Reformulation of Loop gravity in progress, comment?

marcus

I'll recall post #129 at the top of this page, just so we don't get so intrigued by detail that we lose track of the full spectrum of different ways QG is being reshaped in the runup to the main QG conference (Loops 13 July of next year).
==quote post #129==
...
twistorLQG (Speziale's ILQGS talk and 1207.6348)
tensorialGFT (Carrozza's ILQGS talk and 1207.6734)
holonomySF (Hellmann's ILQGS talk and 1208.3388)
dust (Wise's ILQGS talk and 1210.0019)
hybrid LQC
An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (1211.1354)
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep)
GR Thermo and C*-algebra
General relativistic statistical mechanics (1209.0065)
Horizon entanglement entropy and universality of the graviton coupling (Bianchi's ILQGS talk and 1211.0522 and 1212.5183)
Interpretation of the triad orientations in loop quantum cosmology (1210.0418)

I think the last topic is critical, namely general relativistic thermodynamics (broadly interpreted to include statistical mechanics and the operator algebra formulation).

First it is clear that to be fully successful LQG has to encompass the LQC bounce, with matter and inhomogeneity--we already see that beginning to happen. In encompassing the bounce the model seemingly must include the dissipation or shrinkage of horizons and their vonNeumann entropy, with the emergence of a pure state.

I recently added the Kiefer and Schell paper http://arxiv.org/abs/1210.0418 as an indication of where that is going. Kiefer Schell have the purity/mixedness of quantum states run on a continuum from zero to one. A state is a trace-class operator ρ on the hilbert space, a generalized "density matrix". Pure states are those for which tr(ρ²) = 1, a kind of "purity index". As these gradually decohere, the purity index comes down from 1 to zero. In Kiefer Schell's case the quantum state of geometry does this as it interacts with the matter in the environment. If I'm not mistaken, LQG dynamics will be extended to include states of this density matrix ρ type (as Kiefer and Schell do with LQC) and Rovelli's September paper is a step in this direction. ...
==endquote==

Claus Kiefer's recent LQG paper is a step in the direction of the "star algebra" formulation of QG---where the basic mathematical object is (M,ω) an observables algebra M with a state function ρ: M→ℂ which gives the correlations and expectation values.

In the the entanglement entropy part of above post, I added a reference (in red) to a new paper by Bianchi and Myers:
http://arxiv.org/abs/1212.5183
On the Architecture of Spacetime Geometry
Eugenio Bianchi, Robert C. Myers
(Submitted on 20 Dec 2012)
We propose entanglement entropy as a probe of the architecture of spacetime in quantum gravity. We argue that the leading contribution to this entropy satisfies an area law for any sufficiently large region in a smooth spacetime, which, in fact, is given by the Bekenstein-Hawking formula. This conjecture is supported by various lines of evidence from perturbative quantum gravity, simplified models of induced gravity and loop quantum gravity, as well as the AdS/CFT correspondence.
8 pages, 1 figure

marcus

The idea of this thread is to keep track of the full spectrum of different ways QG is being reshaped in the runup to the main QG conference http://www.perimeterinstitute.ca/conferences/loops-13 (Loops 13 at Perimeter Institute in July 2013).

The Bianchi Myers paper noted in previous post seems remarkably rich in useful ideas--I'm not sure what the right word is, "fertile" maybe? At least to me, it suggests how, if LQG were put in C*-algebra form, one might define 3D REGIONS by subsets of the algebra satisfying an entanglement-area condition. Note the word "architecture" in the title, as indicative of how the authors are thinking.

In any case it adds an exciting motivation to the (M, ω) world format. How can a smooth manifold picture emerge from some instance of (M, ω)? Perhaps one can state a condition in terms of entanglement entropy of certain subsets of the algebra. This is mentioned simply for motivation and I won't speculate further. I will list the various reformulation fronts in a different order.

Loop cosmology is getting into inhomogeneous regimes with multiple degrees of freedom and exploring "pre-inflationary" dynamics in more detail. Provisionally I'm calling that "hybrid loop cosmology" because several recent papers join existing LQC bounce with Fock space in a kind of hybrid. I can't list all the papers developing inhomogeneous LQC, so will just mention a couple.
hybrid LQC
Agullo Ashtekar Nelson—An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (http://arxiv.org/abs/1211.1354)
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep)

