gotten along without really tackling that problem. Even back in the 1920's, Einstein, Friedmann and Lemaitre — the founders of modern cosmology — realized there was a singularity at the Big Bang. That somehow, when you trace the universe back, everything went wrong about 14 billion years ago. By go wrong, I mean all the laws of physics break down: they give infinities and meaningless results. Einstein himself didn't interpret this as the beginning of time; he just said, well, my theory fails. Most theories fail in some regime, and then you need a better theory. Isaac Newton's theory fails when particles go very fast; it fails to describe that. You need relativity. Likewise, Einstein said, we need a better theory of gravity than mine.
But in the 1960's, when the observational evidence for the Big Bang became very strong, physicists somehow leapt to the conclusion that it must have been the beginning of time. I am not sure why they did so, but perhaps it was due to Fred Hoyle — the main proponent of the rival steady-state theory — who seems to have successfully ridiculed the Big Bang theory by saying it did not make sense because it implied a beginning of time and that sounded nonsensical.
Then the Big Bang was confirmed by observation. And I think everyone just bought Hoyle's argument and said, oh well, the Big Bang is true, okay, so time must have begun. So we slipped into this way of thinking: that somehow time began and that the process, or event, whereby it began is not describable by physics. That's very sad. Everything we see around us rests completely on that event, and yet that is the event we can't describe. That's basically where things stood in cosmology, and people just worried about other questions for the next 20 years.
And then in the 1980s, there was a merging of particle physics and cosmology, when the theory of inflation was invented. Inflationary theory also didn't deal with the beginning of the universe, but it took us back further towards it. People said, let's just assume the universe began, somehow. But, we're going to assume that when it began, it was full of a weird sort of energy called inflationary energy. This energy is repulsive — its gravitational field is not attractive, like ordinary matter — and the main property of that energy is that it causes the universe to expand, hugely fast. Literally like dynamite, it blows up the universe.
This inflationary theory became very popular. It made some predictions about the universe, and recent observations are very much in line with them. The type of predictions it made are rather simple and qualitative descriptions of certain features of the universe: it's very smooth and flat on large scales; and it has some density variations, of a very simple character. Inflationary theory predicts that the density variations are like random noise — something like the ripples on the surface of the sea — and fractional variation in the density is roughly the same on all length scales. And these predictions of inflation have been broadly confirmed by observation. So people have become very attracted to inflation and many people think it's correct. But inflationary theory never really dealt with the beginning of the universe. We just had to assume the universe started out full of inflationary energy. That was never explained.
My own work in this subject started about ten years ago, when I moved to Cambridge from Princeton. There I met Stephen Hawking, who, with James Hartle, developed a theory about how the universe can begin. So I started to work with Stephen, to do calculations to figure out what this theory actually predicted. Unfortunately, we quickly reached the conclusion that the theory predicted an empty universe. Indeed, this is perhaps not so surprising: if you start with nothing, it makes more sense that you'd get an empty universe rather than a full one. I'm being facetious, of course, but when you go through the detailed math, Hawking's theory seems to predict an empty universe, not a full one.
So we tried to think of various ways in which this problem might be cured, but everything we did to improve that result — to make the prediction more realistic&mdashspoils the beauty of the theory. Theoretical physics is really a wonderful subject because it's a discipline where crime does not pay in the long run. You can fake it for awhile, you can introduce fixes and little gadgets which make your theory work, but in the long run, if its no good, it'll fall apart. We know enough about the universe and the laws of nature, and how it all fits together, that it is extremely difficult to make a fully consistent theory. And when you start to cheat, you start to violate special symmetries which are, in fact, the key to the consistency of the whole structure. If those symmetries fall apart, and then the whole theory falls apart. Hawking's theory is still an ongoing subject of research, and people are still working on it and trying to fix it, but I decided, after four or five years, that the approach wasn't working. It's very, very hard to make a universe begin and be full of inflationary energy. We needed to try something radically different.
So, along with Paul Steinhardt, I decided to organize a workshop at the Isaac Newton Institute in Cambridge, devoted to fundamental challenges in cosmology. And this was the big one: how to sensibly explain the Big Bang. We decided to bring together the most creative theorists in string theory, M theory and cosmology to brainstorm and see if there could be a different approach. The workshop was very stimulating, and our own work emerged from it.
String theory and M theory are precisely the kinds of theories which Einstein himself had been looking for. His theory of gravity is a wonderful theory and still the most beautiful and successful theory we have, but it doesn't seem to link properly with quantum mechanics, which we know is a crucial ingredient for all the other laws of physics. If you try to quantize gravity naively, you get infinities which cannot be removed without spoiling all of the theory's predictive power. String theory succeeds in linking gravity and quantum mechanics within what seems to be a consistent mathematical framework. Unfortunately, thus far, the only cases where we can really calculate well in string theory are not very physically realistic: for example, one can do very precise calculations in static, empty space with some gravitational waves. Nevertheless, because of its very tight and consistent mathematical structure, many people feel string theory is probably on the right track.
