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# Neil Turok

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Interview of Neil Turok by Chris Smeenk on 2002 May 16,

Niels Bohr Library & Archives, American Institute of Physics,

College Park, MD USA,

www.aip.org/history-programs/niels-bohr-library/oral-histories/35129

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### Abstract

In this interview Neil Turok discusses topics such as: inflationary universe; cosmology; Stephen Hawking; Andrei Linde; quantum gravity; string theory; particle physics; theoretical physics; Alan Guth; Paul Steinhardt; Martin Bucher; University of Cambridge; Burt Ovrut; scalar fields; big bang theory; high-energy physics.

### Smeenk:

This is Chris Smeenk interviewing Neil Turok on May 16th, 2002 in his office in Cambridge. So we were talking about a number of different things earlier.

### Turok:

Yes, yes.

### Smeenk:

If you wouldn’t mind backtracking a bit, I’d like to ask you about some of your critical views about inflation.

### Turok:

I think that that noise from that is interfering.

### Smeenk:

Mmm.

### Turok:

You think it’s okay?

### Smeenk:

I think it should be okay, yeah. The microphone is pretty good on this, so we will be recorded over the background.

### Turok:

Okay. So we were talking about inflation.

### Smeenk:

Right. And so you were working on topological defects in the early universe.

### Turok:

That’s right. Yes, that’s right. I’ve always been I guess motivated by desire to understand nature and to investigate theories which have a real chance for being proved, you know, decisively right or wrong. And so what attracted me to topological defects was that if they were right you could see them in the universe today and it would be totally unambiguous. For the same reason, with inflation I was always nervous that in fact one was deluding oneself by postulating an extra field which was only important in an unobservable epoch. And all we could see was fairly vanilla consequences today. We could see flatness, we could see scale invariance, in fact all the sort of simplest predictions you might have made from any cosmology were the predictions of inflation. So there was no smoking gun signature of inflation at all.

### Smeenk:

So it seemed to you that all these properties could be gotten by various other means, that there’s nothing —

### Turok:

Well, the difficulty was — yes, they could be — but the difficulty was there never was an explicit alternative. In fact it’s very, very hard to make a theory which works. One of the issues is causality. If the universe starts so smooth, you have to explain why this is so smooth. But then it has these density variations on scales which have never communicated with each other. How do they know to be scale invariant? Even though you can say it’s a very simple prediction, in fact it is very hard to see how the mechanism could work.

### Smeenk:

Right. Well, let me ask you just in relation to defects regarding that. It seems, as in other cases of phase transitions, you can get patterns on a wide variety of scales that might seem to be a causal.

### Turok:

Yes.

### Smeenk:

Were you ever worried about causality in —?

### Turok:

No. In the defect theory you do get scale invariance, but they are strictly causal. And so what happens is that if you have a tangled network of defects there is always some scale. The way it evolves in time is by straightening itself out, and the energy in the defects gets released into particles or gravity waves or whatever they decay into. But the defects straighten themselves out. So the scale of the network grows with time. And roughly speaking it’s just equal to the speed of light times the time. It just grows linearly with time. And so that is a form of scale invariance in time, which means that at any time, the network looks exactly the same as at any other time. They are just scaled up. So I did some work with some experiments at Bell Labs and we studied experimental systems which had this property. And the people in the lab developing these photos used to say, “Why are you making these photos; because they’re all the same?” That was the whole point! They were made at different times and one was on a very tiny scale and one was on a very large scale, but in fact statistically it looked the same. So yes, I think people have always been interested in scale invariance because it is a generic phenomenon. And the way defects made scale invariant perturbations was through this type of scale invariance in time, that in the early universe they would not be making any large-scale inhomogeneities, they’re just making very small-scale ones. But then as time goes on they make bigger and bigger and bigger and bigger ones. But when they made them, they make them all with the same amplitude, and then you are left with scale invariance. So defects were a very natural way of getting scale invariance. And so that was appealing. I think the unappealing thing about defects is, in a way, they were overkill, because all you need to make a galaxy is a very small amplitude, mild density variation. The defect is this giant string with an enormous energy putting in at length and there’s no evidence that such things exist in the universe at all yet. Unfortunately, it would be great if they did.

### Smeenk:

You also worked… there are a variety of defects, right? There’s strings and textures and —

### Turok:

Textures, monopoles, yes, I worked on all of these.

### Smeenk:

Did textures seem more plausible?

