What caused the shift of interest in quantum cosmology?

[marcus]

...but perturbative string theory fails at some point, while the boundary theory exists. I don't know what the correspondence is then. Presumably one of the string experts on this board will know.

Better ask if the correspondence depends on smooth manifolds. (Which may be just a polite mathematical fiction )

And also what happens to the boundary+bulk setup when there is a cosmological bounce. A crunch+rebound.

 

[Physics Monkey]

AdS/CFT doesn't assume a fixed background metric or "physical dimension". The data specified is only the asymptotic form of configurations i.e. one sums over configurations in the path integral that are asymptotically AdS. However, the bulk may be highly fluctuating to the point where classical geometry is essentially meaningless.

Nevertheless, it is true that in a certain limit, the large N limit, the path integral may be approximated by saddle point and the notion of a classical geometry becomes relevant. This is by far the most explored limit of the duality thus giving the impression that the duality requires a smooth geometry. There are a limited but growing number of tests of the duality away from large N, but this is one of the great open directions for the subject.

 

[fzero]

The strong form of the AdS/CFT conjecture is that the CFT sums over all spacetimes which are asymptotic to $$\text{AdS}\times X$$, where $$X$$ is a sphere in the maximally supersymmetric cases. There are no restrictions on the interior and all string and QG physics can occur there. The corner of coupling constant space everyone is familiar with is the one in which the string coupling is small and the radius of curvature of spacetime is large, so that classical supergravity is reliable and the interior physics is just that of AdS supergravity.

In the case where we have IIB on $$X=S^5$$ and the dual CFT is $$\mathcal{N} =4$$ $$U(N)$$ SYM, the 10D Newton constant scales like $$G_N \sim 1/N^2$$, while the radius of curvature in Planck units is $$R^4/l_p\sim N$$. The inverse string tension is $$\alpha'\sim 1/\sqrt{g^2N}$$. When $$g^2N$$ is large, the massive string modes decouple. For large $$N$$ gravitational corrections are small and classical supergravity dominates. This is region which tends to be the most familiar both in the literature and with nonexperts. One of the reasons for this is, that while the gauge theory side is strongly coupled and hard to calculate, the nature of the CFT means that many observables can be still be defined. Their correlation functions and other dynamics can be computed in the gravitational theory.

Now as we decrease $$N$$, quantum gravitational effects become important in the interior. Note that this large $$g^2$$, small $$N$$ region is one of quantum supergravity, since higher order string modes do not contribute at leading order. So the physics there is that described by any consistent theory of quantum supergravity on spacetimes which are asymptotically AdS. The only requirement is that the quantum theory reduce to supergravity at low energies/weak gravitational coupling.

The conjecture implies that this physics is also completely described by $$\mathcal{N}=4$$ SYM at strong gauge coupling. Now, this dual theory is probably the best understood nonAbelian gauge theory of all, but as is the case in any gauge theory, we have limited tools for studying physics at strong coupling. Perhaps the most promising approach would be lattice gauge theory, whose application to the $$\mathcal{N}=4$$ theory has been seeing steady progress (http://arxiv.org/abs/1102.1725 is one recent paper). I'm not a lattice expert, but I don't think that the problems are likely to be impossible ones to solve.

I'm not aware of any spacetimes that have a bounce and are asymptotic to AdS, so I can't comment on that. There have been discussions what limit is involved trying to extend AdS/CFT to flat space (Polchinski's http://arxiv.org/abs/hep-th/9901076 is an early paper in this direction), as well as of a dS/CFT correspondence (Witten http://arxiv.org/abs/hep-th/0106109 and Strominger http://arxiv.org/abs/hep-th/0106113). More recently Strominger and collaborators have been studying holographic descriptions of black holes via CFTs, see http://arxiv.org/abs/arXiv:1009.5039 for example.

 

[marcus]

AdS/CFT doesn't assume a fixed background metric.

I didn't say it did!

I also did not assume that a "physical dimension" was fixed, whatever that means.

What it does assume is a differential manifold (one that you can put various metrics on) because otherwise you could not get Einstein gravity.

And a manifold has a fixed dimensionality that holds at all scales. That is part of the definition.

Maybe you should read my post more carefully before you start "correcting" it. I would be delighted to get some feedback.

 

[marcus]

There are no restrictions on the interior and all string and QG physics can occur there.

Fzero thanks for commenting! I was gratified to get such good feedback. What I have been trying to say (which I'd like your reaction to) is that there is a BIG restriction on the interior, which is that it is assumed to be a diff. manifold.

Locally diffeomorphic to R^d for some fixed dimensionality d.
===============

If the interior is not a conventional continuum, a manifold with fixed dimensionality d which does not run with scale, then I don't see how "all string physics can occur there".

Indeed I must assume it is a diff. manifold because it always has been in every presentation of AdS/CFT I have seen.

On the other hand in the long run this could be something of a disaster for AdS/CFT, or at least a severe limitation.

There are types of QG that do not use a manifold, at least in the ordinary sense. Some of these can undergo a nonsingular "bounce" during which density (to the extent you can define it) seems to get up near Planckian scale.

So if "all string physics can occur there" it is hard to see how "all QG physics can occur there". I think you see the point I was trying to make.

There are cogent conceptual arguments why a quantum theory of geometry/gravity cannot live on a spacetime manifold. A different mathematical representation of time and spatial geometry would then be required. Several are being worked on currently.

BTW David Gross has repeatedly acknowledged that to move ahead (he means with string/M) we "may need a completely new idea of time and space". But he doesn't specify what that might be.

 

[smoit]

I didn't say it did!

What it does assume is a differential manifold (one that you can put various metrics on) because otherwise you could not get Einstein gravity.

And a manifold has a fixed dimensionality that holds at all scales. That is part of the definition.

Maybe you should read my post more carefully before you start "correcting" it. I would be delighted to get some feedback.

No, that's true only in the large N and small string coupling limit. That's the only regime when the geometric description in terms of a differential manifold makes sense. When the string coupling is large and N is finite it makes no sense to talk about a differential manifold in the bulk, the physically meaningful quantity is the CFT partition function.

 

[fzero]

Fzero thanks for commenting! I was gratified to get such good feedback. What I have been trying to say (which I'd like your reaction to) is that there is a BIG restriction on the interior, which is that it is assumed to be a diff. manifold.

Locally diffeomorphic to R^d for some fixed dimensionality d.

