What is the recent development of Loop Quantum Gravity

[tom.stoer]

I agree that in the end a symmetry reduction in LQG is not what you really want, but perhaps it's easier to motivate LQC by some clever trick than to derive a bounce in full LQG. If this is the case than the symmetry reduction in LQG can at least provide some hint that the bounce in LQC is reasonable.

A simple example why I think this is important: in QED applied to a hollow sphere you find a casimir force. In QM with a finite number of degrees of freedom no similar effect is known..

 

[marcus]

Recently, I am very interested in Loop Quantum Gravity. But I hope I can know more about the recent development of Loop Quantum Gravity. I mean the development from 2000 to 2011. Any conceptual or practical or technical development in this realm?
...

This is a good sort of question to be asking. What are some significant recent developments? I would not go back so far in history as Karmerlo does. I would focus on 2008-2011---just the past 3 or 4 years. So much has happened!

It may be that Karmerlo found out everything necessary and went away, but other people could be wondering about recent developments and have similar questions. So probably we should try to give at least some partial answers.

I'll try to list some significant advances, particularly in the past two years. Other people may want to suggest other things to put the spotlight on, that I miss.

It's important to see the recent advances as opening up new questions and new areas for researchers to investigate.

LQG is in an exciting phase of rapid growth---the best papers now do not provide final solutions so much as they reveal new thesis problems for PhD students to work on. They open up more questions than they resolve. They stir up more issues than they settle Anyway, that is my impression.

The recent growth in the number of people working in LQG, and the numbers of papers published, seems to support this impression. Objectively speaking the level of activity is several times what it was some 5 years ago. So it's more than just a subjective impression.

Let's try to think of some significant developments. Especially those that open up fresh problems for a new entrant PhD student or postdoc to work on.

 

[marcus]

http://arxiv.org/abs/1005.0817
A regularization of the hamiltonian constraint compatible with the spinfoam dynamics
Emanuele Alesci, Carlo Rovelli
(Submitted on 5 May 2010)
We introduce a new regularization for Thiemann's Hamiltonian constraint. The resulting constraint can generate the 1-4 Pachner moves and is therefore more compatible with the dynamics defined by the spinfoam formalism. We calculate its matrix elements and observe the appearence of the 15j Wigner symbol in these.
24 pages

http://arxiv.org/abs/1110.6150
Regularized Hamiltonians and Spinfoams
Emanuele Alesci
(Submitted on 27 Oct 2011)
We review a recent proposal for the regularization of the scalar constraint of General Relativity in the context of LQG. The resulting constraint presents strengths and weaknesses compared to Thiemann's prescription. The main improvement is that it can generate the 1-4 Pachner moves and its matrix elements contain 15j Wigner symbols, it is therefore compatible with the spinfoam formalism: the drawback is that Thiemann anomaly free proof is spoiled because the nodes that the constraint creates have volume.
4 pages, based on a talk given at Loops '11 in Madrid, to appear in Journal of Physics: Conference Series (JPCS)

A possible breakthough. IMHO. The previous hamiltonian has been unsatisfactory for a number of reasons, one being that it did not have a way for space to increase in volume. The nodes it created were only trivalent, could not have volume, and so were not very interesting.

========================

So that is one significant development that happened just in the past couple of years---in response to Karmerlo's question. At last we have a proposed hamiltonian that looks amenable to showing a connection between canonical (i.e. hamiltonian) approach and spinfoam dynamics. This means work for people to do, elaborating and studying the new hamiltonian LQG, and investigating its relation to spinfoam LQG. Might even be equivalent.

 

[marcus]

quote from the "New Hamiltonian" paper of May 2010. It gives an idea of the potential importance of this recent development:

==quote 1005.0817==
...More precisely, instead of writing the curvature as a limit of the holonomy of the connection around a closed loop, we write it as a limit of the spin-network function of the connection, associated to a tetrahedral graph.
The consequences of this alternative regularization are multifold.

• First, the regularized operator appears to be more natural and more symmetric, especially when acting on four-valent nodes, where it admits a natural simplicial interpretation. In particular, the curvature is evaluated on a plane which appears to be natural from a geometric point of view.
  
• Second, and more importantly, when acting on a node the resulting quantum operator generates three new nodes, rather than two, as the old Hamiltonian operator. Therefore the constraint implements the 1-4 Pachner move [2], which is characteristic of the spinfoam dynamics.
  
• Third, the resulting operator creates 4-valent nodes, rather than 3-valent ones, as the old Hamiltonian operator. Since 3-valents nodes have zero volume, the new operator can create nodes with volume.
  
• Finally, when we compute matrix elements of this operator, we find 15j Wigner symbols, as well as fusion coefficients [7, 12], namely the basic building blocks of the spinfoam dynamics.

==endquote==

Alesci is now postdoc in Thiemann's group at Erlangen, so we will see what develops from this.

 

[marcus]

Alesci and Rovelli's papers offer the prospect of a better hamiltonian than has existed in LQG up to now. And clear signs that a connection with properly defined Spinfoam LQG transition amplitudes can be found.

On the other hand there is another quite recent development reported by Jon Engle (physics faculty at Florida Atlantic U.) which offers the possibility of a better spinfoam vertex formula. The spinfoam vertex formula is the key ingredient to calculating transition amplitudes. So this paper is another possible game-changer.

http://arxiv.org/abs/1111.2865
A proposed proper EPRL vertex amplitude
Jonathan Engle
(Submitted on 11 Nov 2011)
As established in a prior work of the author, the linear simplicity constraints used in the construction of the so-called 'new' spin-foam models mix three of the five sectors of Plebanski theory, only one of which is gravity in the usual sense, and this is the reason for certain 'unwanted' terms in the asymptotics of the EPRL vertex amplitude as calculated by Barrett et al.
In the present paper, an explicit classical discrete condition is derived that isolates the desired gravitational sector, which we call (II+), following other authors. This condition is quantized and used to modify the vertex amplitude, yielding what we call the 'proper EPRL vertex amplitude.' This vertex still depends only on standard SU(2) spin-network data on the boundary, is SU(2) gauge invariant, and is linear in the boundary state, as required. In addition, the asymptotics now consist in the single desired term of the form e^iS_Regge, and all degenerate configurations are exponentially suppressed.
25 pages

As Jon Engle explains in the conclusion paragraph, his new vertex amplitude might not be needed if another solution being tried by other people turns out to work, but that is something we can't know in advance, or I can't anyway. And Engle's vertex amplitude needs more work to extend it to a broader range of cases---to remove simplifying assumptions---the usual thing with new mathematical developments.

These are things I'd offer someone like Karmerlo who is considering PhD research in Loop and wants to know about recent developments in the field.

I'd say to read Rovelli's Zakopane tutorial survey 1102.3660. Check out the forthcoming special issue of the free e-journal SIGMA which is devoted to LQG/LQC. It will have many recent articles of which some have already been posted on arxiv. I don't know how it will turn out but it might be interesting.
And if he/she is looking for research topics, here are these new papers by Alesci and by Engle on possibly improved hamiltonian and spinfoam amplitude.

The proposed improvements involve the two main forms of LQG dynamics---there is plenty of research to be done examining extending and exploring their equivalence.

BTW here are links to SIGMA journal and the Loop gravity/cosmology special issue that is being assembled.
http://www.emis.de/journals/SIGMA/about.html
http://www.emis.de/journals/SIGMA/special_issues.html
http://www.emis.de/journals/SIGMA/LQGC.html

LOOP RESEARCH BY YEAR (loop quantum gravity, loop quantum cosmology, spin foam)
2005 http://inspirebeta.net/search?ln=en...2y=2005&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (42 found)
2006 http://inspirebeta.net/search?ln=en...2y=2006&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (77 found)
2007 http://inspirebeta.net/search?ln=en...2y=2007&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (120 found)
2008 http://inspirebeta.net/search?ln=en...2y=2008&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (142 found)
2009 http://inspirebeta.net/search?ln=en...2y=2009&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (145 found)
2010 http://inspirebeta.net/search?ln=en...2y=2010&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (152 found)
2011 http://inspirebeta.net/search?ln=en...2y=2011&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (180 found)

 

[tom.stoer]

The Alesci & Rovelli Hamiltonian is a big step forward.