### Turok:

No, no, not more plausible. The only thing about them, they were slightly more complex, which is why it took longer to think of them. Strings are seen in superconductors and in super-fluids and in fact liquid crystals in LCD displays. All of these things have string defects. But textures were not seen experimentally, and that’s why nobody thought of really looking in cosmology. So I think they’re interesting from that point of view. It also turned out that just for various reasons it was much easier to do calculations in texture theory. And so we could put them onto a supercomputer and even though they are non-linear and so on you could do a very accurate calculation of what the sky should look like. And we only really completed that in 1997. I think we did the definitive calculation of what the micro sky should look like. Just before the whole slew of new data. But the new data came along and just proved them wrong [Laughs] — which is very, very sad for me personally. I really did work for something like four or five years — off and on, you know, it wasn’t continuously, but off and on I did work for four or five years trying to refine the predictions of this theory which I had invented. And obviously you always hope it’s going to work out right. But I think even by the time observations came along I was pretty sure it wasn’t right. Partly for this — I think there were a number of lines of evidence pointing to the fact that the fluctuations in the universe really are very simple at early times. They’re Gaussian random noise, scale invariant — so as I say, the defects were always overkill. They were very appealing from the particle physics side, but from the cosmology side it seemed like you were really involved more than necessary.

### Smeenk:

I think you said this earlier, but one of the features of the defect calculations is that there aren’t tunable knobs in the theory.

### Turok:

That’s right. That was the very attractive feature, is that you got exact scale invariance.

### Smeenk:

No tilt.

### Turok:

No tilt. In inflation you can really get what you want. I mean it’s still true that scale invariance is, if you like, generic in inflation. A gentle potential will give you something nearly scale invariant, but it is tunable and you can — I still believe that basically inflation could give you almost anything. Almost any observational result could be accounted for with inflation. So, one way of saying it is that the recent observations are consistent with the simplest inflation models. But that success I think is more a success of simplicity rather than of inflation. Because what they are consistent with is Gaussian random noise, scale invariance, they are actually inconsistent with exact scale invariance, which is not unique. Inflation doesn’t have to give, in fact never gives exact scale invariance. It always gives some deviation, and even simple models give a small deviation. And the specific signatures of inflation like the existence of a gravitational wave background, which are something specific to the inflationary mechanism, that it amplifies gravity wave in the early universe and we should be able to detect these things today. Those have not yet been tested at all. But they will be. The Planck satellite is going to be sufficiently powerful that it could detect the signature of gravitational waves produced from inflation and in the simple models of inflation. But unfortunately, again inflation is very adjustable, so even in all of Andrei Linde’s models of chaotic inflation, for example, you would see this in the micro sky. And that should happen in 2007 or ‘08. Then presumably if they don’t see that signature inflationary theorists will have to be on the retreat and will have to be dialing these models and adding more fields to try and avoid this observation — which I’m sure they will do. But I think that the theory becomes gradually less credible and —

### Smeenk:

So if you had to place bets at the moment?

### Turok:

Well, I took a bet. [Laughs]

### Smeenk:

Why don’t you describe the bet?

### Turok:

The bet? Well, last summer in August we had a meeting called M theory Cosmology, and I talked about the ekpyrotic model and Stephen Hawking was in the audience and he was quite aggressively against this model. And he said, “I bet” — so our model—

### Smeenk:

I didn’t realize there was actually a bet —

### Turok:

Yes, yes, there’s a bet. Yeah. So our model predicts there should be no gravitational waves left anymore. And in fact that is a cast iron prediction we cannot get out of — I believe. Maybe we just haven’t seen it, but I think there is really no way that we can make spectrum of long wavelength gravitational waves in the universe today. So, if it’s seen, that would be very good evidence for inflation as opposed to our model. So I gave a talk, and at the end of the talk Stephen says, “Okay. I bet you that the gravitational waves are seen by the Planck satellite.” And I said, “Fine. I’ll take the bet at any money, 50/50 odds for any sum of money you care to name,” and so far he hasn’t named the amount! Now the unfortunate thing about the bet is I think Stephen was not very au fait with inflationary model building, and what he hadn’t realized is that even though the simplest model of inflation always are detectable, you can easily tweak them to avoid this background. So in fact when I accepted the bet a number of other people in the audience also said they would accept the bet, and they were inflationary advocates.

### Smeenk:

So it isn’t necessarily a very good discriminant of inflation versus [the ekpyrotic model]. Perhaps for the simplest models.

### Turok:

It’s the simplest model that works. Yes, my feeling is that you see, if you [ask whether] inflation is a theory that can be tested, I’d have to say no. I mean, I can’t think of a conceivable test which would decisively prove inflation wrong. Therefore I don’t think it’s a testable model. If you say is it a theory at all, again in a sense if you want to be strict about it the answer has to be no, because there is no consistent mathematical formulation of inflation. You can write down inflation as a model of gravity coupled to fields which you add by hand. But we all know this is an inconsistent framework at a very deep level. Quantum gravity doesn’t make sense, and inflation involves quantum gravity. So it actually only makes sense providing you ignore higher terms in the expansion, take the lowest order terms and the highest ones you just ignore. You are ignoring infinities all over the place. So —

### Smeenk:

Just one related question. I have often been struck that the slow roll approximation; approximation is based on…

### Turok:

Yes, yes.