No assumptions are being made about the details of how you are supposed to describe physics in the bulk. As I tried to motivate, on the gravity side, we have a theory that reduces to classical supergravity in a certain limit. There the use of a fixed spacetime manifold is completely justified. In a small neighborhood of this point in coupling space, the proper description is the IIB string on the fixed manifold. Far from this point, there is another point where there are strong QG effects, but no string effects. If we had a complete description of QG, we could presumably describe the physics there. Note that this description must reduce to classical supergravity in the appropriate limit, just as Newtonian gravity should emerge from a nonsupersymmetric theory of gravity.

Now, in the absence of such a description of QG, the claim is that the dual CFT provides a completely well-defined description of the physics. However it is not a theory that we can compute very much in, since it is nonperturbative gauge theory. Nor do we really know the dictionary between boundary and bulk observables in the absence of a more concrete description of the QG theory in the bulk.

It's natural to expect, given the framework that this theory is sitting in, that the QG theory is some nonperturbative version of the IIB string. However, even if this were not the case, it is still plausible that the gauge theory remains a correct dual description, since we can identify the adjustment of the gauge theory corresponding to tuning the gravitational coupling away from the classical limit.

 

[suprised]

marcus, as always, is trying to emphasize apparent shortcomings of string theory, and then compares this whatever the current fashion in LQG is. In the present situation, he claims (or spindoctors to the same effect) that string theory would intrinsically rest on smooth geometries and thus would be unsuited to describe quantum geometry at small distances.

Of course, rather the opposite is true. As has been known for years, and as I was emphazing here repeatedly, classical smooth manifolds are relevant only in a certain regime; let's loosely say, of measure zero in the full parameter space. In general there are non-perturbative quantum corrections to the geometry to the effect that it becomes modified to some kind of stringy geometry, which is very different from ordinary classical theory based on smooth manifolds. Many notions of classical geometry become blurred in such non-geometric phases, or even stop to make sense. Examples are topology changing transitions, disappearence of singularities, appearence of some kind of space-time foam, submanifolds of naively different dimension becoming indistinguishable (so that the notion of a submanifold stops making sense), etc etc. All this has been investigated to great detail and has improved our conceptual understanding of quantum geometry at small distances. So string theory is a very rich and prolific toolbox to address exactly this kind of questions.

 

[marcus]

Fzero,
I was quite excited by your post #42 and tried repeatedly to post a few minutes after you put it up. But the system kept giving error messages and losing what I wrote, so i gave up.
What you say, if I understand you, makes AdS/CFT much more interesting, though seemingly contradictory. So what mathematically represents the interior?

The interior is not a smooth manifold---is that correct?
So is it a topological manifold (locally homeomorphic to R^d)?
On rereading several posts, I think it must be that. A manifold but no differential structure.
Or does it have a fragmented differential structure with lots of singularities?
Or a superposition of piecewise linear structures. I'm still not clear on this.
============
Putting that to one side, there is the issue of the big bang or big bounce. And today's accelerated expansion. I think you indicated the bang/bounce can not (as of now) be represented. No solutions on that boundary that exhibit that.
There was more: here's the quote:

I'm not aware of any spacetimes that have a bounce and are asymptotic to AdS, so I can't comment on that. There have been discussions what limit is involved trying to extend AdS/CFT to flat space (Polchinski's http://arxiv.org/abs/hep-th/9901076 is an early paper in this direction), as well as of a dS/CFT correspondence (Witten http://arxiv.org/abs/hep-th/0106109 and Strominger http://arxiv.org/abs/hep-th/0106113). More recently Strominger and collaborators have been studying holographic descriptions of black holes via CFTs, see http://arxiv.org/abs/arXiv:1009.5039 for example.​

 

[marcus]

... classical smooth manifolds are relevant only in a certain regime; let's loosely say, of measure zero in the full parameter space. In general there are non-perturbative quantum corrections to the geometry to the effect that it becomes modified to some kind of stringy geometry, which is very different from ordinary classical theory based on smooth manifolds...

Good! This could be helpful, Suprised. So there still is a manifold in the interior. It just might not be smooth. That was one of the possibilities that I was considering. A topological manifold, locally homeomorphic to R^d.

You make the interior geometry sound very nice---so I could take a liking to it. But how about the big bang? You may have talked about this in other threads, but I haven't seen them, so please tell me. Late universe accelerated expansion? Early universe inflation? Bounce maybe? Does the richness you speak of already include those riches?
I would be glad to hear of positive results, especially if you have links to papers.

I thought Fzero gave a negative indication on one of those, however. Maybe that's in the "work in progress" department.

 

[suprised]

So there still is a manifold in the interior

This is not what I was saying. It is known that more general concepts start to play a role, like sheaves and more abstractl objects in certain categories; only in classical limits these turn back into things we know from classical geometry. This can be much more drastic than a simple discretization or dimensional reduction.

Here an interesting paper about related matters, about "quantum gravitational foam": http://arXiv.org/pdf/hep-th/0312022
This is of course "just" a topological toy model, but nevertheless it provides a glimpse of how things may work in a more realistic situation. They find what contributes to the path integral are certain coherent sheaves and not just naive geometries:

"...The path-integral space for quantum gravity should include classical topologies and geometries. However the actual space we integrate over may well be bigger than that given strictly by manifolds with arbitrary topology and metric, as happens for topological strings..."

So string theory seems well capable to address this kind of questions, in fact other approaches appear quite naive to me in comparison. In the best of all worlds, other approaches like LQG won't give different or contradicting results, but rather complementary ones; I'd expect this to be akin to lattice QCD capturing some non-perturbative aspects of continuum QCD.

 

[marcus]

Sheaves? That's interesting. We studied sheaves when I was in graduate school long long ago.
What other structures in the interior do you remember hearing about?

I have to go to sleep (I am on the Pacific coast) but I look forward to hearing more about this.

You could be right that partial and complementary answers will be provided by several different methodologies.