 

[marcus]

Philipp Höhn mentions the Alesci-Rovelli hamiltonian* in the talk he gave yesterday (29 November) at the ILQGS
http://relativity.phys.lsu.edu/ilqgs/
Höhn's talk was on his effort to develop a causal dynamical triangulations hamiltonian
with Bianca Dittrich. No, that's wrong. He calls it "SIMPLICIAL GRAVITY" rather than CDT. It isn't really CDT but it is strongly reminiscent. Whatever Dittrich gets involved with tends to be interesting.

Here are the slides:
http://relativity.phys.lsu.edu/ilqgs/hoehn112911.pdf

It's probably a significant development in a close neighbor of LQG, which could be a stimulus to the Loop people. The title of the talk is:
A canonical formalism for simplicial gravity

*reference in the "outlook" slide #32 at the end.

 

[marcus]

Alesci and Rovelli's papers offer the prospect of a better hamiltonian than has existed in LQG up to now. And clear signs that a connection with properly defined Spinfoam LQG transition amplitudes can be found.

On the other hand there is another quite recent development reported by Jon Engle (physics faculty at Florida Atlantic U.) which offers the possibility of a better spinfoam vertex formula. The spinfoam vertex formula is the key ingredient to calculating transition amplitudes. So this paper is another possible game-changer.

http://arxiv.org/abs/1111.2865
A proposed proper EPRL vertex amplitude
Jonathan Engle
(Submitted on 11 Nov 2011)
...

The Alesci & Rovelli Hamiltonian is a big step forward.

I certainly agree about the Alesci-Rovelli Hamiltonian. Can't be quite as sure about Jon Engle's new spinfoam formula, but if anyone is interested in hearing his seminar talk about it, here's a link
SLIDES: http://relativity.phys.lsu.edu/ilqgs/engle111511.pdf
AUDIO: http://relativity.phys.lsu.edu/ilqgs/engle111511.wav
There are technical problems with the first 2 minutes 45 seconds of the audio. You can skip to minute 2:45 without missing anything.
For more info google "ILQGS" for international loop QG seminar.
==================================

Very interesting new paper re the Hamiltonian approach:

http://arxiv.org/abs/1111.7195
Spontaneously broken Lorentz symmetry for Hamiltonian gravity
Steffen Gielen, Derek K. Wise
(Submitted on 30 Nov 2011)
In Ashtekar's Hamiltonian formulation of general relativity, and in loop quantum gravity, Lorentz covariance is a subtle issue that has been strongly debated. Maintaining manifest Lorentz covariance seems to require introducing either complex-valued fields or second class constraints, and either option presents a significant obstacle to quantization. After reviewing the sources of difficulty, we present a Lorentz covariant, real formulation free of second class constraints. Rather than a foliation of spacetime, we use a gauge field y, interpreted as a field of observers, to break the SO(3,1) symmetry down to a subgroup SO(3)_y. This symmetry breaking plays a role analogous to that in MacDowell-Mansouri gravity, which is based on Cartan geometry, leading us to a picture of gravity as 'Cartan geometrodynamics.' We study both Lorentz gauge transformations and transformations of the observer field to show that the apparent breaking of SO(3,1) to SO(3) is not in conflict with Lorentz covariance.
10 pages

 

[tom.stoer]

Very interesting new paper re the Hamiltonian approach:

http://arxiv.org/abs/1111.7195
Spontaneously broken Lorentz symmetry for Hamiltonian gravity
Steffen Gielen, Derek K. Wise

Interesting!

It seems that the criticism expressed by Nicolao, Alexandrov and others is taken seriously. There is a handful of papers appeared over the last couple of weeks adressing spacetime foliation, gauge fixing / no gauge fixing, breaking diff.-inv., hamiltonian analysis and constraint algebra, 1st vs. 2nd-class constraints, discretization and singular geometry, re-deriving Ashtekar-Barbero formulation in several different ways, SU(2) vs. SO(3,1) vs SL(2,C) etc. (I guess marcus has a rather exhaustive list)

The new papers shed some light on problems already present in the classical symplectic structure (especially foliation, gauge fixing and constraint algebra). Rovelli's new Hamiltonian may be a hint how to proceed with the genuine quantum issues (regularization, operator topology and convergence, operator algebra and anomalies, renormalization). There is an increasing number of indications that the canonical LQG formulation may be on the right track - although we understand afterwards why some well-known 'drivations' can be justified.

So the general situation may be not as bad as I expressed it a couple of weeks ago.

 

[nates]

without starting a new thread, is LQG and ST/M Theory still the front runners these days? has one moved past the other?

 

[marcus]

without starting a new thread, is LQG and ST/M Theory still the front runners these days? has one moved past the other?

That's a research trends statistics question. Changing research fashions, job demographics, citation standings etc have only indirect bearing on the ultimate validity of math models. But they can give at least a partial picture. Here for example:
Loop and String research trends as of 6 December:
http://howlonguntil.net/ 339/365 of year elapsed

LOOP RESEARCH BY YEAR (loop quantum gravity, loop quantum cosmology, spin foam)
2005 http://inspirebeta.net/search?ln=en...2y=2005&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (42 found)
2006 http://inspirebeta.net/search?ln=en...2y=2006&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (77 found)
2007 http://inspirebeta.net/search?ln=en...2y=2007&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (120 found)
2008 http://inspirebeta.net/search?ln=en...2y=2008&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (142 found)
2009 http://inspirebeta.net/search?ln=en...2y=2009&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (145 found)
2010 http://inspirebeta.net/search?ln=en...2y=2010&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (152 found)
2011 http://inspirebeta.net/search?ln=en...2y=2011&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (201 annualized from 187 found)

STRING,MEMBRANE,AdS/CFT RESEARCH BY YEAR
(search terms "string model", "membrane model" and "AdS/CFT correspondence")
2005 http://inspirebeta.net/search?ln=en...2y=2005&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (988 found)
2006 http://inspirebeta.net/search?ln=en...2y=2006&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1029 found)
2007 http://inspirebeta.net/search?ln=en...2y=2007&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1050 found)
2008 http://inspirebeta.net/search?ln=en...2y=2008&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1128 found)
2009 http://inspirebeta.net/search?ln=en...2y=2009&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1132 found)
2010 http://inspirebeta.net/search?ln=en...2y=2010&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1046 found)
2011 http://inspirebeta.net/search?ln=en...2y=2011&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (946 annualized from 879 found)
========

You probably see how the annualized figure is gotten. 339/365 of the year has elapsed and so far 187 research papers were posted, so if that rate continues for the rest of the year one would have 187*365/339 = 201 papers.

The searches are imperfect, so the absolute numbers probably matter less than whatever change or non-change one sees by repeating the same identical search for each consecutive year.

People's subjective judgments differ as to the ultimate prospects of different lines of research leading to testable predictions of new phenomena, and ultimately to a successful new vision of nature, explaining the big bang etc.

It ordinarily doesn't mean much just to hear people make authoritative-sounding pronouncements about what they think "most physicists" think. You can listen to a certain amount of that but I also believe in watching actual behavior. Departments are hiring fewer string theorists these days (than say 5 years ago) and there is a noticeable shift of people out of research on stringy unification into other areas---some into areas with no clear connection to string at all.
===============

I think it's important to realize that string research and LQG are not rivals in any direct sense. They are very different paths to the physics of the future. And they are far from the only paths being explored!