### Smeenk:

That’s essentially just classical field theory.

### Turok:

Yes.

### Smeenk:

You have a potential that you call the effective potential.

### Turok:

Absolutely.

### Smeenk:

Essentially classical field theory, and I don’t see where — there’s no, you know, no unitary dynamics in Hilbert space. You are doing dynamics for a field rolling down the potential.

### Turok:

Yes, yes. What you have is perturbative, okay. So you say the coupling is small and so I say I’ve got a background classical field and then a small quantum fluctuation. And it sort of hangs together. But the problem is that when you include gravity there is a terrible ultraviolet problem, which is the short wavelength modes. When you calculate quantum corrections in perturbation theory, those corrections are all over. And it means that the theory is just out of control. This is not a well-defined expansion you’re doing. You’re keeping the first order term, but there is no small parameter in the expansion. And so it’s questionable. It’s a questionable procedure. However, I wouldn’t say — I wouldn’t want to overstate that, in the sense that I think there is this body called M theory and string theory, a far more consistent theory where in string theory it’s finite to all orders; in super-gravity and M theory it may be finite to six or seven loops. No one’s quite sure, but it’s believed to go sick after that. But they are certainly more consistent than inflation, than just scalar fields and gravity. But the difficulty with those models is that the same features that make them quantum mechanically consistent make them observationally inconsistent. The world is not super-symmetric, and we don’t live in eleven dimensions, we live in four. You can say inflation isn’t a consistent theory, but then the consistent theories we have aren’t realistic. So what do you do? You have to hope that the consistent mathematical theories are the foundation, that somehow there are quantum corrections or effects that haven’t been properly understood that then make them realistic. And those things could make inflation work.

### Smeenk:

Let me just ask you. Imagine that there is an opposing point of view, which is that you can just, say, talk about inflation in the way you talk about semi-classical quantum gravity. You know that some things are going to work very well, but —

### Turok:

Yes, that’s right.

### Smeenk:

— you can approach it as something that gives you insight into quantum gravity phenomenon.

### Turok:

Right.

### Smeenk:

Which you can try to see how far you can trust.

### Turok:

Right. Yes.

### Smeenk:

And in that division of labor you might find inflation falling on the close side, in the sense that you can do calculations with it.

### Turok:

Yes, I think that’s a good way to look at it. So you know purists who think quantum gravity should be formulated for example as a loop space approach and so on — or they formulate discrete models of gravity. And the problem they have is that yes, these are consistent mathematical models, but they don’t have a long wavelength limit, that you can’t see how gravitational radiation or Newton’s Law or anything interesting comes out of this model. In fact there is no sign that it does. Maybe this is just a discrete model and that’s all it is and it doesn’t have any long wavelength limit. So the long wavelength limit, which is what we usually call the effective field theory, low-energy effective theory, is tremendously important. In fact all of physics is the effective field theory: Newton’s Law, special relativity, all these things are effective field theories. And that’s what all of physics is, so the sort of purity associated with these mathematical models is in fact useless because nobody knows how to connect them to what we call real physics. So yes, you’ve got to try and work from two sides of this mountain and inflation, I think it’ s a good way of trying as you go from the other side. In fact I think much too little has been done to really see how bad these — we know there were these diseases in inflation, but very little work has been done in quantifying them. You know, you’d like to see exactly where the divergences go, how might they get resolved, what type of additional matter is needed to resolve them. People don’t do that. The reason they don’t is it’s hard and these are involved, complicated calculations. Inflation is a very simple framework that has been worked out. It’s very simple, you can do calculations in a short space of time and write a paper about it. And that’s what everyone does. And it doesn’t really address these deeper issues at all.

### Smeenk:

Right. So I’ m wondering if…One thing that’s just surprising to me about the literature on inflation is how rather than doing the sort of calculations you are talking about it’ s, you know, find the newest idea in particle physics and link up with that.

### Turok:

Yes.

### Smeenk:

Just sociologically, that seems really interesting. I mean, it seems that one interesting thing about say Linde’s or Guth’s position on chaotic or eternal inflation is that they seem to undercut the need to even do that.

### Turok:

Right.

### Smeenk:

You just have the simple framework. You have a scalar field, a potential and who cares whether you have the scalar field like that in a particle physics model.