Are you aware of the Zurich conference "Quantum Theory and Gravitation" to be held in mid June 2011 at the ETH.
You may know some of the scheduled plenary speakers. They come from a number of different QG approaches.
http://www.conferences.itp.phys.ethz.ch/doku.php?id=qg11:start
Plenary speakers:

Jan Ambjorn (Copenhagen)*
Joakim Arnlind (AEI Potsdam)
Abhay Ashtekar (Penn State)
Costas Bachas (ENS Paris)
John Baez (Riverside)
John Barrett (Nottingham)
Niklas Beisert (AEI Potsdam)
Matthias Blau (Bern)
Ali Chamseddine (Beirut)
Alain Connes (College de France, Paris)
Ben Craps (Bruxelles)
Axel de Goursac (Louvain)
Lance Dixon (SLAC)
Henriette Elvang (Michigan)
Klaus Fredenhagen (Hamburg)
Laurent Freidel (Perimeter)
Stefan Hollands (Cardiff)
Jens Hoppe (Stockholm)
Ted Jacobson (Maryland)
Jerzy Jurkiewicz (Krakow)
Gandalf Lechner (Wien)
Jerzy Lewandowski (Warsaw)
Renate Loll (Utrecht)*
Roberto Longo (Rom)
Viatcheslav Mukhanov (Munich)
Hermann Nicolai (AEI Potsdam)
Martin Reuter (Mainz)
Carlo Rovelli (Marseille)
Misha Shaposhnikov (EPF Lausanne)
Raimar Wulkenhaar (Münster)

 

[Fra]

Suprised, if I may try to ask a simple question regarding the strategy, concerning some fundamentall by still overall points.

This can be much more drastic than a simple discretization or dimensional reduction.

You mention things like theory spaces.

In MY opinion, discretization serves the purpose of allowing a well defined counting, and thus construction of a measure, Even if we then take a continuum limit, the choice of measure depends on the way the limit is taken.

Those who take the discretness most seriously, like causal sets etc, there the discretization is not really an approximation - it's the continuum that is an approximation.

By taking the continuum limit you loose information, namely how hte limit is taken. And you end up with problems of how to defined measures.

classical smooth manifolds are relevant only in a certain regime; let's loosely say, of measure zero in the full parameter space.

How is the measure on this space physically constructed and justified?

I mean, don't you end up with just an even bigger landscape?

Or put differently, how you do gain more flexibility WITHOUT loosing control? (ie the measure, and thus getting lost in a landscape too larg to process)

Is this not a problem?

/Fredrik

 

[Physics Monkey]

I didn't say it did!

I also did not assume that a "physical dimension" was fixed, whatever that means.

What it does assume is a differential manifold (one that you can put various metrics on) because otherwise you could not get Einstein gravity.

And a manifold has a fixed dimensionality that holds at all scales. That is part of the definition.

Maybe you should read my post more carefully before you start "correcting" it. I would be delighted to get some feedback.

Really, marcus? After all this time, is this really the attitude you're going to take?

I didn't say anything about correcting you nor did I address my post to you. My post was a brief informal note about what ads/cft assumes about the structure of "spacetime". I thought I could discuss physics informally here without having to check every word of my post for compatibility with yours. Perhaps I was mistaken.

Also, I see that others have already pointed out the flaws in your statement above, so I'll leave it at that.

 

[suprised]

How is the measure on this space physically constructed and justified?

I am not claiming that I know, that's why I was writing "loosely". But the point is pretty obvious, in that classical geometry or weakly coupled physics just corresponds, again loosely speaking, to the boundary of the full parameter space. Clearly this boundary is much "less" than the full parameter space itself. Away from the boundary, ordinary notions of geometry generically break down.

I mean, don't you end up with just an even bigger landscape?

Or put differently, how you do gain more flexibility WITHOUT loosing control? (ie the measure, and thus getting lost in a landscape too larg to process)

Is this not a problem?

Problem for what? We are not engineers who design a car according to market demands! We talk here about the parameter space of quantum gravity in the string formulation. That's a question in itself and needs to be investigated, irrespective of feelings whether the landscape becomes "too large". It's like complaining that there would be "too many solutions" of GR, etc.

 

[marcus]

Sorry Physicsmonkey, I mistook the tone of your post. It seems too obvious to need saying that the schema doesn't require a fixed background metric on the bulk, and I thought you were talking to me. It sounded condescending and I momentarily lost my temper. My bad. The rest of your post is concise and informative. So thanks for that!

AdS/CFT doesn't assume a fixed background metric or "physical dimension". The data specified is only the asymptotic form of configurations i.e. one sums over configurations in the path integral that are asymptotically AdS. However, the bulk may be highly fluctuating to the point where classical geometry is essentially meaningless.

Nevertheless, it is true that in a certain limit, the large N limit, the path integral may be approximated by saddle point and the notion of a classical geometry becomes relevant. This is by far the most explored limit of the duality thus giving the impression that the duality requires a smooth geometry. There are a limited but growing number of tests of the duality away from large N, but this is one of the great open directions for the subject.

This may explain why I was under the mistaken impression that the interior manifold has a differential structure!

So now I'm quite interested. What structure does it have? How do you talk about what is going on there, in the bulk?

If you have no differential structure (generically---"except on a set of measure zero" as someone suggested) then how do you describe things. Curvature? Matter fields? Distances? Volumes? Geometric relations among events?

So far I think we just have a topological manifold, not so? Continuous functions only. I'm intensely curious to know how analysis on the bulk can proceed from here. Please educate me!

(May not be able to respond for a few hours this morning because of appointments but if you reply soon I'll see it and be able to think about it while I'm out.)

 

[martinbn]

I don't want to diverge from the original topic, but it is very interesting to me, so I would like to ask a side question. What exactly are the structures used that are nor diff. manifolds, that were mentioned above? What would be great to hear is the mathematical definition or the name of the object or a reference where one could find them. Mentioning the word sheaf is not enough, surely one can and does use sheaves on differential manifolds.

 

[Physics Monkey]

Perhaps others have a different opinion, but I suspect it's too early in the game to start delineating exactly what mathematical structure exists in the bulk.

Instead, I'll give two useful examples.

1. Topology change in string theory: One can arrange situations where the initial and final states are well described by smooth manifolds but with different topology. This means that the intermediate state, even if we drop all smoothness assumptions and work only with continuous manifolds, must undergo an evolution that is not a homeomorphism. So the "bulk" cannot be described at all times by a continuous space with continuous evolution. String theory can describe this situation in terms of a kind of condensation phase transition on the string worldsheet. See for example: http://arxiv.org/abs/hep-th/0502021

2. Matrix models: String theory or M-theory can be described by replacing continuous coordinates by finite dimensional NxN matrices. As in AdS/CFT, the large N limit of the matrix model recovers in some sense the notion of smooth geometry. But in general there is no precise notion of a continuous space in these descriptions; one recovers instead some kind of "fuzzy" geometry. One nice example is described here: http://arxiv.org/abs/hep-th/0002016

 

[Fra]

I am not claiming that I know, that's why I was writing "loosely". But the point is pretty obvious, in that classical geometry or weakly coupled physics just corresponds, again loosely speaking, to the boundary of the full parameter space. Clearly this boundary is much "less" than the full parameter space itself. Away from the boundary, ordinary notions of geometry generically break down.

