SuperCosmologists Think Out of the Box

By cjohnson | August 3, 2005 1:13 am

Well, it is the end of the first day here for me at the Supercosmology workshop at Aspen’s Center for Physics. It was great. Physics discussion was rich and plentiful right from the word go. Ok, at least from 11:15am, when Liam McAllister gave a presentation entitled “Progress and Problems in String Inflation“. He gave an excellent talk, and there was great discussion all the way through. Later, Richard Easther gave a talk entitled “Trans-Planckian Physics and Cosmology”, but I had another meeting to go to and so could not attend.

So what’s with the title? Well, it riffs on a joke I inadvertently made in an earlier post. The kind of cosmology being discussed here focuses on models that try to build our universe by starting outside of it, in some sense. The thing we usually think of as the universe is embedded within the larger dynamics of string theory or M-theory that is “outside the box” that is the universe we normally think about.

So are we just sitting around dreaming? What do we do? Well, lets start with your “normal” cosmologist – even more normal than CosmicVariance’s own Mark or Sean. Being physicists, they write equations for the various quantities that we wish to study, such as the scale size and curvature of the universe, and the densities of various components such as matter, radiation, dark energy, etc. They might even make up various auxiliary dynamical quantities, such as a scalar field called the “inflaton” which has a particular dynamics -controlled by a “potential” function- which provides energy to drive an accelerated expansion phase in the very early universe, making it the really extremely flat universe we see today. The point is that these good people are working “within the box” in that they write equations in the 3+1 dimensional spacetime which we observe. They study the consequences of these equations on our observations in our 3+1 dimensional universe.

brane picture
From what we have learned so far about string theory, the natural starting point for doing physics which makes contact with our world seems to be to start in 9+1 dimensional spacetime. A modern perspective tells us to go further: Strings are not the only important objects in the game, but extended objects of more dimensions called “branes” are also important. (The term comes from starting with “membrane” which is a two dimensional object, calling it a “2-brane” and then having the idea of a “3-brane”, “4-brane” etc. Or just “brane” when you want to be non-specific.) It turns out that we need to consider these objects too. Fully non-perturbative considerations also encourage us to consider “M-theory”, which (at least at low energy) appears as an eleven dimensional (10+1) theory with no strings at all, just branes of a couple of sorts.

Physicists are attracted by the idea of showing that the types of 3+1 dimensional models and equations which the regular cosmologists study actually have their origin “outside the box” in the larger setting of string- or M-theory. Several of the objects, like the inflaton, etc, may well have a geometrical origin where the dynamics of that larger setting explain certain features that have no explanation purely within the 3+1 dimensional setting. For example. the inflaton field might turn out to be secretly the distance between two key objects in this larger setting. The potential function controlling the inflaton would then arise from the dynamics of those objects, like how they attract or repel each other. More on this later.

So this is what people are doing in this game: trying to get certain key aspects of Nature: inflationary cosmologies, the Standard Model of particle physics, etc, out of stringy models. The focus at this workshop is the inflationary side of things, but in his talk Liam correctly emphasized that we should not expect proceed indefinitely by keeping several efforts separate: The quest for a realistic standard model embedding within string theory (including stabilising moduli, i.e. getting rid of the several massless scalar fields that string theory models tend to give) is tied up with finding good inflationary models. These efforts neccessarily talk to each other.

SuperCosmology is – I think – a title coined to remind us that we are starting in supersymmetric 9+1 dimensional spacetime, and then proceeding from there. (“Supersymmetric” means that there is a symmetry between bosons (force particles, roughly) and fermions (matter particles) .) Typically, one has compact parts of the compactification manifold (the space which is hidden) which result in effective 3+1 dimensional models in the uncompactified directions. These manifolds are usually also chosen to preserve some supersymmetry, as it allows us some control. Generically, the manifolds come in families – there a “moduli space” of manifolds – connected by changing a continuous parameter. Meaning? An obvious example is the overall size of a manifold which has everything else fixed. The radius of a sphere might be a good thing to visualize. Changing the radius, you’d not say that the manifold is no longer a sphere, you’d just say that it is a sphere of different radius. In the effective 3+1 dimensional model resulting from having this compact sphere, there would be a scalar field corresponding to this radius, which can take continuous values, with no preferred value. Such a field is called a “modulus” (and the plural is “moduli”).