### Turok:

Right. I think that position is really self-defeating, because they are giving up before they have even started and they are just saying, “We’re not going to worry about the quantum mechanical consistency of this model on a deep level. We’ll just treat it at a superficial level and claim it’s all okay.” I don’t think that’s the history of theoretical physics. You know, theoretical physics has always worked by finding paradoxes and incompleteness’s of theories and really homing in on them, and the people who understood exactly what was wrong were usually the people who could see how to fix it. And I think it’s much more… when you know this theory is riddled with mathematical inconsistencies, you really need to find where they are. So I think it’s more likely that progress will be made that way. But there’s an awful lot of sociology in this field. I mean I think people — there is a tendency for people to claim it’s all over and we’ve won and inflation has been proved right. I think that argument has some appeal for a short space of time to a few people. But in the long run, for example, I mean on the sociological issue, the stuff we’re doing is very radical, very different. I think there’s a huge conceptual component. It may be wrong, you know, and we’ll learn if it’s wrong. But it’s really trying to — I think it’s trying to develop the scientific theory. And inflation has been there for twenty years. It hasn’t really changed these simple models. And all the bright young students who want to work in this field, what do you think they want to do? They all want to work on this. I mean, I’m turning away vast numbers of students who want to work on this crazy brane model.

### Smeenk:

Right.

### Turok:

Not necessarily because they believe it’s the truth, but because it actually is addressing these issues. And if you find disasters in the model in various forms you learn something. Whereas if all you’re doing is recycling the old folklore about inflation twenty years old, it’s clear you’re not doing anything. It’s also interesting the different sociological things. You see, Paul Steinhardt was a very powerful advocate for inflation. And I used to have standup arguments with him. For example he said inflation doesn’t allow an open universe, and me and Martin Bucher, who you’ve met, we have this open inflation, and we said, ‘Yes, you can get it; a bit of contrivance, but not too bad. You can make an open universe.’ And he wouldn’t believe this. And we argued, and then he would give talks saying inflation predicts a flat universe, and I’d stand up something saying no it doesn’t. And we’ve always been good friends, but we argued very heartily about it, and I’ve always felt he was too emphatically in favor of inflation. But he’s such a good scientist. You see that he spent three months here when we started the ekpyrotic model. We organized a workshop together. And I think we both knew that actually it would be great if we could work together — in spite of the fact that we always disagreed on everything before. And he spent three months here, and we had this glimmer of an idea. And Paul, you know, he’s got so much to lose because he’s seen as a founder of inflation, gets a lot of credit for that anyway. The minute Paul sensed that there might be an alternative, then he just jumped on it. “Okay, forget that old thing.”

### Smeenk:

Yes. I was surprised actually when I was talking with him. He was very critical of inflation.

### Turok:

Well, you see, he is a true scientist, and I think the way a true scientist works is you are open-minded. And if only — I mean frankly only a fool would believe that you solve the early universe first time round with so little data that you really got the answer right first time. I mean you have to be mad! The whole point is to explore all possibilities and close them off one by one, either through mathematics, or experiments, or whatever. And once you’ve closed off everything except one, then you can be sure. But we’re a long way from that. A long way from that. I [found] Paul’s attitude [to be] very impressive. He’s excited about the fact that it’s an alternative to inflation. And he says it’s good we’ve got two theories now. We can judge their merits and demerits. And it really refines your thinking to have two alternatives. I mean when you have a model in which time doesn’t begin and you’re competing against a model in which time has to begin, it really makes you think about things differently. You realize all the ways in which you were just putting in by hand the answer that you wanted in the model where time began. So that’s been very interesting and exciting. I think with inflation it has become a rather sort of humdrum field in that the main developments were in the early eighties. If you ask what significant happened after that time…

### Smeenk:

That was my next question.

### Turok:

Not much. I really don’t think much conceptual was added to the framework. Various theorems were proven, no-go theorems for example in M theory. There is a theorem that you cannot get inflation in M theory.

### Smeenk:

Is it that you can’t get de Sitter space or is it that you don’t have a scalar field?

### Turok:

You can’t have inflation. No, you actually cannot get inflation in M theory. So de Sitter space is perfect exponential expansion forever. Inflation is a temporary phase of exponential expansion followed by something else. But you can’t even get that in M theory. And the reason is, essentially it’s a trivial reason, which is that inflation requires negative pressure. If the pressure is negative — the acceleration of the universe is proportional to the density plus three times the pressure.

### Smeenk:

For a perfect —

### Turok:

For a perfect fluid. If the pressure is positive, the universe always decelerates. If the pressure is less than minus a third of the density, it will accelerate. Now in M theory the starting point is this eleven dimensional theory, which has no scalar fields. It has a gauge field and it has a fermion field and it has gravity. That’s it. None of these fields have negative pressure, because the gauge field and the fermion only have positive pressure. Now the next step in the argument is to show that if I have a theory with positive pressure only and I dimensionally reduce can I ever get a theory with negative pressure? And the answer is no. It’s a theorem, providing you dimensionally reduce on any smooth manifold. So there are some caveats here, that providing it’s on a smooth manifold, you can never get negative pressure.