I'm with you that the notions of geometry and manifold must break down in more general cases. I have no objection to, on the contrary. I'm rather fishing for what the more generalized structures are (agreeing they aren't manifolds) and from my perspective, beeing able to count/measure them are a key point. In fact my point would be that a constraint is that they have to be measurable, or we are on the wrong track.

Problem for what?

A problem for inference. I think to be able to make inferences/predictions/expectations and to LEARN about nature is what this is all about, I presume we agree. I try to not loose this focus must never be lost in mathematics.

Normally: one theory => one inference (though it can be inductive rather than deductive).

Now if a theory is not known, but rather we have a space of theories, and accordingly a space of inferences, then if there is any physical basis between this space, then there theory space itself should be the result of another inference: ie you have a bigger theory, from which other (more specific) theories follow. And if this theory is a proper inference, there must exists a justified measure on the theory space.

My point beeing that, if some kind of ideas come up with this theory space, without a measure or means of inference and selection I would personally take this as a clear sign that something just isn't right about that reasoning.

Note that I am not picking on the NOTION of theory space or theory of theory; that is somehow the ambition ST has. This is good. What I feel, is that this "theory of theory" may in fact not be a proper inferencial theory.

Of course no one has all these answers, but I was just trying to pick in a constructive way. I think said before but I think that lack of this measure is because the theory space is describe from an external perspective (say the chair of the physicist) rather than from each subsystem of the universe.

This is why this theory space that is Externally described, IS not measureable from the inside. This is also why it's not an intrinsic theory in the first place.

I think curing this in ST therms, means providing a more clever solution to the landscape problem, in terms of some evolution. And I'm not just talking about antrophics I think something more in line with smolins evoluiotary law is neeeded. If ST is generalized, beyond strings and beyond manifolds, (meaning it's not really "strings" anymore) then I do see how the string program might converge in this direction. So it doesn't look totally dark to me. My favoured picture involves a discrete combinatorial approach where strings may be explained as large complexit limits of such discrete structures, in a way where the continuum strings are just limiting cases. And it's when you TAKE the limit, you loose contact with ground. So it seems the historial starting point of ST is responsbile for plenty of confusion. Maybe there is an alternative starting point... that makes more sense also to ignorant people like me.

/Fredrik

 

[marcus]

Perhaps others have a different opinion, but I suspect it's too early in the game to start delineating exactly what mathematical structure exists in the bulk.
...

Wow! thanks for that viewpoint. I can't respond in any substantive way because I have to be out for most of today. Just in briefly now.

I would like to ask you to take a look at this short Loop tutorial
http://arxiv.org/abs/1102.3660
It is a manifoldless math structure possibly able to describe 4D geometry and matter in the bulk.
Putting matter in has really only just got started.

The basic structure is a non-embedded cellular complex---a 2-complex.
With a graph as boundary.

Suprised conjectured that several different languages for describing the geom+matter in the bulk might turn out to be "complementary".

I am interested in the AdS/CFT language (as well as the spinfoam/GFT language) because I think I hear you say it could possibly be manifoldless.
Or at least the structure is in doubt---and at least it is not a smooth manifold.

So that is interesting. One may be able to compare and one might even find unexpected similarities.

What is in this 20-page tutorial 1102.3660 is a new form of LQG which only appeared in 2010 (although I saw hints of it back in fall 2009). It looks like it has been already or is being adopted by a substantial part of the Loop community (which as you know is still comparatively small, so far only 100-200 or so come to the biannual conferences, though this could now be increasing.)

I'd like to know your reaction to this alternative math language. It is a bulk+boundary schema where the boundary contains the initial final or side conditions, and one is calculating an amplitude.

Also, to amplify Martin BN's question, can anyone speculate for us what some possible CANDIDATES might be for the mathematical structure of the bulk in the AdS/CFT picture?

It would be very interesting to hear about any you can think of. Thx.

 

[marcus]

Well we have had some interesting and informative posts from Physicsmonkey, Fzero, and Suprised (among others). Are we any closer to answering the main question posed in post #1 of the thread?

Why the shift of interest (illustrated by research citations but not confined to that) in quantum cosmology?

AdS/CFT was discussed a lot. Could the answer have anything to do with AdS/CFT?

Perhaps others have a different opinion, but I suspect it's too early in the game to start delineating exactly what mathematical structure exists in the bulk...

The strong form of the AdS/CFT conjecture is that the CFT sums over all spacetimes which are asymptotic to $$\text{AdS}\times X$$, where $$X$$ is a sphere in the maximally supersymmetric cases...
...

I'm not aware of any spacetimes that have a bounce and are asymptotic to AdS, so I can't comment on that. There have been discussions what limit is involved trying to extend AdS/CFT to flat space (Polchinski's http://arxiv.org/abs/hep-th/9901076 is an early paper in this direction), as well as of a dS/CFT correspondence (Witten http://arxiv.org/abs/hep-th/0106109 and Strominger http://arxiv.org/abs/hep-th/0106113). More recently Strominger and collaborators have been studying holographic descriptions of black holes via CFTs, see http://arxiv.org/abs/arXiv:1009.5039 for example.

Fzero had a number of interesting points in the next post, here are excerpts with just a few:

I think the lead up to the commissioning of the LHC made pursuit of phenomenologial issues at least slightly more interesting than pursuing fundamental issues...

...The basic issue is that the fixed background in string theory is an important part of perturbation theory. Perturbation theory is valid when we the energy and density of probes is small enough that we can neglect the backreaction on the spacetime geometry. When curvatures become large, perturbation theory fails to be a good technique to describe the physics...

...Finally, I'd like to comment about linking AdS/CFT to cosmological issues. One the one hand, I don't think anyone in the field would try to base a serious model of cosmology on spacetimes that are asymptotically AdS. So there is no real reason to see inflation or bounces in AdS scenarios. However, I do think that most people would hope that there are significant lessons to be learnedi...