Now this is all well and good, but there’s a problem. Nobody has ever observed such a massless scalar field in Nature. These came from a supersymmetric model, and the trick is to break supersymmetry (since we don’t see that in Nature either) and get all the scalar fields to freeze at specific values. The manner in which this is being done a lot these days is to use wrapped branes and also “fluxes” of various fields that are in the spectrum of the string- or M-theory model. These fluxes (certain distributed energy densities of these fields) are spread out over the surface of the manifold in question (our sphere example, say), and expanding the sphere actually reduces energy in the model (it dilutes the flux).

A brane wrapped on a sphere can compete with that effect. This is because branes have tension (mass per unit volume) and so if it is wrapped on the sphere, growing the sphere costs energy. So you get a competition between the two effects, and there is an optimum value of the radius where balance is achieved. This is what is meant by “freezing” or “stabilizing” the modulus field.

This example is not perfect, since it turns out that the sphere as a
compactification does not give a lower dimensional theory with a modulus corresponding to its size (“volume modulus”) showing up. Turns out that a sphere’s curvature costs energy in the lower dimensional model and in fact the sphere tries to shrink itself away -there is a “runaway potential” off to zero size. It is not a supersymmetric model. You can stabilize this runaway by putting flux on the sphere of just the right sort so that since the sphere now does not like to shrink away, it stabilizes at some finite value (given by the number of units of flux, roughly) and the resulting model is supersymmetric. The value of the energy density of the model at this stabilised point translates, it turns out, into a negative vacuum energy -negative cosmological constant- for the model. (This is a nice way of thinking about anti-de Sitter models in string theory, emphasized in some nice notes by Eva Silverstien – we’re good at those models, and like them because of the AdS/CFT correspondence. More on that some other time.)

What we want, in addition to using branes and/or fluxes to stabilize moduli, is to generate a non-supersymmetric model with a positive cosmological constant. In other words, new ingredients (other fluxes other types of brane, etc) can be introduced to add a new element to the competition between components which (meta)stabilizes everything as before, but at a point where the vacuum energy is positive. This is hard, but there seems to be plently of parameter space to allow you to argue that you ought to be able to do it in a variety of models. What is really hard is demonstrating that you can do it using the techniques we currently have available in string theory (going beyond just perturbative arguments and including non-perturbative effects). The most celebrated class of models that seem to achieve this are the “KKLT” models. Explicit demonstrations are still very difficult, however, and not everyone in the field is convinced that fully convincing models have been exhibited, although all agree that the mechanism should do the trick in principle. This is an area of interesting and very hard work -using very interesting and beautiful physical and mathematical techniques- that continues.

So what are the supercosmologists doing? They want to go a bit further: Stabilize moduli, generate naturally a scalar field (with the right potential) which would play the role of the inflaton with the right physical properties to make contact with experiement (“phenomenological properties”), and get the Standard Model of particle physics in there as well. Such models -using some of the concepts and ingredients I described above- are the sort about which Liam McAllister was giving us an update.

One key ingredient that I should mention is that several models these days use the idea that our 3 spatial dimensions in which we live is simply that of a 3-brane embedded in the higher dimensions of string theory! So our universe is a dynamical object in this scenario which can move around, bump into other branes, etc. We’ve put “the box” into a much larger dynamical context. The inflaton could well be a scalar field representing the distance between our 3-brane (on which we live) and another brane, or some other structure in the theory. The inflaton arises from the details of the forces of attraction/repulsion between our dynamical objects. This is a very important picture which appears in a lot of approaches to fundamental physics right now (and I should say here that CosmicVariance’s very own JoAnne is an expert on testing some of the observational particle physics consequences of such scenarios.)