LQG research traditionally aims to re-envision geometry, to successfully demonstrate a quantum theory of spacetime geometry, and then to invite the matter fields to come and live in that new version of space and time.

It is far less concerned with explaining the matter fields of the current standard model---as if thinking "first let's get the world's uncertain changing geometry right."

By contrast, the String program has traditionally been concerned with matter defined on some fixed geometry. You could say that in some respects it is far more ambitious, because of its wider scope, but also in another respect less ambitious (in the quantum geometry department.)

So it's apples and oranges. There is no clear set rivalry to achieve a unique goal. And there are also important bananas. Other paths being pursued towards the physics of the future.

Loop is one of several programs going after several different goals. It's an interesting one to watch. And the whole scene is interesting, partly because it is so indefinite and unpredictable.
==================================
I've thought of another way to answer your question
Here is a long beautifully written paper by Richard Woodard (a particle theorist who studied under Sidney Coleman at Harvard)
http://arxiv.org/abs/0907.4238
It explains the whole complicated situation discussing SEVERAL approaches in what I think is a calm unbiased way and explaining just why the problems are difficult and what has caused the different programs to veer off in various directions.
It is 105 pages, but it is written in a helpful pedagogical style, so beginners can get something from it even if they just skip around and grab a section or two here and there. If you just understand 20 pages you will have gotten something worthwhile out of it.

He is not betting on this or that pet project. He is trying to help you understand the whole complex enterprise and the obstacles that Nature has set up for us. I'd like to meet the guy. It doesn't get any better, in my opinion. And I say this understanding probably less than half.

Of course it's out of date. 2009. Quite a lot has happened since. That's the breaks. It's like surveying an expanding universe---you can't.

 

[marcus]

Still another approach to answering your question, Nate.

Look at this very recent top-level workshop that brought together leading people from a number of different research programs (string, early universe cosmo, LQG, asym safe QG, causal triangulations QG, group field theory, simplicial QG...)

http://www.physics.ntua.gr/cosmo11/Naxos2011/sci_prog.html

Many speakers' slides PDF files are accessible online.
The workshop was held in September 2011. Richard Woodard's talks were on Friday and Saturday 16 and 17 Sept.

The island of Naxos in the Aegean. The organizers gathered the best people from all the fields of research that they thought could have something to say about quantum gravity and quantum cosmology. It's the right thing to do. A synthesis will emerge that we cannot envision ahead of time.

 

[nates]

as always, you couldn't be more helpful, marcus.

thanks!

 

[marcus]

...
Very interesting new paper re the Hamiltonian approach:

http://arxiv.org/abs/1111.7195
Spontaneously broken Lorentz symmetry for Hamiltonian gravity
Steffen Gielen, Derek K. Wise
(Submitted on 30 Nov 2011)

Interesting!

It seems that the criticism expressed by Nicolao, Alexandrov and others is taken seriously. There is a handful of papers appeared over the last couple of weeks adressing spacetime foliation, gauge fixing / no gauge fixing, breaking diff.-inv., hamiltonian analysis and constraint algebra, 1st vs. 2nd-class constraints, discretization and singular geometry, re-deriving Ashtekar-Barbero formulation in several different ways, SU(2) vs. SO(3,1) vs SL(2,C) etc. ...

The new papers shed some light on problems already present in the classical symplectic structure (especially foliation, gauge fixing and constraint algebra). Rovelli's new Hamiltonian may be a hint how to proceed with the genuine quantum issues (regularization, operator topology and convergence, operator algebra and anomalies, renormalization). There is an increasing number of indications that the canonical LQG formulation may be on the right track - although we understand afterwards why some well-known 'drivations' can be justified.

So the general situation may be not as bad as I expressed it a couple of weeks ago.

Continuing this discussion, a couple of papers appeared yesterday which brought problems with EPRL into sharper focus and suggested a possible improvement to the spin foam vertex amplitude.

Noui and Geiller are exploring (in 3d toy version) some idea they have for additional constraints.

http://arxiv.org/abs/1112.1965
Testing the imposition of the Spin Foam Simplicity Constraints
Marc Geiller, Karim Noui
(Submitted on 8 Dec 2011)
We introduce a three-dimensional Plebanski action for the gauge group SO(4). In this model, the B field satisfies quadratic simplicity constraints similar to that of the four-dimensional Plebanski theory, but with the difference that the B field is now a one-form. We exhibit a natural notion of "simple one-form", and identify a gravitational sector, a topological sector and a degenerate sector in the space of solutions to the simplicity constraints. Classically, in the gravitational sector, the action is shown to be equivalent to that of three-dimensional first order Riemannian gravity. This enables us to perform the complete spin foam quantization of the theory once the simplicity constraints are solved at the classical level, and to compare this result with the various models that have been proposed for the implementation of the constraints after quantization. In particular, we impose the simplicity constraints following the prescriptions of the so-called BC and EPRL models. We observe that the BC prescription cannot lead to the proper vertex amplitude. The EPRL prescription allows to recover the expected result when, in this three-dimensional model, it is supplemented with additional secondary second class constraints.
30 pages. 18 figures

Marc Geiller is at Paris 7 (Univ of Paris "Diderot" campus) and it looks like Noui is joining him there. Noui is a former coauthor with Alejandro Perez, one of the Marseille group, who is mentioned in the acknowledgments. Geiller and Noui have another paper just posted coauthored with Sergei Alexandrov, to be included in the special LQG issue of SIGMA.

http://arxiv.org/abs/1112.1961
Spin Foams and Canonical Quantization
Sergei Alexandrov, Marc Geiller, Karim Noui
(Submitted on 8 Dec 2011)
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev-Viro spin foam model, and how the Ponzano-Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the four-dimensional case, we recall a Lorentz-covariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possesses in order to be consistent with the canonical quantization, and suggest a new model illustrating these results.
88 pages. Invited review for SIGMA Special Issue "Loop Quantum Gravity and Cosmology"

 

[marcus]

without starting a new thread, is LQG and ST/M Theory still the front runners these days? has one moved past the other?

Part of understanding the situation and status of the LQG program is to keep in mind what other active approaches to QG there are and it's not just front runners (although they are important!) I tried to list them a few days ago in a different context https://www.physicsforums.com/showpost.php?p=3673983&postcount=9 but the list might be useful here. Not a complete list, just those that immediately came to mind:

Asymptotic Safe QG is one possibility. (Steven Weinberg's idea now much expanded by Reuter Percacci and friends)

Triangulations QG is another (see Renate Loll's SciAm I told you about, link in my sig)

Simplicial QG approach (a team of young researchers led by Bianca Dittrich)

A new thing called Shape Dynamics (see papers by Gomes and Koslowski)

There are several approaches to gravity inspired by condensed matter physics (see e.g. X.G. Wen's papers, and a recent one by Liberati Finazzi Sidoni).

Group Field Theory (Oriti and co-workers)

The quantization of Cartan's GR (new papers by Derek Wise and Steffen Gielen)

Erik Verlinde's entropic gravity (2009 not so much lately)

Petr Horava's anisotropic gravity (2009 not so much lately)

Verlinde and Horava were formerly prominent string theorists. Their alternative non-string QG approaches got a lot of attention a couple of years ago but not so much now.

Maybe its fair to say there could be many ways up the mountain and several separate parties of climbers seem to be making progress towards the summit.

 

[Harv]

Part of understanding the situation and status of the LQG program is to keep in mind what other active approaches to QG there are

But for many reasons, the leading program by far is still string theory.

 

[suprised]

But for many reasons, the leading program by far is still string theory.