### Smeenk:

So you would essentially be satisfying the strong energy condition…?

### Turok:

I always forget which one is which, but I think that’s right. I think that’s right. I think it is the weak, in fact, rho plus… The strong energy condition I believe is that — I always forget which one is which.

### Smeenk:

Yeah. I always get it wrong too.

### Turok:

It’ll be in here [as he picks up a copy of Hawking and Ellis 1973]. Strong energy condition… let’s figure out what this is.

### Smeenk:

Is it the principle pressures, something like that?

### Turok:

Yes. Let me look up the weak. Yes. This says that the pressure is positive. Yes.

### Smeenk:

Okay. That’s interesting. I had never heard that result. I had heard these vague claims that inflation is hard to accommodate in string theory.

### Turok:

The weak energy condition is that the energy is positive. Strong energy is that the equation. I think it’s at ρ plus 3p. I think it’s that. I think it’s ρ plus 3p. There’s lambda, so here’s μ, which I think is the energy and some of the pressures, so this is ρ plus 3p. Exactly. So, the strong energy condition does not allow inflation. Yes, so super-gravity does satisfy the strong energy condition. There are ways out. You say maybe compactify on some singular manifold. That leads you into all sorts of dubious mathematics associated with singularities. Or you say there are quantum corrections, and that’s only a classical result. And maybe it’s quantum corrections. But then the trouble is, the only situation where the quantum corrections are under control is where you have a lot of super-symmetry, and super-symmetry essentially makes the classical theory correct. So it’s hard to avoid this result. It doesn’t mean it can’t be. I wouldn’t put too much weight on that result. I don’t think it disproves inflation in any way, but —

### Smeenk:

It’s at least a red flag…

### Turok:

Yes, yes. So I certainly think one should raise it as challenge to inflationist to produce a quantum mechanically consistent model, because none of them are.

### Smeenk:

So in your work with Paul, do you think your motivations were similar or —?

### Turok:

Yes, I think we were both interested in branes actually, and I think that — we in fact organized a workshop on branes, partly so we could learn about them.

### Smeenk:

So the brane world scenarios, these all involve the large extra dimensions where you have —

### Turok:

They don’t have to.

### Smeenk:

They don’t have to?

### Turok:

The origin of the brane worlds is in the work of Horava and Witten, and basically they realized that if you take eleven dimension super-gravity and you have one of the dimensions being bounded by two branes, then you could reconcile string theory with… Basically in string theory there was a problem. String scale was not — I shouldn’t say — the GUT scale in physics, particle physics — that problem. So in their model the branes are only separated by about 10,000 Planck lengths.

### Smeenk:

Only?

### Turok:

Only. Right, so it’s only 10^{-29} centimeters.

### Smeenk:

Right. Given 10^{-33} for Planck.

### Turok:

Right. So it’s nothing like a large extra dimension. It’s a very small extra dimension. But that 10,000 was important because it actually is the ratio between the blank Planck scale and the GUT scale. So there was a motivation point. But separation can be tiny. And our first ekpyrotic model was in that framework, so we were thinking about this extra dimension being really very, very tiny still. So our work wasn’t really directly connected to large extra dimensions at all, and in fact the origin of the branes idea is in straight super-gravity and connecting it to particle physics — and that doesn’t involve a large extra dimension. So I think they’re really quite separate ideas. The large extra dimension ideas are certainly terrifically interesting and important, because it says we might be able to see evidence of extra dimensions even at quite low energies. None of our framework relies on that, and I think probably most particle physics model builders, I don’t know if you should take them seriously, but most of them would say that it’s easier to make models from string theory where the extra dimensions are small, very small. These large extra dimensions…in fact, I don’t think anyone has constructed standard model particle physics out of string theory with such a large dimension. It is very difficult to do. So they are really different ideas.

### Smeenk:

So you had three months of working with Paul and there was also this conference on M theory and cosmology.

### Turok:

Well, we started this in ‘99 and we actually worked for two years on this without telling anyone.

### Smeenk:

I remember I got an email from you at one point after I’d first mentioned the possibility of coming to Cambridge and you said, “I’ve got some new ideas about inflation” or early universe cosmology.

### Turok:

Right. Okay.

### Smeenk:

And I was wondering after I saw these papers eventually whether you were referring to that.