It's hard to know what to call the next development. Perhaps "C*-quantum gravity, T-time, and entanglement entropy".
Work towards general covariant (GC) analysis such as GC-thermo, GC statistical (quantum) mechanics seems to motivate an (M,ω) formulation. This finally solves the time problem because one gets an observer-independent (Tomita) flow on the observables algebra. But how do we recover the regional STRUCTURE of space in the (M,ω) context? I see Bianchi Myers paper in this light. The key word "architecture" in the title is a signal. Also Kiefer Schell paper leans in that direction.
C*-quantum gravity, T-time, entanglement
Rovelli—General relativistic statistical mechanics (http://arxiv.org/abs/1209.0065)
Bianchi—Horizon entanglement entropy and universality of the graviton coupling (ILQGS talk and http://arxiv.org/abs/1211.0522)
Bianchi Myers—On the Architecture of Spacetime Geometry (http://arxiv.org/abs/1212.5183)
Kiefer Schell—Interpretation of the triad orientations in loop quantum cosmology (http://arxiv.org/abs/1210.0418)
Besides the above there are several other clear reformulation initiatives under way.
twistorLQG (Speziale's ILQGS talk and http://arxiv.org/abs/1207.6348)
tensorialGFT (Carrozza's ILQGS talk and http://arxiv.org/abs/1207.6734)
holonomySF (Hellmann's ILQGS talk and http://arxiv.org/abs/1208.3388)
dust (Wise's ILQGS talk and http://arxiv.org/abs/1210.0019)

marcus

The ILQGS (international LQG seminar) is a good pointer to active areas of QG research---one can see this in the previous post: several of the themes we identified were represented not only by recent papers but also by Fall 2012 semester talks. Jorge Pullin organizes the ILQGS and I think he does a great job.

Part of the Spring 2013 schedule is posted now and we can examine it to help get a clearer picture of current research developments.

Jan 29th Entanglement in loop quantum gravity — Eugenio Bianchi — Perimeter Institute.
Feb 12th Dynamical chaos and the volume gap — Hal Haggard — CPT Marseille
Feb 26th Gravity electroweak unification — Stephon Alexander — Haverford College
Mar 12th ..................
Mar 26th Bianchi I LQC — Brajesh Gupt — LSU

The 26 March talk by Gupt exemplifies the current trend in Loop cosmology towards cosmic models which are less uniform: not homogeneous and isotropic. For many years at the beginning LQC deal with uniform models with a correspondingly small number of degrees of freedom. Now they are running models which achieve a bounce (where the singularity used to be) but involve more complex variation. The socalled "Bianchi I" models are only one example.

Others of the talks are on topics that feature in our 4th quarter MIP poll. I have to go---there's more to say about this.

marcus

As suggested in preceding post, we can get an idea of the active directions in Loop research by seeing what the Spring semester ILQGS talks will be about. For instance, I think the 29 January talk by Bianchi will be important and could be based on his November 2012 paper. This I think is a breakthrough paper, as I will explain.
http://arxiv.org/abs/1211.0522
Horizon entanglement entropy and universality of the graviton coupling
Eugenio Bianchi
(Submitted on 2 Nov 2012)
We compute the low-energy variation of the horizon entanglement entropy for matter fields and gravitons in Minkowski space. While the entropy is divergent, the variation under a perturbation of the vacuum state is finite and proportional to the energy flux through the Rindler horizon. Due to the universal coupling of gravitons to the energy-momentum tensor, the variation of the entanglement entropy is universal and equal to the change in area of the event horizon divided by 4 times Newton's constant - independently from the number and type of matter fields. The physical mechanism presented provides an explanation of the microscopic origin of the Bekenstein-Hawking entropy in terms of entanglement entropy.
7 pages

This is a breakthrough because a radical simplification. You can calculate the entanglement entropy, in this case, just from the entanglement entropy of the gravitons alone.
You do not have to put matter fields into the calculation because the gravitons FEEL the matter thoroughly and reflect its entanglements.

Eventually, I suspect, the entropy associated with different regions will be algebraically definable in a C* context, based on correlations between observables. The entropy-area relation will facilitate exploring the geometry in a situation where no manifold is given to start with. This will advance the program of recovering geometric relationships in a C* picture of the world, IMHO. So I think this is an outstanding paper with long-range significance. If someone disagrees with this assessment of 1211.0522, please tell me--I'd be interested in hearing a different opinion.

So later this month, as 29 January approaches, some of us will probably decide to take a look at the November paper to prepare for listening to the online seminar titled:
Entanglement in loop quantum gravity by Eugenio Bianchi.

marcus

The idea of this thread is to keep track of the full spectrum of different ways QG is being reshaped in the runup to the main QG conference http://www.perimeterinstitute.ca/conferences/loops-13 (Loops 13 at Perimeter Institute in July 2013).