True. For some reasons, the most successful program that decribes quantum gravity (though certainly not all aspects of it) is routinely left out here in this list. It's quite ironic that one needs to translate "quantum gravity" as commonly used here, as "attempts at quantum gravity other than string theory".

 

[marcus]

Just as a reminder the topic of the thread is recent developments in LQG. But people regularly want to know about the QG alternatives to String and Loop.

... what are the other possibilities beside it [LQG] and String Theory? ...

And I think it's helpful to call attention to some other smaller lines of QG research that are NOT the two front runners. Otherwise people can get the impression that the two that everyone has heard of are all there are or all that matters. I posted this impromptu list of non-string and non-loop approaches here in reaction to Nate's post.

without starting a new thread, is LQG and ST/M Theory still the front runners these days?

 

[marcus]

without starting a new thread, is LQG and ST/M Theory still the front runners these days? has one moved past the other?

I'll update my earlier response with stats as of today 24 December.

That's a research trends statistics question. Changing research fashions, job demographics, citation standings etc have only indirect bearing on the ultimate validity of math models.

==updated quote==
But they can give at least a partial picture. Here for example:
Loop and String research trends as of 24 December:
http://howlonguntil.net/ 358/365 of year elapsed
==update of earlier post==
LOOP RESEARCH BY YEAR (loop quantum gravity, loop quantum cosmology, spin foam)
2005 http://inspirebeta.net/search?ln=en...2y=2005&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (42 found)
2006 http://inspirebeta.net/search?ln=en...2y=2006&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (77 found)
2007 http://inspirebeta.net/search?ln=en...2y=2007&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (120 found)
2008 http://inspirebeta.net/search?ln=en...2y=2008&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (142 found)
2009 http://inspirebeta.net/search?ln=en...2y=2009&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (145 found)
2010 http://inspirebeta.net/search?ln=en...2y=2010&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (152 found)
2011 http://inspirebeta.net/search?ln=en...2y=2011&sf=&so=a&rm=citation&rg=25&sc=0&of=hb (203 found to date = annualized 207)

STRING,MEMBRANE,AdS/CFT RESEARCH BY YEAR
(search terms "string model", "membrane model" and "AdS/CFT correspondence")
2005 http://inspirebeta.net/search?ln=en...2y=2005&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (988 found)
2006 http://inspirebeta.net/search?ln=en...2y=2006&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1029 found)
2007 http://inspirebeta.net/search?ln=en...2y=2007&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1050 found)
2008 http://inspirebeta.net/search?ln=en...2y=2008&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1128 found)
2009 http://inspirebeta.net/search?ln=en...2y=2009&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1132 found)
2010 http://inspirebeta.net/search?ln=en...2y=2010&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (1046 found)
2011 http://inspirebeta.net/search?ln=en...2y=2011&sf=&so=a&rm=citation&rg=10&sc=0&of=hb (912 found to date = annualized 930)

The searches are imperfect, so the absolute numbers probably matter less than whatever change or non-change one sees by repeating the same identical search for each consecutive year.
==endquote==

People's subjective judgments differ as to the ultimate prospects of different lines of research leading to testable predictions of new phenomena, and ultimately to a successful new vision of nature, explaining the big bang etc.

It ordinarily doesn't mean much just to hear people make authoritative-sounding pronouncements about what they think "most physicists" think. You can listen to a certain amount of that but I also believe in watching actual behavior. Departments are hiring fewer string theorists these days (than say 5 years ago) and there is a noticeable shift of people out of research on stringy unification into other areas---some into areas with no clear connection to string at all.
===============

I think it's important to realize that string research and LQG are not rivals in any direct sense. They are very different paths to the physics of the future. And they are far from the only paths being explored!

LQG research traditionally aims to re-envision geometry, to successfully demonstrate a quantum theory of spacetime geometry, and then to invite the matter fields to come and live in that new version of space and time.

It is far less concerned with explaining the matter fields of the current standard model---as if thinking "first let's get the world's uncertain changing geometry right."

By contrast, the String program has traditionally been concerned with matter defined on some fixed geometry. You could say that in some respects it is far more ambitious, because of its wider scope, but also in another respect less ambitious (in the quantum geometry department.)

So it's apples and oranges. There is no clear set rivalry to achieve a unique goal. And there are also important bananas. Other paths being pursued towards the physics of the future.

Loop is one of several programs going after several different goals. It's an interesting one to watch. And the whole scene is interesting, partly because it is so indefinite and unpredictable.

 

[marcus]

We could bring this thread up to date on recent developments.
Today I noted something really strange in Ashtekar Pawlowski paper on Lqc with Λ>0.

It makes me think of the Cai Easson picture where inflation is driven by a brief epoch of huge cosmological constant, so you don't need a "graviton", and a "curvaton" field supplies the fluctuations in the CMB.

What Ashtekar Pawlowski get is a PLANCK SCALE LIMIT ON THE SIZE OF LAMBDA.
So if it is running up as you go back in time (as the energy scale k is increasing) there is a limit to how big it can get.

I'll get the link
http://arxiv.org/abs/1112.0360
Positive cosmological constant in loop quantum cosmology
Tomasz Pawlowski, Abhay Ashtekar
(Submitted on 1 Dec 2011)
The k=0 Friedmann Lemaitre Robertson Walker model with a positive cosmological constant and a massless scalar field is analyzed in detail. If one uses the scalar field as relational time, new features arise already in the Hamiltonian framework of classical general relativity: In a finite interval of relational time, the universe expands out to infinite proper time and zero matter density. In the deparameterized quantum theory, the true Hamiltonian now fails to be essentially self-adjoint both in the Wheeler DeWitt (WDW) approach and in LQC. Irrespective of the choice of the self-adjoint extension, the big bang singularity persists in the WDW theory while it is resolved and replaced by a big bounce in loop quantum cosmology (LQC). Furthermore, the quantum evolution is...
36 pages

Look on page 20, right after equation (4.9):
==quote Ashtekar Pawlowsk page 20i==
However, because this Θ_Λ is negative, the physical Hilbert space is now zero dimensional! (For proofs, see [18].) Thus, in striking contrast to the WDW theory, in LQC a non-trivial quantum theory exists only when the cosmological constant Λ is less than a critical value, Λ_c. Although this result is not phenomenologically relevant because Λ_c is of Planck scale, it is of considerable conceptual interest. In the rest of this section, then, we will with work Λ < Λ_c.
==endquote==

To connect that to the Cai Easson picture:
Think of k as momentum or wavenumber or as inverse length. Then k² is inverse area.
The cosmological constant Λ is also curvature quantity, an inverse area. So the dimensionless couping number which presumably runs to safety is λ = Λ/k². This is what goes to a finite limit as k→∞. The only way this can happen is if the dimensionful cosmo constant Λ becomes huge as k increases.
But Ashtekar and Pawlowski find that it can only get so large.
Nice to have a mathematical handle---a grip on the cosmological constant.

In the Loop bounce the Hubble expansion rate parameter, an inverse time, reaches Planck scale in a natural period of inflation that does not require assuming an "inflaton" field. this is even without a positive cosmo constant. The Hubble parameter reaches approximately Planck frequency, as I recall.