 

[fzero]

Well we have had some interesting and informative posts from Physicsmonkey, Fzero, and Suprised (among others). Are we any closer to answering the main question posed in post #1 of the thread?

Why the shift of interest (illustrated by research citations but not confined to that) in quantum cosmology?

AdS/CFT was discussed a lot. Could the answer have anything to do with AdS/CFT?

I think the lead up to the commissioning of the LHC made pursuit of phenomenologial issues at least slightly more interesting than pursuing fundamental issues. Part of this could be related to the corresponding increase in pheno jobs, but also due to the fact that most theorists, given the chance, would like to see their work make contact with experiment. To this end, the twistor formulation of gauge amplitudes might have had more of an influence than AdS/CFT, though application of the latter to heavy ion physics was fairly successful theme. Along the same vein, WMAP stimulated interest in cosmology that could be approached from many directions other than quantum cosmology.

You also have to understand that the deep, difficult problems have a tougher risk-reward ratio than more modest problems. A younger physicist has to select problems with an eye towards producing a record of publications. The use of citation count as a metric of quality also tends to make it safer to work on existing hot topics, since it's usually a given that someone else in the field will cite your work.

In any case, it might be a more fruitful question to ask "what are people working on instead of quantum cosmology?" or "what are the quantum cosmologists working on now?"

As for the AdS/CFT issues, other people have expounded upon the difference between classical geometry in one corner of the correspondence. I believe that a lot of the confusions are due to simplified explanations of things for a popular audience. The basic issue is that the fixed background in string theory is an important part of perturbation theory. Perturbation theory is valid when we the energy and density of probes is small enough that we can neglect the backreaction on the spacetime geometry. When curvatures become large, perturbation theory fails to be a good technique to describe the physics.

In some cases, we can regain some perturbative picture by changing the background, especially by adding nonperturbative, solitonic objects, like D-branes. This is often necessary when representing a breakdown in geometry by studying what happens at singularities of manifolds. For specific classes of singularities, we have learned that the divergence is due to new degrees of freedom, not seen in perturbation theory, becoming light as a submanifold shrinks to zero size. These new degrees of freedom are wrapped D-branes and by properly introducing them one restores the consistency of the string picture.

For other nonperturbative problems, we still don't have a complete picture of what the correct degrees of freedom are. As was also brought up, matrix theory provides a new set of degrees of freedom that exhibit both emergent geometry and emergent perturbative gravity from a quantum mechanical theory that is in many respects simple.

Finally, I'd like to comment about linking AdS/CFT to cosmological issues. One the one hand, I don't think anyone in the field would try to base a serious model of cosmology on spacetimes that are asymptotically AdS. So there is no real reason to see inflation or bounces in AdS scenarios. However, I do think that most people would hope that there are significant lessons to be learned from holography in more general cases. Since the AdS/CFT correspondence is the best example of a holographic theory, it's a place to learn, if not directly apply to those kinds of things. So the presence or absence of cosmologically relevant behavior in AdS spaces is a red herring.

 

[crackjack]

Also, to amplify Martin BN's question, can anyone speculate for us what some possible CANDIDATES might be for the mathematical structure of the bulk in the AdS/CFT picture?

In addition to the structures that http://www.stringwiki.org/wiki/Matrix_theory" .

 

[marcus]

In addition to the structures that http://www.stringwiki.org/wiki/Matrix_theory".

Thanks crackjack! This could give us a clue as to why there has been that shift in quantum cosmology that I asked about in post #1.

Suprised said something earlier about a "rich and prolific toolbox" which your list corroborates:

...Of course, rather the opposite is true. As has been known for years, and as I was emphazing here repeatedly, classical smooth manifolds are relevant only in a certain regime; let's loosely say, of measure zero in the full parameter space. In general there are non-perturbative quantum corrections to the geometry to the effect that it becomes modified to some kind of stringy geometry, which is very different from ordinary classical theory based on smooth manifolds. Many notions of classical geometry become blurred in such non-geometric phases, or even stop to make sense. Examples are topology changing transitions, disappearence of singularities, appearence of some kind of space-time foam, submanifolds of naively different dimension becoming indistinguishable (so that the notion of a submanifold stops making sense), etc etc. All this has been investigated to great detail and has improved our conceptual understanding of quantum geometry at small distances. So string theory is a very rich and prolific toolbox to address exactly this kind of questions.

I think we're slowly getting a better understanding of the transformation in quantum cosmology over the past dozen years or so. It may have to do with the prolific richness of the toolbox which Surprised told us about.

Also could have to do with what Fzero said here: "... I don't think anyone in the field would try to base a serious model of cosmology on spacetimes that are asymptotically AdS. So there is no real reason to see inflation or bounces in AdS scenario..." Roughly speaking the real universe appears to be the opposite of AdS. This may have dampened the interest of cosmologists somewhat.

There must be a number of factors and it's a slow job to sort them out and see which are the important ones.

 

[marcus]

I think the lead up to the commissioning of the LHC made pursuit of phenomenologial issues at least slightly more interesting than pursuing fundamental issues...

That sounds plausible but I have two reservations:
1. Early universe cosmology has an observational side, and quantum cosmology has some phenom potential. Don't want to bore you but I'll get some links to illustrate.

2. The timing is wrong. It looks to me as if much of the shift occurred roughly around 2002-2004 long before the "lead up to the commissioning of the LHC."

If we just repeat the Inspire searches for "top ten" quantum cosmology papers given in post #1, but for consecutive 3-year intervals, we find that string representation in the list dropped off fairly early:

Papers in the QC top ten
Years   1996-1998  1999-2001  2002-2004  2005-2007  2008-2010
String       3          3          1          2          1
Loop         0          4          7          7          8

Most of the other points you make in your post strike me as quite plausible and in part convincing, but the timing seems to be wrong for a "LHC effect".

 

[mitchell porter]

3,3,1,2,1 is not trending anywhere. 0,4,7,7,8 goes from nothing to a plateau and stays there. So I repeat that there is no decline in "string quantum cosmology" research here, there is just the rise from nothing of "loop quantum cosmology".

There is no unified "string quantum cosmology" research program. The people who created quantum cosmology - like Guth, Vilenkin, Linde, Hawking - have at times introduced the stringy version of quantum gravity into their models, but it's only a technical modification, e.g. modifying Hawking's no-boundary proposal so it contains supergravity. In my opinion, the most distinctive convergence of thought between cosmology and string theory is the way that eternal inflation allows the whole string landscape to be realized in the one universe (in different inflationary patches), and it is not at all established that this is the right way to think about cosmology in string theory.