### Turok:

Yes, it could be. I mean, we started this in 1999, yeah, it would have been June ‘99, and then we didn’t publish anything until last year April, so that’s April 2001. So it’s nearly two years — And just because the math was involved and we went down lots of wrong alleys. But I think what excited us first about the idea is something totally naive, which is just that we knew these branes are central to M theory and string theory, and they govern all sorts of fascinating phenomenon like when two branes merge the gauge group changes. You know, if you have two branes you get a gauge group of U1 times U1 if they’ re separated, but if they’ re on top of each other it goes to U2, two by two matrices, and now it has four gauge bosons instead of two. And if you have three branes, it gives you SU3. And so the phenomenon of non-Abelian gauge groups is intimately tied to branes coinciding and coming apart. So it’s very clear these are extremely deep ideas behind the branes. And our thought was just completely naive, you know, surely when two branes run into each other there’ s a release of energy because the particle physics changes nonadiabatically. So you have gauge group U1 x U1 and then all of a sudden the gauge group U2, something dramatic is going to happen. That will release radiation, and that sounds like a Big Bang. So that was our first immediate thought. Then we started trying to describe exactly how these things approach and it’ s very, very complicated. And we didn’t think it was worth publishing at all. We had worked very hard for about two years, piles of notes, calculations. What I think changed everything is that we realized if you assumed a certain force between the branes — namely you assume the force between the branes gets weak as they go to large separations and strong as they come near — then it turns out that automatically as the branes approach you get a scale invariant pattern of ripples on the branes.

### Smeenk:

Okay. So that’s the density perturbations?

### Turok:

That’s the density perturbations. So when we saw scale invariance coming out of this simple assumption — all it requires is that the force between the branes vanishes at large distances very fast. If that is true, then whenever branes approach they will get scale invariant density perturbations. So that was really the point of our first paper. It was a very long paper and it was excessively technical, but the key point was just we had found a way of getting density fluctuations which were scale invariant. And you see this is conceptually the alternative to inflation. In inflation you do it within, if you like, in the early moments of the Big Bang, when you have a period of exponential expansion, you stretch everything to big scales, and then you go into the hot radiation era. The only other way that is known for making density variations larger than the horizon scale is to have them made in a period before t=0. So you have a conventional Big Bang right back to — actually not back [t=0], but to some finite temperature, which is when the branes collide and that makes a finite temperature. But then you just have time before that, and you generate the density perturbations.

### Smeenk:

So you’d be able to generate space-like correlations.

### Turok:

Exactly. So if you look in our model, I mean the density variations we see on the horizon today were generated when their wavelength was hundreds of kilometers. So you have these two branes approaching us and then you take a wave from a hundred kilometers on each brane and just because the force is getting stronger as they approach the amplitude is amplified and that is what leads to scale invariance. But when the density variations are generated they are actually huge, great objects, and it’s nothing like inflation. In inflation these are generated when they are only, you know 10^{5} Planck lengths or something. Tiny wavelengths. So ours is just completely opposite. We generate everything through very long wavelength physics described in very conventional terms, a scalar field, it is described with the scalar field actually, but you know we have an interpretation which is the geometry of the branes.

### Smeenk:

Just the one conditional that you have stated over and over again is the assumption regarding this force between the branes. Is that something that you derive from the —?

### Turok:

No. We had up ‘til now just made the assumption that this force is some particular form, and you know we tried to justify this by saying if the force is due to the exchange of massive particles then generically it will follow a strong wavelength distance. Burt Ovrut, who is our collaborator, has spent at least six months doing very detailed calculations of this force — which you can do in these M theory models. You can actually calculate the force. The trouble is it depends on many, many things. It depends on the state of the branes. There are six extra dimensions, which is this Calabi-Yau manifold — which can be in all sorts of configurations and the force depends on the configuration of those. It depends on whether there are charged particles localized on the branes and all sorts of complications. The long and short of it is that Burt can get potentials which are qualitatively of this form, but not quantitatively what we need to make the scenario work. I haven’t been so focused on that issue, because ultimately it’s important, but I think it will be the last bits of the puzzle to put in place in the sense that we don’t know which the right model is yet. We don’t know what Calabi-Yau manifolds to take, we don’t even know if we should take a Calabi-Yau manifold. Maybe it’s some other kind of orbifold or — there’s a huge phase space of string theory models. And so to us — at least to me — it was more, I still think it’s more important to see can you get through the singularity.

### Smeenk:

Right. Take this reasonable ansatz and we’ll see what —

### Turok:

Yes, just see what happens. So I’m more interested in those aspects of it. But I think it is true that unless we have a first principles calculation of a potential — that’s what we want obviously — I think that would be a weakness.