 

[marcus]

I think the Ashtekar Pawlowski and the Cai Easson papers offer a remote chance of linking LQC and AS cosmologies, with a running cosmological constant driving inflation.
Here is some bibliography on the Cai Easson paper, to have for convenient reference if anyone is interested:

http://arxiv.org/abs/1202.1285
Higgs Boson in RG running Inflationary Cosmology
Yi-Fu Cai, Damien A. Easson
(Submitted on 6 Feb 2012)
An intriguing hypothesis is that gravity may be non-perturbatively renormalizable via the notion of asymptotic safety. We show that the Higgs sector of the SM minimally coupled to asymptotically safe gravity can generate the observed near scale-invariant spectrum of the Cosmic Microwave Background through the curvaton mechanism. The resulting primordial power spectrum places an upper bound on the Higgs mass, which for canonical values of the curvaton parameters, is compatible with the recently released Large Hadron Collider data.
5 pages

==Cai Easson page 1==
...In this paper, we propose that the Higgs boson may play an important role in the early inflationary universe if the gravitational theory is asymptotically safe. In the frame of AS gravity, the gravitational constant G and cos- mological constant Λ are running along with the energy scale, and thus vary throughout the cosmological evolution. It has been argued that if there are no intermediate energy scales between the SM and AS scales, the mass of the Higgs boson is predicted to be m_H = 126 GeV with only several GeV uncertainty [14]. We find a suitable inflationary solution can be obtained in a cosmological system which contains a Higgs boson and AS gravity, along the lines of [15]. In this model, there are effectively two scalar degrees of freedom, one being the adiabatic mode and the other being an iso-curvature mode. We find the corresponding perturbation theory leads to both the primordial power spectrum for the curvature perturbation and the entropy perturbation. When the cutoff scale runs lower than a critical value, inflation abruptly ends and the Higgs field can give rise to a reheating phase. During this phase, the fluctuations seeded by the Higgs field can be converted into the curvature perturbation through the curvaton mechanism [16, 17]. We derive a relation between the spectral index of the primordial power spectrum and the Higgs mass. We confront this relation with the latest cosmological observations and collider experiment data, and find they are consistent under a group of canonical values of curvaton parameters.
==endquote==
Cai Easson references:
[14] M. Shaposhnikov and C. Wetterich, Phys. Lett. B 683, 196 (2010) http://arxiv.org/abs/0912.0208
[15] Y. -F. Cai and D. A. Easson, Phys. Rev. D 84, 103502 (2011)
http://arxiv.org/pdf/1107.5815.pdf (warning: involves Jordan-Brans-Dicke variant of GR.)
[16]D. H. Lyth and D. Wands, Phys. Lett. B 524, 5 (2002)
http://arxiv.org/abs/hep-ph/0110002
Generating the curvature perturbation without an inflaton
David H. Lyth, David Wands
(Submitted on 28 Sep 2001)
We present a mechanism for the origin of the large-scale curvature perturbation in our Universe by the late decay of a massive scalar field, the curvaton. The curvaton is light during a period of cosmological inflation, when it acquires a perturbation with an almost scale-invariant spectrum. This corresponds initially to an isocurvature density perturbation, which generates the curvature perturbation after inflation when the curvaton density becomes a significant fraction of the total. The isocurvature density perturbation disappears if the curvaton completely decays into thermalised radiation...
8 pages.

 

[marcus]

I'll try to assemble a select bunch of links I think relevant to current directions in LQG research
Google "alesci rovelli hamiltonian arxiv" and get http://arxiv.org/abs/1005.0817 [second hit]

Google "ashtekar introduction 2012" and get http://arxiv.org/pdf/1201.4598.pdf [review]

Google "rovelli zakopane" and get http://arxiv.org/abs/1102.3660 [tutorial, research problems]

Google "pawlowski positive cosmological arxiv" and get http://arxiv.org/abs/1112.0360 [loop with lambda > 0]

Google "freidel geiller ziprick" and get http://arxiv.org/abs/1110.4833 [loop classical gravity]

Google "jonathan ziprick pirsa" and get http://pirsa.org/12020096 [loop classical gravity video]

Google "freidel speziale BF" and get http://arxiv.org/abs/1201.4247 [ways to get GR from BF]

Google "hossenfelder emission spectra" and get http://arxiv.org/abs/1202.0412 [curious dark matter conjecture, idea for QG test]

Google "wise symmetry gravity" and get http://arxiv.org/abs/1112.2390 [different approach to hamiltonian]

 

[marcus]

Latest on the classical/semiclassical limit that I'm aware of. There may be more recent.
http://arxiv.org/abs/1108.2258
Emergence of gravity from spinfoams
Elena Magliaro, Claudio Perini
(Submitted on 10 Aug 2011)
We find a nontrivial regime of spinfoam quantum gravity that reproduces classical Einstein equations. This is the double scaling limit of small Immirzi parameter (gamma), large spins (j) with physical area (gamma times j) constant. In addition to quantum corrections in the Planck constant, we find new corrections in the Immirzi parameter due to the quantum discreteness of spacetime. The result is a strong evidence that the spinfoam covariant quantization of general relativity possesses the correct classical limit.
9 pages, Europhysics Letters 95:30007,2011

http://arxiv.org/abs/1110.5899
Einstein-Regge equations in spinfoams
Claudio Perini
(Submitted on 26 Oct 2011)
We consider spinfoam quantum gravity on a spacetime decomposition with many 4-simplices, in the double scaling limit in which the Immirzi parameter γ is sent to zero (flipped limit) and the physical area in Planck units (γ times the spin quantum number j) is kept constant. We show that the quantum amplitude takes the form of a Regge-like path integral and enforces Einstein equations in the semiclassical regime. In addition to quantum corrections which vanish when the Planck constant goes to zero, we find new corrections due to the discreteness of geometric spectra which is controlled by the Immirzi parameter.
4 pages, based on a talk given at Loops '11 in Madrid, to appear in Journal of Physics: Conference Series (JPCS)

http://arxiv.org/abs/1109.6538
Lorentzian spinfoam propagator
Eugenio Bianchi, You Ding
(Submitted on 29 Sep 2011)
The two-point correlation function is calculated in the Lorentzian EPRL spinfoam model, and shown to match with the one in Regge calculus in a proper limit: large boundary spins, and small Barbero-Immirzi parameter, keeping the size of the quantum geometry finite and fixed. Compared to the Euclidean case, the definition of a Lorentzian boundary state involves a new feature: the notion of past- and future-pointing intertwiners. The semiclassical correlation function is obtained for a time-oriented semiclassical boundary state.
13 pages

http://arxiv.org/abs/1105.0216
Regge gravity from spinfoams
Elena Magliaro, Claudio Perini
(Submitted on 1 May 2011)
We consider spinfoam quantum gravity in the double scaling limit γ → 0, j → ∞, with γj=const., where γ is the Immirzi parameter, j is the spin and γj gives the physical area in Planck units. We show how in this regime the partition function for a 2-complex takes the form of a path integral over continuous Regge metrics and enforces Einstein equations in the semiclassical regime. The Immirzi parameter must be considered as dynamical in the sense that it runs towards zero when the small wavelengths are integrated out. In addition to quantum corrections which vanish for h → 0, we find new corrections due to the discreteness of geometric spectra which is controlled by γ.
11 pages
===============
Incidental information
I just noticed an interesting lineup of speakers at Princeton Institute for Advanced Study this spring.
Princeton has a regular High Energy Theory Seminar, which is sometimes held in the IAS Bloomberg Lecture Hall and sometimes in a seminar room at the PCTS (Princeton Center for Theoretical Science)
http://www.princeton.edu/physics/events/

High Energy Theory Seminar - IAS - Andrew Strominger, Harvard University
Apr 9, 2012 · 2:30 p.m.– 3:30 p.m. · Bloomberg Lecture Hall

High Energy Theory Seminar - Erik Verlinde, University of Amsterdam - TBA
Apr 16, 2012 · 2:30 p.m.– 3:30 p.m. · PCTS Seminar Room

High Energy Theory Seminar - IAS - Carlo Rovelli, Aix-Marseille University, France - Loop quantum Gravity: Recent Results and Open Problems
Apr 23, 2012 · 2:30 p.m.– 3:30 p.m. · Bloomberg Lecture Hall
Description: The loop approach to quantum gravity has developed considerably during the last few years, especially in its covariant ('spinfoam') version. I present the current definition of the theory and the results that have been proven. I discuss what I think is still missing towards of the goal of defining a consistent tentative quantum field theory genuinely background independent and having general relativity as classical limit.