Now with only 6 months left before conference there has appeared what I think is maybe the MOST ambitious reformulation initiative. This is via GAUGE NETWORK and GAUGE FOAM analogs by Marcolli and van Suijlekom (at Caltech and Nijmegen). These are analogous to the spin networks and spin foams that are already used in the current LQG formulation, except now the chunks of space are equipped with noncommutative geometry.

http://arxiv.org/abs/1301.3480
Gauge networks in noncommutative geometry
Matilde Marcolli, Walter D. van Suijlekom
(Submitted on 15 Jan 2013)
We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. The configuration space of quiver representations (modulo equivalence) in the category of finite spectral triples is studied; gauge networks appear as an orthonormal basis in a corresponding Hilbert space. We give many examples of gauge networks, also beyond the well-known spin network examples. We find a Hamiltonian operator on this Hilbert space, inducing a time evolution on the C*-algebra of gauge network correspondences...
...
The people:
http://www.its.caltech.edu/~matilde/
http://www.math.ru.nl/~waltervs/index.php?page=home
(Walter Daniel van Suijlekom b. 1978, dual career as professional musician, interesting. PhD 2005 at SISSA Trieste. Since 2007 postdoc at Nijmegen, same place as Renate Loll. Has taught some interesting courses at Nijmegen including NCG, i.e. spectral geometry.)

I think this Marcolli van Suijlekom initiative could lead to a C* algebra formulation of LQG. Already they have a Hamiltonian and time evolution of gauge networks (at least in some case they are considering). At the end of the paper there is a proposal for how to do gauge FOAMS and what the PARTITION FUNCTION should look like, i.e. a PATH INTEGRAL approach coming out. And it looks in a very general way rather like what you see in Zakopane Lectures (2011)

The idea is to have chunks of ALMOST COMMUTATIVE space (represented by finite dimensional spectral triples, spectral polyhedra?) at the vertices of the network, and have the links be morphisms somehow joining the vertices. Almost commutative spectral geometry is how Connes and friends realized the Standard Model. So in spirit very much like current LQG except chunks of almost commutative space at the vertices instead of chunks of ordinary commutative space.

I think these things are all related and am not sure what to call this development. Perhaps "C*-quantum gravity, T-time, entanglement entropy, gauge networks".
I should recall that work towards general covariant (GC) analysis such as GC-thermo, GC statistical (quantum) mechanics seems to motivate a star algebra (M,ω) formulation because this finally solves the time problem. One gets an observer-independent (Tomita) flow on the observables algebra. Then how do we recover the regional STRUCTURE of space in the (M,ω) context? I see Bianchi Myers paper in this light. The key word "architecture" in the title is a signal. Also Kiefer Schell paper leans in that direction.
======================
C*-quantum gravity, T-time, entanglement, gauge networks
Marcolli van Suijlekom—Gauge networks in noncommutative geometry (http://arxiv.org/abs/1301.3480)
Rovelli—General relativistic statistical mechanics (http://arxiv.org/abs/1209.0065)
Bianchi—Horizon entanglement entropy and universality of the graviton coupling (ILQGS talk and http://arxiv.org/abs/1211.0522)
Bianchi Myers—On the Architecture of Spacetime Geometry (http://arxiv.org/abs/1212.5183)
Kiefer Schell—Interpretation of the triad orientations in loop quantum cosmology (http://arxiv.org/abs/1210.0418)

===================
The LQG-LQC bridge, hybrid LQC, matter bounce
Alesci and Cianfrani have established a clear derivation of LQC from the full LQG theory--canonically quantizing first and then reducing to the cosmo case. Loop cosmology is getting into inhomogeneous regimes with multiple degrees of freedom and exploring "pre-inflationary" dynamics in more detail. Provisionally I'm calling that "hybrid loop cosmology" because several recent papers join existing LQC bounce with Fock space in a kind of hybrid. I can't list all the papers developing inhomogeneous LQC, so will just mention a small sample.
Alesci Cianfrani—Quantum-Reduced Loop Gravity: Cosmology (http://arxiv.org/abs/1301.2245)
Agullo Ashtekar Nelson—An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (http://arxiv.org/abs/1211.1354)
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep)
Wilson-Ewing—The Matter Bounce Scenario in Loop Quantum Cosmology (http://arxiv.org/abs/1211.6269)
====================