Well, having been careful to try to give you – possibly an interested non-expert -
some flavour of what the basic issues are, I find myself with no time or energy to run through the highlights of Liam’s talk! The clock says it is 12:17am and the warm fuzzyness that is seven hour jetlag is setting in. I also need to be bright-eyed and bushy-tailed for working tomorrow.

I should continue this discussion a bit later. I do hope I at least set the scene for what we’re up to in this part of the field, and here at Aspen.


  • tmccort

    Clifford, I have some general questions. First, why is it called string ‘theory’? I always thought that evidence has to be collected from experiment in order for something to graduate to theory status (At least that’s what they told me in school).

    All this speculation that is being done on strings, branes and supersymmetry is all well and good but it is still only speculation and in the media often taken to be fact.

    For example, take the Ptolemaic model of the solar system. The more they worked on it the more accurate it became at describing the motions of the planets, yet the more they worked on it the further it became from having anything to do with reality. When they found problems I guess it just meant that they had more work to do.

    I don’t mean to sound flippant, but what’s the difference between the assumption of Geocentrism and the assumptions of strings, branes or supersymmetry really?

    Could all this just be an elaborate human construct?

    Interested non-expert

  • TM

    Clifford – Not meaning to depress you with too elementary questions,
    but what exactly is the difference between a perturbative and non-
    perturbative theory (the former is a kind of statistical approximation
    of the latter that is more mathematically tractable?); and more
    embarassingly, what is a manifold? This came up in reading sean’s
    relativity notes as well.

  • bittergradstudent


    A perterbative theory is one when the person analyzes it takes the original equations describing the equation to have “free” part and an “interacting” part. The free part usually has the mathematical structure closely analogous to the dynamics of a spring, which is easily solved. The “interacting” part is considered to be multipled by a “small” constant (called a “coupling constant”). The theory can then be approximated as the ‘free’ theory, plus a small, “first-order” correction, proportional to the coupling constant, plus an even smaller ‘second order’ correction, proportional to the coupling constant sqared, etc… Feynman’s diagrams are a pictoral way ot expressing this ‘perturbation series’, where the free theory is deformed by interactions. This technique is very well understood, but is only valid for interactions that are small relative to the ‘free’ part. Some examples of quantum field theories well suited to perturbative methods are the Weinberg-Glasgow-Salam model of the weak interaction and Quantum Electrodynamics

    Non-perturbative theories are ones that do not use the above process in deriving the quantum mechanics above. Quantum Chromodynamics, the currently accepted theory of the strong interaction, is not well described by perturbative techniques, as the ‘interacting’ part is large with respect to the ‘free’ part at low energies (though perturbative theory is useful at high energies for QCD, as shown by Wilcek). Loop quantum gravity makes the argument that since general relativity is not logically seperable into a ‘free’ and ‘interacting’ part, it must therefore NOT be treated with perturbative techniques. Typically, any non-perturbative approach is very mathematically intractable and difficult, though progress is being made on this front, especially using computer simulations.

    A manifold is simply a fancy, technical word which roughly translates to ‘space’ or ‘space-time’ (depending on the signature–i.e., whether it is 4 dimensional [=space] or 3+1 dimensional [=space-time]). The main feature that a manifold has is that it has enough structure to allow calculus to be done on it (directional derivatives are well defined, etc…)

    hope that helped!

  • Mark

    Nice job bittergradstudent!

  • Clifford

    Oh, these questions are great! Thanks. I did want to write something that was useful to a wider non-expert audience to give you an idea of what we’re up to, and I feared that last night in my jetlagged haze that I did not define enough terms, but the post was long enough already.

    tmccort: Its called string theory of M-theory for want of a better name. What people don’t tell you much is that we know it is not a theory of strings. We basically don’t know what it is a theory of at all, in fact. We know that in some regimes, the physics is “stringy”, and in other regimes it is something else, but we have not yet formulated the theory in a way that does not have to refer to one limit (regime) or another for us to properly understand what is going on. This is the biggest and most important aspect of the puzzle of this approach to fundamental physics. So nobody is bothering to find new names until we have better ideas for what the thing is. Not knowing what it is makes it no less dazzling in its scope and physical richness.