I checked out the IAS calendar and they have a neat thing planned for the 23rd April. From 12:30 to 1:30 they have a LUNCH DISCUSSION on Early Universe Cosmology.
Then an hour for leisurely reflection followed by Rovelli's talk at 2:30.
http://www.ias.edu/calendar/2012-04-23?mini=calendar%2F2012-04
Nice menu planning...timing.

 

[marcus]

Continuing to bring this thread on current LQG developments up to date, as I noted elsewhere there was (IMHO) an important January paper by Bee, Leonardo, and Isabeau which had this key conclusion paragraph.
Google "hossenfelder emission spectra" and get http://arxiv.org/abs/1202.0412 [curious dark matter conjecture, idea for QG test]

==QUOTE 1202.0412==
4 Conclusion
We have derived here an approximate analytic expression for the emission spectrum of self-dual black holes in the mass and temperature limits valid for primordial black holes evaporating today. The idea that primordial black holes are dark matter candidates is appealing since it is very minimalistic and conservative, requiring no additional, so far unobserved, matter. This idea has therefore received a lot of attention in the literature. However, the final stages of the black hole evaporation seem to be amiss in observation, and so there is a need to explain why primordial black holes were not formed at initial masses that we would see evaporating today. The self-dual black holes we have studied here offer a natural explanation since they evaporate very slowly. The analysis we have presented here allows to calculate the particle flux from such dark matter constituted of self-dual black holes, and therefore is instrumental to test the viability of this hypothesis of dark matter constituted of self-dual black holes against data.
==endquote==

In short, the main (perhaps only) problem with tiny primordial BH as DM is that by conventional Hawking model temperature rises as the thing evaporates, going as mass inverse, so tiny BH are hot and evaporate too fast.
But rightly or not in the interesting mass range Modesto's Loop BH temperature goes down with mass. So in the very long run, the tiny BH could conceivably even come into equilibrium with the CMB or at any rate last a long time.
This gives a conservative (and testable!) way to account for Dark Matter. One does not need a new particle.

Testable because if the observed clouds of DM do indeed consist of these tiny Loopish BH then the clouds should have a characteristic radiation spectrum
I think it is not only this interesting and testable idea which is important, but also the
*minimalistic conservative* THEME which is underscored in the paper.

Figuring out how to explain stuff without imagining exotic unobserved particles/fields.

That's a desideratum to keep in mind when looking over current research. We may start seeing more of it. To me it's strongly represented in the Cai Easson paper which seems aimed at explaining inflation without the need for an inflaton field!
I talked about that in post #56:

http://arxiv.org/abs/1202.1285
Higgs Boson in RG running Inflationary Cosmology
Yi-Fu Cai, Damien A. Easson
(Submitted on 6 Feb 2012)
An intriguing hypothesis is that gravity may be non-perturbatively renormalizable via the notion of asymptotic safety. We show that the Higgs sector of the SM minimally coupled to asymptotically safe gravity can generate the observed near scale-invariant spectrum of the Cosmic Microwave Background through the curvaton mechanism. The resulting primordial power spectrum places an upper bound on the Higgs mass, which for canonical values of the curvaton parameters, is compatible with the recently released Large Hadron Collider data.
5 pages

And for sure the Cai Easson idea could be wrong! That is part of why it is interesting. There could really be a mysterious "inflaton" field able to quantum fluctuate and all that jazz. But it might also just be the running of a coupling constant. Plus fluctuations in a field we already need and see signs of, the Higgs field.

What I want to do is try to use this *minimalistic conservative* THEME that comes out explicitly in Bee and Leonardo and Isabeau's paper, to try to organize how I view current research. What other recent papers bear out this trend? If it is a trend. How does research by other people (like Freidel, Bianchi, Dittrich...) fit into this picture, if it does?

 

[marcus]

I looked just now at the PERIMETER INSTITUTE colloquium schedule for Winter term 2012. Their winter term is Jan-April. Spring in Canada does not start until May.
I'll get the link
http://www.perimeterinstitute.ca/en/Scientific/Seminars/Colloquium/

Apr. 4     2:00 pm	Carlo Rovelli     Universite de la Mediterranee	     TBA

And probably we should watch the QG seminar schedule too.
http://www.perimeterinstitute.ca/en/Scientific/Seminars/Quantum_Gravity/
They don't have anything scheduled yet for April.

A couple of posts back I noted that Princeton IAS is having Rovelli give a colloquium talk on Loop gravity in April, paired with a discussion of Early Universe Cosmology earlier in the day.

...
I just noticed an interesting lineup of speakers at Princeton Institute for Advanced Study this spring.
Princeton has a regular High Energy Theory Seminar, which is sometimes held in the IAS Bloomberg Lecture Hall and sometimes in a seminar room at the PCTS (Princeton Center for Theoretical Science)
http://www.princeton.edu/physics/events/

High Energy Theory Seminar - IAS - Andrew Strominger, Harvard University
Apr 9, 2012 · 2:30 p.m.– 3:30 p.m. · Bloomberg Lecture Hall

High Energy Theory Seminar - Erik Verlinde, University of Amsterdam - TBA
Apr 16, 2012 · 2:30 p.m.– 3:30 p.m. · PCTS Seminar Room

High Energy Theory Seminar - IAS - Carlo Rovelli, Aix-Marseille University, France - Loop quantum Gravity: Recent Results and Open Problems
Apr 23, 2012 · 2:30 p.m.– 3:30 p.m. · Bloomberg Lecture Hall
Description: The loop approach to quantum gravity has developed considerably during the last few years, especially in its covariant ('spinfoam') version. I present the current definition of the theory and the results that have been proven. I discuss what I think is still missing towards of the goal of defining a consistent tentative quantum field theory genuinely background independent and having general relativity as classical limit.

I checked out the IAS calendar and they have a neat thing planned for the 23rd April. From 12:30 to 1:30 they have a LUNCH DISCUSSION on Early Universe Cosmology.
Then an hour for leisurely reflection followed by Rovelli's talk at 2:30.
http://www.ias.edu/calendar/2012-04-23?mini=calendar%2F2012-04
...

That seems like a really good idea on the IAS part. I explained why in a post in the waterfall's thread "Alternatives to QFT". I think Loop may be on the path to unification and a new quantum field theory, even though it is not itself attempting to take the final step. A necessary step on the way could be reformulating the geometry that you put matter fields on.
https://www.physicsforums.com/showthread.php?p=3756881#post3756881

 

[marcus]

Some interesting recent developments in LQG.

http://arxiv.org/abs/1201.2187
A spin-foam vertex amplitude with the correct semiclassical limit
Jonathan Engle
(Submitted on 10 Jan 2012)
Spin-foam models are hoped to provide a dynamics for loop quantum gravity. All 4-d spin-foam models of gravity start from the Plebanski formulation, in which gravity is recovered from a topological field theory, BF theory, by the imposition of constraints, which, however, select not only the gravitational sector, but also unphysical sectors. We show that this is the root cause for terms beyond the required Feynman-prescribed exponential of i times the action in the semiclassical limit of the EPRL spin-foam vertex. By quantizing a condition isolating the gravitational sector, we modify the EPRL vertex, yielding what we call the proper EPRL vertex amplitude. This provides at last a vertex amplitude for loop quantum gravity with the correct semiclassical limit.
4 pages

see also Alesci Rovelli's proposal for new Hamiltonian:
Google "alesci rovelli hamiltonian arxiv" and get http://arxiv.org/abs/1005.0817

and the Freidel Geiller Ziprick paper:
Google "freidel geiller ziprick" and get http://arxiv.org/abs/1110.4833

More discussion here:
https://www.physicsforums.com/showthread.php?p=3637688#post3637688
https://www.physicsforums.com/showthread.php?p=3643430#post3643430
https://www.physicsforums.com/showthread.php?p=3624456#post3624456

 

[tom.stoer]

In order not to confuse the reader:

A "proper vertex amplitude" to recover the correct semicalssical limit is a necessary but not a sufficient condition for the model to be "correct". Of course one must recover GR as low energy theory, but in the deep QG regime there may very well be a whole bunch of inequivalent theories with the same semiclassical limit.