Besides the above there are several other clear reformulation initiatives under way.
twistorLQG (Speziale's ILQGS talk and http://arxiv.org/abs/1207.6348)
tensorialGFT (Carrozza's ILQGS talk and http://arxiv.org/abs/1207.6734)
holonomySF (Hellmann's ILQGS talk and http://arxiv.org/abs/1208.3388)
dust (Wise's ILQGS talk and http://arxiv.org/abs/1210.0019)

marcus

The twistorial reformulation of LQG has taken a big step forward with:
http://arxiv.org/abs/1301.5859
Hamiltonian spinfoam gravity
Wolfgang M. Wieland
(Submitted on 24 Jan 2013)
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
28 pages, 2 figures

To get a sense of Wieland you could watch some of this Perimeter talk (February 2012):
http://pirsa.org/12020129/

marcus

In 3 days, Bianchi's ILQGS talk: Entanglement entropy in LQG
The slides PDF may be posted beforehand (this has happened with ILQGS) and the URL will probably be: http://relativity.phys.lsu.edu/ilqgs/bianchi012913.pdf
After the talk the audio URL will probably be http://relativity.phys.lsu.edu/ilqgs/bianchi012913.wav
He has shown that the BH horizon entropy and the CEH (cosmic event horizon) entropy can both be understood as entanglement.
The state on the accessible side must be MIXED because entangled with the state on the other side. This gives a simple handle on the entropy, as he shows.

The talk will necessarily take as its point of departure his November paper. http://arxiv.org/abs/1211.0522 This is a classic: a major landmark, very short (4 pages), simply worded, and effecting a radical change of perspective.
The November paper was not set in any one theory---e.g. not specifically a LQG paper. It was quite general.
So now we will see what's new since then, what specifically QG development can have grown out of it.

If one is rereading the papers in order to prepare to understand the online talk, there is also Bianchi's December paper with Rob Myers (http://arxiv.org/abs/1212.5183) which I mentioned two posts back.

MTd2

I think it should be remarked that this time time is only a dimension like in GR.

marcus

Bianchi's slides http://relativity.phys.lsu.edu/ilqgs/bianchi012913.pdf are exceptionally clear, visual, and conceptually intuitive.
"Entanglement and the Bekenstein-Hawking entropy"
The B-H entropy is explained simply as the entang. entropy between the two regions

It concludes with the Bianchi-Myers conjecture, which remains a conjecture (quite an interesting one.)

I just checked the audio link http://relativity.phys.lsu.edu/ilqgs/bianchi012913.wav and that part is not yet online.

marcus

The audio for Bianchi's 29 Jan ILQGS talk has been posted:
http://relativity.phys.lsu.edu/ilqgs/bianchi012913.wav

Next up (12 February) is Hal Haggard's talk:
Dynamical chaos and the volume gap

http://relativity.phys.lsu.edu/ilqgs/
Interestingly, Haggard's research has already been "covered" (as they say in the music business) by a prominent particle theorist named Berndt Müller.
The existence of a smallest observable volume (a gap in the vol operator spectrum between zero and the smallest positive eigenvalue) is the key to the discreteness/finiteness feature of LQG. There is an analogy between "energy conserving" Hamiltonian dynamics and "volume preserving" shape-shifting of polyhedra that lets one treat it as a dynamical system. Classical chaos tends to go along with discrete spectrum at the quantum level. So the work here is supportive.
==============

Here are some of the more interesting papers that appeared this month, giving us an idea of directions the field will be going in 2013. I'll have to factor these into the reformulation themes already identified in this thread.

It is important that the relation between LQG and the cosmology application LQC has been clarified by the Alesci Cianfrani and the Engle papers. One can do the symmetry reduction AFTER quantization. So there is no obstacle to viewing LQC as a straightforward application of the full theory. In fact Engle shows that one can EMBED LQC in full theory without ever invoking the piecewise linear category, or fixing on some particular graph structure.
This opens the way to testing full LQG theory by confronting LQC predictions with early universe observation. So it's a 2013 milestone.

http://arxiv.org/abs/1301.1264
Inflation as a prediction of loop quantum cosmology
Linda Linsefors, Aurelien Barrau
(Submitted on 7 Jan 2013)

http://arxiv.org/abs/1301.2245
Quantum-Reduced Loop Gravity: Cosmology
Emanuele Alesci, Francesco Cianfrani
(Submitted on 10 Jan 2013)
We introduce a new framework for loop quantum gravity: mimicking the spinfoam quantization procedure we propose to study the symmetric sectors of the theory imposing the reduction weakly on the full kinematical Hilbert space of the canonical theory. As a first application of Quantum-Reduced Loop Gravity we study the inhomogeneous Bianchi I model. The emerging quantum cosmological model represents a simplified arena on which the complete canonical quantization program can be tested. The achievements of this analysis could elucidate the relationship between Loop Quantum Cosmology and the full theory.

http://arxiv.org/abs/1301.6210
Embedding loop quantum cosmology without piecewise linearity
Jonathan Engle
(Submitted on 26 Jan 2013)
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), directly at the quantum level. Such a firmer understanding would increase confidence in the reduced theory as a tool for formulating predictions of the full theory,...The present paper constructs an embedding of the usual state space of LQC into that of standard LQG, that is, LQG based on piecewise analytic paths. The embedding is well-defined even prior to solving the diffeomorphism constraint, at no point is a graph fixed, and at no point is the piecewise linear category used. ...