### Smeenk:

Right. You described earlier that it was split in the string theory community. Is it split along these lines, that some people see this as more reasonable —

### Turok:

Yes, impasse. Yes, impasse. I think that this question of the potential, some people have looked at this model and said, “Well, what sort of potentials do I know about?” And then quickly come to the conclusion that they’re not of a form that would make our scenario work. And therefore they have given up. And I think there are quite a few people around like that. Actually the same thing happened with inflation. When inflation was invented, in fact Burt Ovrut was one of the people at that time working on super-gravity who tried to get an inflation model from super-gravity. And they worked and worked and wrote papers, and after a few years they abandoned it, leaving inflation to the more phenomenological people willing to just play with fields. And so I think, you know, these things have happened in the past and inflation has never really gotten over this barrier that we are trying to get over or would like to get over. So that’s not very encouraging. It’s hard. It’s very hard to get a complete model.

### Smeenk:

But are there complete M theory models in other projects, or is this something that in all the applications —?

### Turok:

No. So you see, every M theory model of particle physics — I mean, the best models have some successes. They get the gauge group right of the standard model and they get the right number of families, for example.

### Smeenk:

But there is no calculation of the mass spectrum?

### Turok:

No, that doesn’t come out, and secondly you can ask is there a fifth force, for example. See, typically in string theory and M theory there is always more than gravity. There are other massless fields which mediate long-range forces.

### Smeenk:

They also spin two fields or —?

### Turok:

No, scalar fields, all scalar fields. In fact the distance between the branes is exactly one of these fields, and it’s massless to all orders in perturbation theory and string theory. It’s massless. Nobody knows of any way of getting in a mass. And this field would look today like what’s called the Brans-Dicke scalar, and that’s inconsistent with observations. So this is probably the biggest problem in matching string theory with the data is that it’s not known how to decouple this field. And then if you treat the field theory as best as is known mathematically, there is this wrong field with mad couplings. Now it’s sort of paradoxical, because in our model it’s precisely that field that makes the whole thing work. Because when these branes approach, essentially the reason why the density of matter, the singularity, is finite — you see when two branes hit, the density is finite here. There is no infinity in the density, which is why we claim we can pass through. There is no infinity there.

### Smeenk:

Right.

### Turok:

But the way it works is that this scalar field, which measures the distance, couples to matter in such a way that it undoes the gravitational blue shift, so essentially — this was not realized before our work — that in conventional cosmology if you have a big crunch density goes to infinity. In our model we have a big crunch followed by a Big Bang, but the density is finite everywhere. The way it happens is that even though the Einstein scale factor shrinks to zero, this scalar field runs off to infinity in such a way as to exactly cancel that, and makes the whole thing finite.

### Smeenk:

So this scalar field is representing the other…?

### Turok:

The distance, yes. If you look at the theory, this is the weird thing about our model. If you look at the theory in five-dimensional geometrical terms, nothing is infinite anywhere — just the two branes come in, finite density, and they come out again. That looks completely non-singular. It is strictly speaking singular, because one dimension disappears for one instant of time. But that is the weakest possible singularity you can ever have. It’s also like a cone. You know, if you take a cone where a circle shrinks to a point and then the circle re-expands, a double cone, that’s singular. But it’s very mild, what’s called an analytic singularity, you can analytically continue through it. That’s what we have.

### Smeenk:

Right. Hmm.

### Turok:

So, and in fact we’ve shown now you can analytically continue fields through the singularity and uniquely predict what comes out the other side. But we can only do that because it’s one dimension shrinking. So now you can take this theory where you have 5-D gravity in these branes and try and say, “Well, let me just try and describe this in terms of GR and scalar fields,” and you can, you see, because the distance between the branes is a four-dimensional scalar. It’s invariant under repara-meterizing this surface. So that’s a scalar. And then so you can try to reformulate the theory, just in new variables, which has a scalar field and gravity. When you do that you find that from that point of view the scale factor of the universe is shrinking to zero, and then this collision, and then the scalar field is zooming off to infinity. So it turns the distance between the branes is e^{Φ}, where Φ is the scalar field. Φ goes to minus infinity when they collide. So it’s a very nontrivial map, and in that map what looks regular in 5-D becomes hopelessly singular in 4-D. So in fact that’s what we argue, that really our world is 5-D. It looks 4-D now because the scalar field is constant, but when you go towards the Big Bang or Big Crunch this scalar field starts to move, and that’s a reflection that the distance is changing. The scalar field goes on to infinity at this moment, and that infinity is exactly what you need to undo the Einstein singularity so that now densities are finite, all the Riemannian curvature is finite, in our model of singularity, as you approach the singularity. And so you know we claim that in fact this field resolves the singularity.

### Smeenk:

And this field is also the dark energy.

### Turok:

It’s also the dark energy, so it does everything, this scalar — it washes up, makes the dinner, washes up, cleans up. [Both laugh.] Because the dark energy cleans up, does everything. So that is kind of appealing that it’s all one field. And it has a geometrical interpretation. So I mean I think all these things do make it more conceptually interesting than inflation.