This is the main reason why some people insist on
1) a completion of the canonical formulation (constructing a "correct" H) plus
2) a consistent quantization in terms of spin foams plus
3) a proof of equivalence of (1) and (2)

All three pathways are being investigated, but up to now neither completion of 1) or 2) nor convergence in the sense of 3) can be claimed.

@marcus: did you spent some time in looking into the 2011 Thiemann papers? There are some interesting aspects like going beyond dim=4 and incorporating SUSY.

 

[marcus]

Another recent development. The cosmological constant Λ put into spinfoam cosmology and one gets a nontrivial solution to the Einstein equation out: de Sitter space.

It's kind of beautiful. The Friedmann equation with cosmo constant is derived from the Zakopane spinfoam amplitude (with Λ inserted). And this turns out to be compatible with the treatment where Lambda is a quantum group deformation parameter. Several things brought together in one paper.

Google "bianchi krajewski spinfoam cosmology" and get
http://arxiv.org/abs/1101.4049
Cosmological constant in spinfoam cosmology
Eugenio Bianchi, Thomas Krajewski, Carlo Rovelli, Francesca Vidotto
(Submitted on 20 Jan 2011)
We consider a simple modification of the amplitude defining the dynamics of loop quantum gravity, corresponding to the introduction of the cosmological constant, and possibly related to the SL(2,C)q extension of the theory recently considered by Fairbairn-Meusburger and Han. We show that in the context of spinfoam cosmology, this modification yields the de Sitter cosmological solution.
4 pages, 2 figures

for the treatment where Λ appears in quantum group, related to the q-deformation, see papers by Muxin Han and by Fairbairn Meusberger. It's fascinating that in that treatment one would expect that Λ running to large values (as in asym safe gravity) with high energy density corresponds to a decline in angular resolution---angles get fuzzy things are either in the same direction or they are not, lacking fine angular distinctions. It's intriguing.
But one does not have to deal with the quantum group idea of how Λ arises. One can simply insert it in the Zakopane spinfoam amplitude---or in the Friedmann equation---and treat it as a constant the way cosmologists customarily do.

this paper was a "sleeper". I'm not sure we recognized its importance back in the first quarter of 2011.

 

[marcus]

Tom, raised an interesting point in the Shapo-Wetter thread, which this paper could serve as partially answering.

I think it's amazing that such an enormous work and resulting profound insights can perhaps (!) be traced back to a wrong assumption ;-) That does not necessarily mean that the reults are wrong, of course

It would be interesting to find a close relationship between AS and LQG.

I saw some recent results on AS applied to Holst action with different results as for Einstein-Hilbert. This is striking.

The cosmological constant is treated differently in both approaches; in LQG one tries to incorporate it already when defining the algebraic foundations as a q-deformation of SU(2); in AS it behaves as a standard running coupling 'constant'; these two ideas seem to be incompatible at a very fundamental level.

What the Bianchi Krajewski et al paper suggests to me is that the two ideas (which Tom points out SEEM to be incompatible) are not actually incompatible.

You can see from 1101.4049 equation (2) that in LQG the cosmological constant can indeed be treated as a "standard running coupling", as it is in the Asymptotic Safe approach.

And it can also be treated as a q-deformation of SL(2,C) as per Han, Meusberger, Fairbairn and others. The paper tentatively suggests the two ways of including Λ are "possibly related"!

 

[marcus]

Since it may be possible to MERGE Asym Safe QG with Loop QG (and get something that works better than AS currently does at the cosmo singularity) I want to pay close attention to recent AS talks and papers. Here is the abstract for Frank Saueressig's 15 February video lecture:

Google "saueressig pirsa fractal" and get
http://pirsa.org/12020088/
Fractal Space-times Under the Microscope: a RG View on Monte Carlo Data
Frank Saueressig
The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In particular the spectral dimension, which measures the return probability of a fictitious diffusion process on space-time, provides a valuable probe which is easily accessible both in the continuum functional renormalization group and discrete Monte Carlo simulations of the gravitational action. In this talk, I will give a detailed exposition of the fractal properties associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). Comparing these continuum results to three-dimensional Monte Carlo simulations, we demonstrate that the resulting spectral dimensions are in very good agreement. This comparison also provides a natural explanation for the apparent conflicts between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.
Date: 15/02/2012 - 4:00 pm

and also recall the Bianchi et al paper from 2 posts back:

Google "bianchi krajewski spinfoam cosmology" and get
http://arxiv.org/abs/1101.4049
Cosmological constant in spinfoam cosmology
Eugenio Bianchi, Thomas Krajewski, Carlo Rovelli, Francesca Vidotto
(Submitted on 20 Jan 2011)
We consider a simple modification of the amplitude defining the dynamics of loop quantum gravity, corresponding to the introduction of the cosmological constant, and possibly related to the SL(2,C)q extension of the theory recently considered by Fairbairn-Meusburger and Han. We show that in the context of spinfoam cosmology, this modification yields the de Sitter cosmological solution.
4 pages, 2 figures

They derive the Friedman equation for deSitter space starting from the Zakopane dynamics equation with a λ term inserted for cosmo constant.

 

[marcus]

Several interesting parallels between AsymSafe QG and Loop are appearing. One is an explanation of dark matter as clouds of small black holes. We see this from Modesto in the Loop case and from Easson in the Safe QG case. Modesto has been working on this for several years---I'll get a recent paper of his with Hossenfelder and you can check the references.
Google "modesto emission spectra" and get http://arxiv.org/abs/1202.0412
Emission spectra of self-dual black holes
Sabine Hossenfelder, Leonardo Modesto, Isabeau Prémont-Schwarz
(Submitted on 2 Feb 2012)
We calculate the particle spectra of evaporating self-dual black holes that are potential dark matter candidates. We first estimate the relevant mass and temperature range and find that the masses are below the Planck mass, and the temperature of the black holes is small compared to their mass. In this limit, we then derive the number-density of the primary emission particles, and, by studying the wave-equation of a scalar field in the background metric of the black hole, show that we can use the low energy approximation for the greybody factors. We finally arrive at the expression for the spectrum of secondary particle emission from a dark matter halo constituted of self-dual black holes.
15 pages, 6 figures,

Small conventional BH don't last long since they get hotter as they lose mass and evaportion speeds up. By contrast, small Loop BH last a very long time since they get colder as they lose mass.