    The process of doing science is what you are asking about. The media seem uninterested in talking about that and present everything as the “truth for today”. This is one of the reasons we have this blog, in my opinion – to help people see that science is an ongoing dialogue with Nature. So string theory is an attempt to find answers to several questions that arise when you study Nature. We do not know the answers in advance. We formulate a framework within which to answer those questions, and within that framework theories are constructed that take as input what we already know, and -if we’re smart enough and if we’ve done a good job- the theories give an answer to the questions we care about, *and predict further things*, sometimes things that we had not thought of when we set out to ask those initial questions.

    This is true in any field of science. String theory is no different. It will take more time to develop it to the point that we can confront it with real observations from Nature. But the scientific procedure that is going on is just as sound as in any other field.

    TM. In this context, perturbative just means that you are formulating and calculating the physics in a regime where the strength of the interaction between the individual strings is rather weak. This strength (or “coupling strength”) controls how likely a string is to split into more strings, or join with other strings. This is the regime which gave the theory its name. In later years, we learned a bit about the regime which is not like this, where the strings interact so strongly that they can do very new things to the physics. This regime is so profoundly different that the individual strings are often completley absent from the physics, and the description is best done in terms of other things, such as the branes of which I spoke. This is a much harder regime in which to work, and is the key to understanding the whole story. This is partly because the strings happen to have the abiltiy to dynamically change the coupling and you can get driven to a regime of strong coupling when you started out in weak coupling.

    A manifold has a precise definition which I won’t trouble you with. It suffices for the purposes of reading the article too substitute the word “space”, and have in mind a few candidate shapes. The surface of a ball is a two dimensional sphere, and there are higher dimensional versions of such things, which I used in the article. Also, the two dimensional surface of a table top (ignoring the edges for now, imagine its a big table) is another two dimensional example. One is “compact” and the other is “non-compact”. Another one is the surface of a ring doughnut (donut), which is a two dimensional manifold called a “torus”. It has more interesting “topology” than a sphere as you can see by the fact that you can get a loop of string stuck on it (so that the loop can’t contract), where is there is no way of doing so with a sphere.

    These are all manifolds. There is a great deal of interest in studying higher dimensional versions of these spaces, with lots of interesting properties. These are spaces which string theory suggests as possibilities for the dimensions of spacetime that we don’t see directly. One of the things string theory must do is give predictions for experimental signatures that give clues to the nature of this internal manifold. As you can see, you can distinguish between them due to how strings propagate on them -getting tangled or not has experimental consequences.

    If you want a defintion of a manifold you can do it as follows. In the local neighbourhood of any point on the space, it should be enough to get around by locally treating itlike the tabletop space (called R^n in n dimensions.) Then you need nice conditions on how to translate between such local maps as you move from neighbourhood to neighbourhood. There are sveral good books on this, but that’s the idea.



  • Clifford

    Oh! More comments since I began writing my long reply. A good one too. Thanks bittergraduatestudent! -cvj

  • TM

    Thanks to Clifford and bgs!

  • Sean

    And as I type these words here at SLAC, I’m listening to Eva give a very nice talk on string cosmology, emphasizing the possibility of observable signatures like cosmic strings and non-Gaussian perturbations. All part of cosmology’s master plan to absorb string theory whole.

  • Clifford

    Yes, Liam talked about some of that here yesterday.

    It’s nice to see that our Jedi mind trick worked on you, as a cosmologist, making you think that *you’re* absorbing *us*. Keep thinking that while we swallow you up. And do wriggle a bit while we chew. Makes it more fun. -cvj

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  • Qubit

    “What is this?” thought Qubit, “I do not see anything at all. That is terrible! Am I stupid? Am I unfit to be a Qubit? That would indeed be the most dreadful thing that could happen to me.”

    String theory… Brilliant I like it, “it’s very beautiful”.


    “What elephant?”

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