Also in my opinion, string theory so far lacks a compelling cosmological vision. As I said, you can plug existing string models into existing cosmological models, e.g. by having something distinctively stringy (like motion of a D-brane) provide the inflaton field of the inflationary model. But it has a rather arbitrary feel. I believe eternal inflation + string landscape is the most natural fit so far proposed, but that's more because you have one great multiplicity (of inflationary domains) being paired up with another great multiplicity (of string vacua). It doesn't arise from a deep theoretical principle.

If a "dS/CFT correspondence" could be made to work, that would be big news, because it might describe the real world. But ideas about how to do string theory in de Sitter space are still preliminary at best. That might be the fundamental reason why string cosmology is still a mishmash of divergent ideas.

The role of nonclassical geometry in the bulk, in the AdS/CFT correspondence, for low numbers of QCD-like "colors" in the CFT gauge group, is a very interesting fact that this thread has turned up. I have started taking an interest in how difficult it would be to get something like the standard model from N=4 super-Yang-Mills, by projecting out particular amplitudes and by distributing D3-branes in the AdS bulk so that there are massive open string states, and of course the standard model doesn't have many colors (at least, not many compared to "infinity", which is the limit usually considered in AdS/CFT). So it's very interesting to hear that the nonclassical bulk geometry should show up for such a theory; it makes a connection to the noncommutative standard model (of Connes et al) conceivable.

 

[marcus]

Mitchell, as I think you realize, there definitely has been a shift or marked change in the makeup of the QC top ten, and it requires explanation. You have suggested here what could very possibly be the explanation, or at least one important factor:

Also in my opinion, string theory so far lacks a compelling cosmological vision. As I said, you can plug existing string models into existing cosmological models, e.g. by having something distinctively stringy (like motion of a D-brane) provide the inflaton field of the inflationary model. But it has a rather arbitrary feel. I believe eternal inflation + string landscape is the most natural fit so far proposed, but that's more because you have one great multiplicity (of inflationary domains) being paired up with another great multiplicity (of string vacua). It doesn't arise from a deep theoretical principle.
...

Recent papers making the top ten is an index of researcher interest in the recent papers, not the gross output. When I gave this a quick look a few days ago I didn't see a decline in string quantum cosmology output, the main change was the string QC papers coming on line were just not getting cited much by the research community.

Representation in top-cited papers in some category is not a linear scale, so "trend" is not quite the appropriate concept. Once you get up near 10 here there is not much room for improvement and once you get down near zero you can't go much lower. "Trend" is a linear-scale thing, so we don't look for trends with an index like this. That's why I spoke of a shift, or marked change.

3,3,1,2,1 is not trending anywhere. 0,4,7,7,8 goes from nothing to a plateau and stays there. So I repeat that there is no decline in "string quantum cosmology" research here, there is just the rise from nothing of "loop quantum cosmology".
...

What interests me, and what I meant the thread to discuss, is not a particular index or way of measuring research interest, but the physics explanation for the shift. That was made clear in the first post.

Your reasons in the "compelling cosmological vision" paragraph impress me as perceptive and cogently expressed. They have to do with physics. (They are not merely excuses having to do with social or historical accidents.)

I'm sure you know that the String program had a "cosmological vision" in the 1990s presented in many papers by Maurizio Gasperini and Gabriele Veneziano (one of the early founders who initiated the String program).Their stringy "Pre-Big-Bang" scenario attracted quite a lot of interest. So String was making a splash in quantum cosmology when it had a convincing vision.

You point out that on the one hand some string gambits "have an arbitrary feel"---and on the other hand the natural match with Multiverse ideas does not "arise from a deep physical principle".

As I read what you say, it seems to me that your hope or constructive suggestion (judging from what you say about the wish for a dS/CFT to replace AdS) would be for the program to get a quantum cosmology vision that addresses the problem of modeling the Big Bang.

I would would add one desideratum to yours. The need for the vision to be testable---it should rivet the attention of early universe phenomenologists. I promised back in post #60 that I would get some links to illustrate the EU phenomenology business, so I better do that.

 

[atyy]

marcus, does your search pick up papers like http://arxiv.org/abs/hep-th/0204168 ? Or a review like http://arxiv.org/abs/0907.2562 ?

 

[marcus]

Atyy, it's fascinating that there was that 2002 paper by Liu Moore Seiberg!

First though I should say that I'm just going with what the new Stanford-SLAC search tool ("Inspire") says.
With the search, I just put "quantum cosmology" in the keyword field and rank by citecount and go.
The main thing is to do the same search consistently year after year and look for change.
I just count how many make the top 10, there are other things. I could count how many make the top 25, or I could add up the number of cites I suppose. But it would be more bother and this is just meant to illustrate what I think must be a widely shared impression.

I will give the links so you can easily see what Inspire gives, and does not give!
This is exactly like in post #1 except I do it for all the successive 3-year intervals, not just 1996-1998

1996-1998 http://inspirebeta.net/search?ln=en...2y=1998&sf=&so=a&rm=citation&rg=10&sc=0&of=hb

1999-2001 http://inspirebeta.net/search?ln=en...2y=2001&sf=&so=a&rm=citation&rg=10&sc=0&of=hb

2002-2004 http://inspirebeta.net/search?ln=en...2y=2004&sf=&so=a&rm=citation&rg=10&sc=0&of=hb

2005-2007 http://inspirebeta.net/search?ln=en...2y=2007&sf=&so=a&rm=citation&rg=10&sc=0&of=hb

2008-2010 http://inspirebeta.net/search?ln=en...2y=2010&sf=&so=a&rm=citation&rg=10&sc=0&of=hb

Here are the Spires keywords for the Liu Moore Seiberg:
http://www.slac.stanford.edu/spires/find/hep/wwwtopics?key=4908902
I see no mention of anything quantum cosmological. I'll have to take a look at the paper: it is interesting that they have a certain kind of space perform a bounce! I don't think however that they have a quantum universe wave function perform a bounce. I'll check.

It is an interesting distinction. Often in the String program one has a fixed background geometry in which the strings can live and vibrate. The geometry is classical. I think that is what is happening here. The classical background geometry undergoes a bounce. Then the question is can some of the strings pass through the bounce point.