String theory introduces some weird new concepts. One is that every particle we see is actually a little piece of string. Another is that there are objects called branes, short for membranes, which are basically higher-dimensional versions of string. At the time of our workshop, a new idea had just emerged: the idea that the three dimensions of space we experience could in fact be the dimensions along one of these branes. The brane we live on could be a sort of sheet-like object floating around in a higher dimension of space. This underlies a model of the universe which fits particle physics very well and which consists of two parallel branes separated by a very, very tiny gap. Many people were talking about this model in our workshop, including Burt Ovrut, and Paul and I asked the question of what happens if these two branes collide. Until then, people had generally only considered a static setup. They described the branes sitting there, with particles on them, and they found that this setup fit a lot of the data we have about particles and forces very well. But they hadn't considered the possibility that branes could move, even though that is perfectly allowed by the theory. And if the branes can move, they can collide. Our initial thought was that, if they collide, that might have been the Big Bang. The collision would be a very violent process, in which the clash of the two branes would generate lots of heat and radiation and particles… just like a Big Bang.
Burt, Paul and I began to study this process of the collision of the branes carefully. We realized that, if it worked, this idea would imply that the Big Bang was not the beginning of time but, rather, a perfectly describable physical event. We also realized this might have many implications, if it were true. For example, not only could we explain the Bang, we could explain the production of radiation which fills the universe, because there was a previous existing universe, within which these two branes were moving. And what explained that, you might ask? That's where the cyclic model came in. The cyclic model emerged from the idea that each Bang was followed by another, and that this could go on for eternity. The whole universe might have existed forever, and there would have been a series of these Bangs, stretching back into the infinite past, and into the infinite future.
For the last five years, we've worked on refining this model. The first thing we had to do was to match the model to observation, to see if it could reproduce some of the inflationary model's successes. Much to our surprise, we found that it could, and in some cases in a more economical way than inflation. If the two branes attract one another, then as they pull towards one another they acquire ripples, like the ripples on the sea I mentioned before. Those ripples turn into density variations as the branes collide and release matter and radiation, and these density variations later lead to the formation of galaxies in the universe.
We found that, with some simple assumptions, our model could explain the observations to just the same accuracy as the inflationary model. That's instructive, because it says there are these two very different mechanisms which achieve the same end. Both models explain rather broad, simple features of the universe: that it is nearly uniform on large scales. That it is flat, like Euclidean space, and that it has these simple density variations, with nearly the same strength on every length scale. These features are explained either by the brane collision model or by the inflation model. And there might even be another, better model which no-one has yet thought of. In any case, it is a healthy situation for science to have rival theories, which are as different as possible. This helps us to clearly identify which critical tests — be they observational or mathematical/logical — will be the key to distinguishing the theories and proving some of them wrong. Competition between models is good: it helps us see what the strengths and weaknesses and our theories are.
In this case, a key battleground between the more established inflationary model and our new cyclic model is theoretical: each model has flaws and puzzles. What happened before inflation? Does most of the universe inflate, or only some of it? Or, for the cyclic model, can we calculate all the details of the brane collision, and turn the rough arguments into precise mathematics? It is our job as theorists to push those problems to the limit to see whether they can be cured, or whether they will instead prove fatal for the models.
Equally, if not more important, is the attempt to test the models observationally, because science is nothing without observational test. Even though the cyclic model and inflation have similar predictions, there is at least one way we know of telling them apart. If there was a period of inflation — a huge burst of expansion just after the beginning of the universe — it would have filled space with gravitational waves, and those gravitational waves should be measurable in the universe today. Several experiments are already searching for them and, next year, the European Space Agency's Planck satellite will make the best attempt yet: it should be capable of detecting the gravitational waves predicted by the simplest inflation models. Our model with the colliding branes predicts that the Planck satellite and other similar experiments will detect nothing. So we can be proved wrong by experiment.
Something I'm especially excited about right now is that we have been working on the finer mathematical details of what happens at the Bang itself. We've made some very good progress in understanding the singularity, where, according to Einstein's theory, everything becomes infinite; where all of space shrinks to a point, so the density of radiation and matter go to infinity, and Einstein's equations fall apart.