### Smeenk:

Right. I mean, it just seemed to me one of the difficulties with inflation when you don’t have a tight connection with particle physics, it seems that you are suspended between making really strong assumptions about Planck scale physics that you don’ t know how to justify.

### Turok:

That’s right.

### Smeenk:

And then not having a tight connection to particle physics.

### Turok:

That’s right, yes.

### Smeenk:

Like Brandenberger’s work on the trans-Planckian… seem to illustrate this.

### Turok:

Trans-planckian, yes, sure. I think there are always going to be ambiguities like that. Essentially I think you could rephrase his work as saying, “We don’t know what the initial conditions were.” He doesn’t quite say it that; he says you know there is some transplanckian physics. I think probably a simpler way of saying it is that we just don’t know what the initial conditions were before inflation. And everything depends on what you assume. So Linde can say, you know, well, the field is going to be roughly smooth on some scale and then on smaller scales it will be a vacuum, but there is no real justification for it. So it just amounts to starting the universe and letting it go in the state which you want. And this is Penrose’s objection to the whole thing.

### Smeenk:

Right.

### Turok:

The advantage of the cyclic model is that the cycle will only work if the initial conditions are correct to keep recycling. And then it determines the initial conditions itself next time around. So you’re not just starting it. You are looking for an attractor solution in phase space which cycles and cycles and cycles, and that’s — you know, so once you are in the attractor you don’t care about initial conditions. It’s the same thing as when we look at the Earth going around the Sun. We don’t worry about the initial conditions of the solar system because in fact the orbit is periodic and all of its properties are determined by the system itself. It’s a bit better. I think it’s a bit better for us in cosmology because the, how to say… I guess you would say there are certain aspects of the Earth going around the Sun you would never even attempt to predict. Just due to accidents. In the cyclic model the condition of cyclicity demands various things. One is it demands that the vacuum energy be positive. Because you have to clean out the universe in order to start again. Otherwise the stuff will pile up — density variations, matter will just pile up every cycle. You have to empty it all, and that requires positive energy. Also you have to have some relationships between the density of matter and radiation of dark energy. If you have too much radiation relative to the other things it tends to damp away the motion of branes and stop the cycling. We’re just beginning to explore these things actually.

### Smeenk:

Right, right. And that’s —

### Turok:

In principle it’s a new selection principle for the initial data. They have to be such as to allow repetition.

### Smeenk:

That is interesting. So in very large terms, do you see this as one example of tying early universe cosmology much more closely to particle physics and high-energy physics than it has been?

### Turok:

Yes, I hope so. I think that has started to happen, because you see the issue like the shrinking of the extra dimension and reappearance. That’s a very concrete scenario, which you can look at in string theory and you can say does it makes sense. And since our work a lot of string theorists are now writing papers on Big Crunch — Big Bang space times. And so you construct toy models in string theory where you can examine these conceptual issues. But you know the virtue of the scenario is that it’s posing questions which are very deep. For example, if you prove in string theory that this really makes sense, that if I shrink to a singularity time continues through it. Everything changes in cosmology. You suddenly realize, “Oh, right. Obviously there was time before the Big Bang,” you know. “Why did we ever doubt it?” There wasn’t creation. So I think it’s more happening that way. The conceptual aspects of the scenario are attracting people to play with it. It’s not that they have to believe the scenario, but it provides sort of stimulus to exploring very deep and fundamental issues. It also relates to what happens in a black hole. See if we can get through a singularity in cosmology, what happens inside a black hole?

### Smeenk:

So in general all of these cases where you’d have in extendable incomplete geodesics —

### Turok:

Yes.

### Smeenk:

Those would look like cases where —

### Turok:

Yes. All of this should work. So my hope is that inside a black hole you can find exactly the same…

### Smeenk:

That’s interesting.

### Turok:

And in fact what’s going on in the black hole is you have two parallel branes and then as you form the black hole singularity that’s when the two branes touch. And then they cross each other, and it’s a little bottle of region the wrong way round. And that’s actually what’s inside the singularity of a black hole. And when a black hole evaporates away it’s just the branes untangling. It’s releasing all the information —

### Smeenk:

Oh, okay, so you don’t have to…

### Turok:

Information will come back.

### Smeenk:

So you have a connection with the black hole evaporation.

### Turok:

Yes, yes, yes. That has to be connected to that. So yes, I think it gives you other ways of looking at those problems too. But this is something I haven’t worked much on. I’ve done a little bit of work on it, enough that this sort of works, but I haven’t finished. I haven’t written any paper. Yes. I better go.

### Smeenk:

I was going to ask you how much time you had left.