Here are the Inspire records for 3 papers by Liu Moore Seiberg that came out in 2002 and 2003:
http://inspirebeta.net/record/585639?ln=en
http://inspirebeta.net/record/588898?ln=en
http://inspirebeta.net/record/605720?ln=en

We'll see if any of the string folks (Supr. Fzero?) comment. I could of course be wrong, but I had a look just now and it seems to be the fixed background geometry situation usual with perturbative string theory. What is quantized is the PARTICLES not the geometry they live in. One ignores possible backreaction of the matter on the geometry.

I only glanced, but here are a couple of indicative passages. See what you think:
Page 1

In section 2 we describe the model and its geometry. In section 3 we study the functions on our spacetime which are the wave functions of the first quantized particles. In sections 4 and 5 we quantize free strings in the light-cone and conformal gauges and compute the torus partition function. Section 6 is devoted to a preliminary analysis of the interactions and backreaction. Our conclusions are presented in section 7.​

Page 23

The issue of backreaction is currently under study, and might prove to be a serious problem with future development of this example. One way backreaction could ruin the orbifold is through the coupling of gravity to the large energy momentum of particles which are blue shifted near the singularity. Indeed, we found that although the tree level...​

 

[atyy]

Another paper that the key words may not have picked up is http://arxiv.org/abs/hep-th/0506180

 

[atyy]

Here are some interesting perspectives from various reviews

http://arxiv.org/abs/gr-qc/0301001
"We now see that classical string theory is also singular in such orbifolds and cannot be trusted. ... There are at least three possibilities for the interpretation of the singularity:
1. The singularity is a beginning or end of time. In this case we need to understand the appropriate initial conditions at the singularity. For some discussion of these issues see [23,24].
2. Time has no beginning or end. Then one needs to understand how to pass through the singularity (for recent discussions see e.g. [9,25]).
3. The most likely possibility, it seems to us,is that in string theory time is a derived concept.
In conclusion, let us elaborate on the third possibility above. In toroidal compactifications of string theory there is a minimal distance, thanks to T-duality: shrinking radii past the string scale does not produce a theory at shorter distances. In more elaborate compactifications (such as Calabi-Yau compactifications) it turns out that there can be smooth topology-changing processes, and “quantum geometry” can lead to many counterintuitive types of behavior. These examples show that, in string theory, standard notions of topology and geometry are not fundamental but are rather emergent concepts in certain physical regimes (e.g. in regions of large complex and Kahler structure parameters, in the Calabi-Yau context). In another line of development, Matrix theory and the related advent of noncommutative field-theoretic limits of string theory further indicate that the notion of distance and space ceases to make sense in certain otherwise sensible regimes of the theory. Given the principle of relativity it seems quite likely, perhaps even inevitable, that similar statements hold for time as well as for space."

http://arxiv.org/abs/0705.2643
"In other words, we are led to the conclusion that space — and thus, upon quantization, also space-time — actually disappears (or ‘de-emerges’) as the singularity is approached. There is no ‘quantum bounce’ bridging the gap between an incoming collapsing and an outgoing expanding quasi-classical universe. Instead ‘life continues’ at the singularity for an infinite affine time, however, with the understanding that (i) dynamics no longer ‘takes place’ in space, and (ii) the infinite affine time interval ... corresponds to a sub-Planckian interval 0 < T < TPlanck of geometrical proper time."

http://arxiv.org/abs/1001.4367
"In principle, one would like to carry out the following program. Start with a state in the bulk theory (with modified boundary conditions) corresponding to a large, asymptotically AdS space-time with some profile for the scalar field. Translate this state, using the AdS/CFT correspondence, to a state in the dual field theory on the boundary (with a steep unbounded potential). In the dual field theory, evolve the state through the singularity using a self-adjoint extension (if a consistent and natural self-adjoint extension exists). Finally, translate the evolved state back to a state in the bulk theory, and ask whether it has a geometric interpretation. If the boundary theory described only homogeneous modes, experience with self-adjoint extensions in quantum mechanics would suggest that the final state would roughly resemble the initial state, which would suggest a cosmological bounce. Inhomogeneous modes can drastically change this picture, though: particle creation can be potentially attractive for cosmology, but one needs to make sure that backreaction is sufficiently small for the computations to be reliable."

 

[marcus]

I see you got a 2007 paper co-authored by Hermann Nicolai! Intriguing notions pursued in that one--completely unfamiliar to me. http://arxiv.org/abs/0705.2643

 

[atyy]

I see you got a 2007 paper co-authored by Hermann Nicolai! Intriguing notions pursued in that one--completely unfamiliar to me. http://arxiv.org/abs/0705.2643

A more extensive review of those ideas can be found at http://relativity.livingreviews.org/Articles/lrr-2008-1/ . I have no idea if these really are the symmetries of M-theory (my vote is with twistors and AdS/CFT at the moment;) but the work is very pretty.

Mitchell Porter in a different thread pointed out David Berman's http://arxiv.org/abs/1008.1763 which may link that work up to mainstream string theory.

A different line of speculation also starting from BKL is Carlip's http://arxiv.org/abs/1009.1136

 

[marcus]

You are finding some interesting papers! However I want to explore the reasons for the change in quantum cosmology and one potential reason could be that QC has become observational. I said earlier I would list some observational-QC papers, to indicate the scope of activity. The following papers are all 2009-2011, quite recent.

Here are two Spires searches using the keyword "power spectrum" with two other keywords (quantum cosmology, loop space and quantum gravty, loop space). It will not exhaust the field, since other tags besides "power spectrum" could be used to get more. But it will give an idea:

http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+DK+QUANTUM+gravity%2C+LOOP+SPACE+AND+DK+POWER+SPECTRUM+AND+DATE+%3E+2008&FORMAT=www&SEQUENCE=citecount%28d%29

1) Cosmological footprints of loop quantum gravity. 33 cites
J. Grain, (APC, Paris & Paris, Inst. Astrophys.) , A. Barrau, (LPSC, Grenoble & IHES, Bures-sur-Yvette) . Feb 2009. (Published Feb 27, 2009). 7pp.
Published in Phys.Rev.Lett.102:081301,2009.
e-Print: arXiv:0902.0145 [gr-qc]