Our new work is based on a very beautiful discovery made in string theory about ten years ago, with a very technical name. It's called the Anti-De Sitter Conformal Field Theory correspondence. I won't attempt to explain that, but basically it's a very beautiful geometrical idea, which says that if I've got a region of space and time, which might be very large, then in some situations I can imagine this universe surrounded by what we call a boundary — which is basically a box enclosing the region we are interested in. About ten years ago, it was shown that even though the interior of this container is described by gravity, with all of the difficulties that brings&mdashlike the formation of black holes and the various paradoxes they cause — all of that stuff going on inside the box can be described by a theory that lives on the walls of the box surrounding the interior. That's the correspondence. A gravitational theory corresponds to another theory which has no gravity, and which doesn't have any of those gravitational paradoxes. What we've been doing recently is using this framework to study what happens at a cosmic singularity which develops in time, within the container. We study the singularity indirectly, by studying what happens on the surface of the box surrounding the universe. When we do this, we find that if the universe collapses to make a singularity, it can bounce, and the universe can come back out of the bounce. As it passes through the singularity, the universe becomes full of radiation–very much like what happens in the colliding brane model — and density variations are created.
This is very new work, but once it is completed I think it will go a long way towards convincing people that the Big Bang, or events like it, are actually describable mathematically. The model we're studying is not physically realistic, because it's a universe with four large dimensions of space. It turns out that's the easiest case to do, for rather technical reasons. Of course, the real universe has only three large dimensions of space, but we're settling for a four-dimensional model for the moment, because the math is easier. Qualitatively, what this study is revealing is that you can study singularities in gravity and make sense of them. I think that's very exciting and I think we're on a very interesting track. I hope we will really understand how singularities form in gravity, how the universe evolves through them, and how those singularities go away.
I suspect that will be the explanation of the Big Bang — that the Big Bang was the formation of a singularity in the universe. I think by understanding it we'll be better able to understand how the laws of physics we currently see were actually set in place: why there is electro-magnetism, the strong force, the weak force, and so on. All of these things are a consequence of the structure of the universe, on small scales, and that structure was set at the Big Bang. It's a very challenging field, but I'm very happy we're actually making progress.
The current problem which is dominating theoretical physics — wrongly, I believe, because I think people ought to be studying the singularity and the Big Bang since that's clearly where everything came from, but most people are just avoiding that problem — is the fact that the laws of physics we see, according to string theory, are a result of the specific configuration of the extra dimensions of space. So you have three ordinary dimensions, that we're aware of, and then there are supposed to be six more dimensions in string theory, which are curled up in a tiny little ball. At every point in our world there would be another six dimensions, but twisted up in a tiny little knot. And the problem is that there is a huge number of ways of twisting up these extra dimensions. Probably, there are an infinite number of ways. Roughly speaking, you can wrap them up by wrapping branes and other objects around them, twisting them up like a handkerchief with lots of bits of string and elastic bands wound around.
This caused many people to pull their hair out. String theory was supposed to be a unique theory and to predict one set of laws of physics, but the theory allows for many different types of universes with the extra dimensions twisted up in different ways. Which one do we live in? What some people have been doing, because they assume the universe simply starts after the Bang at some time, is just throwing a dice. They say, okay, well it could be twisted up in this way, or that way, or the other way, and we have no way of judging which one is more likely than the other, so we'll assume it's random. As a result, they can't predict anything. Because they don't have a theory of the Big Bang, they don't have a theory of why those dimensions ended up the way they are. They call this the landscape; there's a landscape of possible universes, and they accept that they have no theory of why we should live at any particular place in the landscape. So what do they do?
Well, they say, maybe we need the anthropic principle. The anthropic principle says, the universe is the way it is because if it was any different, we wouldn't be here. The idea is that there's this big landscape with lots of universes in it, but the only one which can allow us to exist is the one with exactly the laws of physics that we see. It sounds like a flaky argument&mdashand it is. It's a very flaky argument. Because it doesn't predict anything. It's a classic example of postdiction: its just saying, oh well, it has to be this way, because otherwise we wouldn't be here talking about it. There are many other logical flaws in the argument which I could point to, but the basic point is that this argument doesn't really get you anywhere. Its not predictive and it isn't testable. The anthropic principle, as it's currently being used, isn't really leading to any progress in the subject. Even worse than that, it is discouraging people from tackling the important questions, like the fact that string theory, as it is currently understood, is incomplete and needs to be extended to deal with the Big Bang. That's just such an obvious point, but at the moment surprisingly few people seem to appreciate it.
I'm not convinced the landscape is real. There are still some reasonable mathematical doubts, about whether all these twisted up configurations are legitimate. It's not been proven. But if it is true, then how are you going to decide which one of those configurations is adopted by the universe? It seems to me that whatever you do, you have to deal with the Big Bang. You need a mathematical theory of how Big Bangs works, either one which describes how time began, or one which describes how the universe passes through an event like the Big Bang and, as it passes through, there's going to be some dramatic effect on these twisted-up dimensions. To me, the most plausible resolution of a landscape problem would be that the dynamics of the universe will select a certain configuration as the most efficient one for passing through Big Bangs and allowing a Universe which cycles for a very long time.