Curiously enough Easson has come up with a similar conclusion in the Safe QG case.
Google "easson safe black hole" and get http://arxiv.org/abs/1007.1317
Black holes in an asymptotically safe gravity theory with higher derivatives
Yi-Fu Cai, Damien A. Easson
(Submitted on 8 Jul 2010)
We present a class of spherically symmetric vacuum solutions to an asymptotically safe theory of gravity containing high-derivative terms. We find quantum corrected Schwarzschild-(anti)-de Sitter solutions with running gravitational coupling parameters. The evolution of the couplings is determined by their corresponding renormalization group flow equations. These black holes exhibit properties of a classical Schwarzschild solution at large length scales. At the center, the metric factor remains smooth but the curvature singularity, while softened by the quantum corrections, persists. The solutions have an outer event horizon and an inner Cauchy horizon which equate when the physical mass decreases to a critical value. Super-extremal solutions with masses below the critical value correspond to naked singularities. The Hawking temperature of the black hole vanishes when the physical mass reaches the critical value. Hence, the black holes in the asymptotically safe gravitational theory never completely evaporate. For appropriate values of the parameters such stable black hole remnants make excellent dark matter candidates.
22 pages, 3 figures; version to appear in JCAP



==links to some recent papers==
New Hamiltonian:
Google "arxiv alesci rovelli hamiltonian" and get http://arxiv.org/abs/1005.0817

Intro, Survey, Tutorial, Open Problems for Research:
Google "ashtekar introduction 2012" and get http://arxiv.org/abs/1201.4598
Google "rovelli zakopane" and get http://arxiv.org/abs/1102.3660

Cosmological Constant:
Google "bianchi cosmic constant spinfoam" and get http://arxiv.org/abs/1101.4049
Google "pawlowski cosmic constant" and get http://arxiv.org/abs/1112.0360

Loop Classical Gravity--the right version of GR to quantize:
Google "freidel geiller ziprick" and get http://arxiv.org/abs/1110.4833
Google "jonathan ziprick pirsa" and get http://pirsa.org/12020096

Small black holes and dark matter:
Google "modesto emission spectra" and get http://arxiv.org/abs/1202.0412
Google "easson safe black hole" and get http://arxiv.org/abs/1007.1317

Miscellaneous:
Google "freidel speziale BF" and get http://arxiv.org/abs/1201.4247 [ways to get GR from BF]
Google "wise symmetry gravity" and get http://arxiv.org/abs/1112.2390 [different approach to hamiltonian]

 

[torsten]

Thanks marcus for the recent overview and thanks tom for the very interesting discussion.

Like Tom, I also have some trouble with LQG. Especially I think some of the problems came form the lack of understanding the 'local-global' problems (or sometimes mix them).
But no one considers the relation (and the special features) between 3 and 4 dimensions.
After the breakthrough of Perelman, we know that the relation between homogenous gemetries in 3 dimensions and 3-manifold topology is very close.
A general 3-manifold consist of a mix of 8 possible gemetries (related to the Bianchi model I to IX). This close relation is the reason that the Einstein-Hilbert action in 3 dimensions is a topological invaraint (Chern-Simons invaraint).
The situation changes dramatically in 4 dimensions. The relation between geometry and topology is lost but there is a new one between the smoothness structure (the maximal smooth atlas) and the topology.
This new relation is essential for the understanding of the dynamics: the sum over 3-geometries will automatically lead to the inclusion of pathes like:
spherical 3-geometry -> hyperbolic 3-geometry -> spherical 3-geometry
The corresponding 4-manifold can have the topology \(\displaystyle S^3\times R\) but an exotic smoothness structure (I considered this case in http://arxiv.org/abs/1201.3787 )

This fact has also an impact on spin foam models. Usually one try to relate thise models to a triangulation of the 4-manifold. But smoothness structures and piecewise-linear structures (as a kind of triangulations) are equivalent.
Therefore oen has something like an exotic triangulation.
To address these questions, one has to consider the class of topspin models (Marcolli, Dustopn et. al.) using branched coverings. In this approach one sees the problem:
every 3-manifold can be obtained by a 3-fold covering of the 3-sphere branched along a 1-dimensional complex, a knot or link, and
every 4-manifold can be obtained by a 4-fold covering of the 4-sphere branched along a 2-dimensional complex, a surface, but the surface contains 2 singularities: the cusp and the fold.
The appearance of cusp singularities was already discussed in the spin foam literature as conical singularities.

I agree with marcus and tom, that the Alesci/Rovelli hamiltonian is a real breakthrough, it considers a more global change of spacetime.

So again thanks for the overview, I will go more deep into these new papers.

Torsten

 

[marcus]

Hi Torsten!
You could give some general words on what you expect first and foremost from a QG theory, to provide a context.

For me the basic requirement is a clear testable one that reproduces classical geometry (where applicable) and resolves the cosmo singularity.

That's what I want from QG first and foremost, and then if there are several QG theories successful in this basic way then I will ask which one follows Dirac quantization plan most transparently, which one has both hamiltonian and path integral versions most clearly equivalent and so on.

Because if you have more than one theory that works, these niceties can be useful in selecting from among them.

But right now i do not see a multitude of QG theories that meet the basic requirements.
As for Loop, I see steady progress, a growing understanding of how to set up the classical phase space, quantize it, and get a hamiltonian version, mounting evidence that classical GR is recovered, that the cosmological singularity is resolved, and that it is testable. Numerous papers on all these fronts.

So I *expect* a hamiltonian version to be constructed that will be equivalent to the Zako spinfoam version or whatever it has evolved into by that time. The present formulation is remarkably clear and simple so it is hard to imagine how it could change, but it could of course.

But my basic desiderata are not that (unless there are several equally good theories to choose from). My requirements, as I said, are a clearly formulated testable theory which reproduces classical GR where valid and can model the start of expansion---forming the basis for cosmology.

I'm curious about what you would say instead of this. You are actively engaged in your own QG program. You must have some basic goals, primary objectives. You may have summed up your philosophy in one or more of your papers and can just give a page/paragraph reference or paste something in here. Or maybe it is something you can say informally in just a few words.

 

[tom.stoer]

Like Tom, I also have some trouble with LQG. Especially I think some of the problems came form the lack of understanding the 'local-global' problems (or sometimes mix them).

Thanks Torsten; it's is comforting when an expert identifies similar issues.

The situation changes dramatically in 4 dimensions. The relation between geometry and topology is lost but there is a new one between the smoothness structure (the maximal smooth atlas) and the topology. ... This fact has also an impact on spin foam models. Usually one try to relate thise models to a triangulation of the 4-manifold. But smoothness structures and piecewise-linear structures ... are equivalent.

It's clear that this must be your perspective ;-) but I agree, problems regarding PL and smoothness structures have been overlooked (or ignored) in the LQG community for a long time.

Here I have one central question: what is the fundamental structure of (L)QG:
1) PL or smooth manifolds with diffeomorphisms factored away - resuting in triangulations?
2) generic spin networks?

Not all generic spin networks are dual to some triangulation (of a manifold), and therefore there are spin networks for which no triangulation of a manifold does exist (at least the dimension of the manifold can be rather large).

... every 4-manifold can be obtained by a 4-fold covering of the 4-sphere branched along a 2-dimensional complex, a surface, but the surface contains 2 singularities: the cusp and the fold.

This results in another central question: in (L)QG, do we have to use a 3-dim. or a 4-dim manifold to start with?

My impression is that the SF models rely in some sense on some fundamental structures of the underlying 4-manifold, whereas the generic spin networks do have no such limitations. It's interesting that spin networks arise from manifolds with rather severe restrictions (3-space foliations of globally hyperbolic 4-manifolds, local diffeomorphisms, i.e. no singularites) but that once the construction is completed they seem to be agnostic regarding these restrictions.

So spin networks are a much richer structure than triangulations.

 

[marcus]

Interesting comments, Tom, I hope Torsten will discuss some of your questions. About your central question you know there are different formulations, and some do use 3D and 4D manifolds. "Do we have to?" It seems not since not every formulation of the theory does. The version I am most familiar with does not have these structures embedded. It uses both spin networks and spinfoams but they are not immersed in any continuum.

You are totally correct that "not all generic spin networks" are dual to triangulations! For one thing a spin network is not restricted to having just 4-valent nodes (which would correspond to tetrahedra in the dual). It's normal to have nodes with valence > 4 corresponding (fuzzily, indefinitely) to many-sided polyhedral chunks of space.