2) Inverse volume corrections from loop quantum gravity and the primordial tensor power spectrum in slow-roll inflation. 13 cites
J. Grain, (APC, Paris & Paris, Inst. Astrophys.) , A. Barrau, (LPSC, Grenoble & IHES, Bures-sur-Yvette) , A. Gorecki, (LPSC, Grenoble) . Apr 2009. (Published Apr 2009). 15pp.
Published in Phys.Rev.D79:084015,2009.
e-Print: arXiv:0902.3605 [gr-qc]

3) Fully LQC-corrected propagation of gravitational waves during slow-roll inflation. 11 cites
J. Grain, (Paris, Inst. Astrophys.) , T. Cailleteau, A. Barrau, A. Gorecki, (LPSC, Grenoble) . Oct 2009. (Published Jan 15, 2010). 9pp.
Published in Phys.Rev.D81:024040,2010.
e-Print: arXiv:0910.2892 [gr-qc]

http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+DK+QUANTUM+COSMOLOGY%2C+LOOP+SPACE+AND+dk+power+spectrum+and++DATE+%3E+2008&FORMAT=www&SEQUENCE=citecount%28d%29

1) Possible observational effects of loop quantum cosmology. 20 cites
Jakub Mielczarek, (Jagiellonian U., Astron. Observ. & LPSC, Grenoble) . Aug 2009. (Published Mar 15, 2010). 11pp.
Published in Phys.Rev.D81:063503,2010.
e-Print: arXiv:0908.4329 [gr-qc]

2) ...duplication from other list...

3) Observational constraints on a power spectrum from super-inflation in Loop Quantum Cosmology. 12 cites
Masahiro Shimano, Tomohiro Harada, (Rikkyo U.) . Sep 2009. (Published Sep 15, 2009). 17pp.
Published in Phys.Rev.D80:063538,2009.
e-Print: arXiv:0909.0334 [gr-qc]

4) Tensor power spectrum with holonomy corrections in LQC. 10 cites
Jakub Mielczarek, (Jagiellonian U.) . Feb 2009. (Published Feb 2009). 13pp.
Published in Phys.Rev.D79:123520,2009.
e-Print: arXiv:0902.2490 [gr-qc]

5) Loop Quantum Cosmology corrections on gravity waves produced during primordial inflation. 8 cites
J. Grain, (Paris, Inst. Astrophys.) . Nov 2009. 9pp.
To appear in the proceedings of INVISIBLE UNIVERSE INTERNATIONAL CONFERENCE: Toward a new cosmological paradigm, Paris, France, 29 Jun - 3 Jul 2009.
Published in AIP Conf.Proc.1241:600-608,2010.
e-Print: arXiv:0911.1625 [gr-qc]

6) Inflation in loop quantum cosmology: dynamics and spectrum of gravitational waves. 8 cites
Jakub Mielczarek, (Jagiellonian U.) , Thomas Cailleteau, (LPSC, Grenoble) , Julien Grain, (Paris, Inst. Astrophys.) , Aurelien Barrau, (LPSC, Grenoble) . Mar 2010. (Published May 15, 2010). 11pp.
Published in Phys.Rev.D81:104049,2010.
e-Print: arXiv:1003.4660 [gr-qc]

7) Chaplygin inflation in loop quantum cosmology. 4 cites
Xin Zhang, (Shenyang, Northeast U. Tech.) , Jing-fei Zhang, (Shenyang, Northeast U. Tech. & Dalian U. Tech.) , Jing-lei Cui, Li Zhang, (Shenyang, Northeast U. Tech.) . Feb 2009. 6pp.
Published in Mod.Phys.Lett.A24:1763-1773,2009.
e-Print: arXiv:0902.0928 [gr-qc]

8) Observational constraints on loop quantum cosmology. 1 cite
Martin Bojowald, Gianluca Calcagni, Shinji Tsujikawa, . IGC-11-1-1, AEI-2011-004, Jan 2011. 4pp. Temporary entry
e-Print: arXiv:1101.5391 [astro-ph.CO]

After excluding the one duplication, we see that the searches yield 10 papers---primarily observational-QC and mostly written by early universe phenomenologists rather than QC folks themselves.

There are also these that using "cosmic background radiation" instread of "power spectrum" would have caught
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+DK+QUANTUM+COSMOLOGY%2C+LOOP+SPACE+AND+Dk+cosmic+background+radiation+anD+DATE+%3E+2008&FORMAT=www&SEQUENCE=citecount%28d%29

1) ...duplicate...
2) ...duplicate...

3) Constraints on standard and non-standard early Universe models from CMB B-mode polarization. 4 cites
Yin-Zhe Ma, (Cambridge U., KICC & Cambridge U., Inst. of Astron.) , Wen Zhao, (Cardiff U.) , Michael L. Brown, (Cambridge U., KICC & Cambridge U., Inst. of Astron. & Cambridge U.) . Jul 2010. 41pp.
Published in JCAP 1010:007,2010.
e-Print: arXiv:1007.2396 [astro-ph.CO]

4) Observational hints on the Big Bounce. 3 cites
Jakub Mielczarek, (Jagiellonian U., Astron. Observ.) , Michal Kamionka, (Wroclaw U., Astro. Inst.) , Aleksandra Kurek, (Jagiellonian U., Astron. Observ.) , Marek Szydlowski, (Jagiellonian U., Astron. Observ. & Jagiellonian U.) . May 2010. 24pp.
Published in JCAP 1007:004,2010.
e-Print: arXiv:1005.0814 [gr-qc]

5) Observing the Big Bounce with Tensor Modes in the Cosmic Microwave Background: Phenomenology and Fundamental LQC Parameters. 2 cites
Julien Grain, (Paris, Inst. Astrophys. & Orsay, LAL) , Aurelien Barrau, Thomas Cailleteau, (LPSC, Grenoble) , Jakub Mielczarek, (Jagiellonian U.) . Nov 2010. (Published Dec 15, 2010). 12pp.
Published in Phys.Rev.D82:123520,2010.
e-Print: arXiv:1011.1811 [astro-ph.CO]

So that makes a total of 13 in all.

 

[marcus]

Here's a proposed list of quantum cosmology criteria

The bulk should have some definite mathematical structure that represents it.
Asymptotically it should look deSitter (accelerated expansion) or at least not the opposite (which is AdS, accelerated contraction).
There should be a quantum state of bulk geometry which exhibits a bounce.
The bounce should either lead to adequate inflation or, if not, the model should produce the usual effects expected from inflation in some other way.
The model should be testable and attract the attention of phenomenologists so they can study means of testing it.