For example, just to give a trivial example: if you ask, why is the gas in this room smoothly distributed, we need a physical theory to explain it. It wouldn't be helpful to say, well if it wasn't that way, there would be a big vacuum in part of the room and if I walked into it, I would die. If the distribution of gas wasn't completely uniform, we wouldn't last very long. That's the anthropic principle. But it's not the scientific explanation. The explanation is that molecules jangle around the room and when you understand their dynamics you understand that it's vastly more probable for them to settle down in a configuration where they're distributed nearly uniformly. It's nothing to do with the existence of people.
In the same way, I think the best way to approach the cosmological puzzles, is to begin by understanding how the Big Bang works. Then, as we study the dynamics of the Bang, we'll hope to discover that the dynamics lead to a universe something like ours. If you can't understand the dynamics, you really can't do much, except give up and resort to the anthropic argument. It's an obvious point, but strangely enough it's a minority view. In our subject, the majority view at the moment is this rather bizarre landscape picture where somebody, or some random process, and no one knows how it happens, chooses for us to be in one of these universes.
The idea behind the cyclic universe is that the world we experience, the three dimensions of space, are actually an extended object, which you can picture as a membrane as long as you remember that it is three-dimensional, and we just draw it as two-dimensional because that is easier to visualize. According to this picture, we live on one of these membranes, and this membrane is not alone, there's another partner membrane, separated from it by a very tiny gap. There are three dimensions of space within a membrane, and a fourth dimension separating the two membranes. It so happens that in this theory there are another six dimensions of space, also curled up in a tiny little ball, but let's forget about those for the moment.
So you have this set-up with these two parallel worlds, just literally geometrically parallel worlds, separated by a small gap. We did not dream up this picture. This picture emerges from the most sophisticated mathematical models we have of the fundamental particles and forces. When we try to describe reality, quarks, electrons, photons, and all these things, we are led to this picture of the two parallel worlds separated by a gap, and our starting point was to assume that this picture is correct.
These membranes are sometimes called "end of the world branes." Basically because they're more like mirrors; they're reflectors. There is nothing outside them. They're literally the end of the world. If you traveled across the gap between the two membranes, you would hit one of them and bounce back from it. There's nothing beyond it. So all you have are these two parallel branes with the gap. But these two membranes can move. So imagine we start from today's universe. We're sitting here, today, and we're living on one of these membranes. There's this other membrane, very near to us. We can't see it because light only travels along our membrane, but the distance away from us is much tinier than the size of an atomic nucleus. It's hardly any distance from us at all. We also know that, in the universe today, there's something called "dark energy." Dark energy is the energy of empty space. Within the cyclic theory, the energy associated with the force of attraction between these two membranes is responsible, in part, for the dark energy.
Imagine that you've got these two membranes, and they attract each other. When you pull them apart you have to put energy into the system. That's the dark energy. And the dark energy itself causes these two membranes to attract. Right now the universe is full of dark energy; we know that from observations. According to our model, the dark energy is actually not stable, and it won't last forever. If you think of a ball rolling on a hill, the stored energy grows as the ball gets higher: likewise the dark energy grows as the gap between membranes widens. At some point, the ball turns around and falls back downhill. Likewise, after a period of dark energy domination, the two branes start to move towards each other, and then they collide, and that's the Bang. It is the decay of the dark energy we see today which leads to the next Big Bang, in the cyclic model.
Dark energy was only observationally confirmed in 1999 and it was a huge surprise for the inflationary picture. There is no rhyme or reason for its existence in that picture: dark energy plays no role in the early universe, according to inflationary theory. Whereas in the cyclic model, dark energy is vital, because it is the decay of dark energy which leads to the next Big Bang.
This picture of cyclic brane collisions actually resolves one of the longest-standing puzzles in cyclic models. The idea of a cyclic model isn't new: Friedmann and others pictured a cyclic model back in the 1930's. They envisaged a finite universe which collapsed and bounced over and over again. But Richard Tolman soon pointed out that, actually, it wouldn't remove the problem of having to have a beginning. The reason those cyclic models didn't work is that every bounce makes more radiation and that means the universe has more stuff in it. According to Einstein's equations, this makes the universe bigger after each bounce, so that every cycle lasts longer than the one before it. But, tracing back to the past, the duration of each bounce gets shorter and shorter and the duration of the cycles shrinks to zero, meaning that the universe still had to begin a finite time ago. An eternal cyclic model was impossible, in the old framework. What is new about our model is that by employing dark energy and by having an infinite universe, which dilutes away the radiation and matter after every bang, you actually can have an eternal cyclic universe, which could last forever.