==========
The Marcolli Suijlekom paper opens a possible path to building the standard matter field model into LQG. It lets the NODES of the network be SPECTRAL GEOMETRY CHUNKS instead of ordinary geometry chunks. Alain Connes and others have shown that a version of the standard matter model lives in spectral geometry. It does not have to be laid on by hand. A LQG spin network is re-named a "gauge network" when the nodes are spectral.

http://arxiv.org/abs/1301.3480
Gauge networks in noncommutative geometry
Matilde Marcolli, Walter D. van Suijlekom
(Submitted on 15 Jan 2013)
We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. ... beyond the well-known spin network examples. We find a Hamiltonian operator on this Hilbert space, inducing a time evolution on the C*-algebra of gauge network correspondences...

=============
Wolfgang Wieland's paper puts the whole business of secondary constraints, reality conditions etc on a new footing. We should recognize that it changes the terms of the discussion. So it is a major paper.

http://arxiv.org/abs/1301.5859
Hamiltonian spinfoam gravity
Wolfgang M. Wieland
(Submitted on 24 Jan 2013)
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
28 pages, 2 figures

marcus

The papers of Engle and by Alesci Cianfrani mentioned in above post indicate that Loop cosmology can be embedded in the full LQG theory, or derived from it. Reductions to the interesting cases for cosmology can be done AFTER the quantum theory is constructed. It has been pointed out that this opens the way for testing the full LQG theory. It has to give the right answers about the early universe.

Hence the relevance of this paper by Agullo Ashtekar Nelson that appeared today:
http://arxiv.org/abs/1302.0254
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations
Ivan Agullo, Abhay Ashtekar, William Nelson
(Submitted on 1 Feb 2013)
Using techniques from loop quantum gravity, the standard theory of cosmological perturbations was recently generalized to encompass the Planck era. We now apply this framework to explore pre-inflationary dynamics. The framework enables us to isolate and resolve the true trans-Planckian difficulties, with interesting lessons both for theory and observations. Specifically, for a large class of initial conditions at the bounce, we are led to a self consistent extension of the inflationary paradigm over the 11 orders of magnitude in density and curvature, from the big bounce to the onset of slow roll. In addition, for a narrow window of initial conditions, there are departures from the standard paradigm, with novel effects ---such as a modification of the consistency relation between the ratio of the tensor to scalar power spectrum and the tensor spectral index, as well as a new source for non-Gaussianities--- which could extend the reach of cosmological observations to the deep Planck regime of the early universe.
64 pages, 15 figures

The main actively researched QG rival to LQG in modeling the early universe has been the Asymptotic Safe QG program. String and Causal Dynamical Triangulations don't seem to have much to say about the start of expansion---or at least not much is being written from those perspectives.
However, the AS program may have experienced a severe setback with the appearance of Hamber's result that a QG theory in which the cosmological constant runs cannot be general covariant. For some discussion:
http://www.physicsforums.com/showthread.php?t=668612

tom.stoer

Marcus, what about some kind of "status report" of LQG?

We have several new ideas in the field:
- non-interacting dust defining field of physical observers and physical Hamiltonian
- spinor / twistor variables and changes in the constraint structure
- some relations (but still no proof of equivalence) for canonical and spin foam models

What do you think? Where are the main results and what are the key issues?

marcus

That's a nice question. I will have to respond in several stages. First, a general introduction, the overall context, how LQG fits into the picture, where I think it's going.

The overall program is Quantum Cosmology (QC). Humans should understand particle theory in dynamic geometry because our historic big job now is to accurately model the start of expansion. We have an enormous amount of data resulting from the start of expansion---a "big bounce" I expect but that remains to be seen.

That is the top of the mountain that the LQG climbers and other teams are working towards. So locating their current "status" means (for me) locating relative to that goal. Where are they relative to that goal?

Part of the goal, also, is to understand where Dark Matter comes from, and if possible to explain the size of the classical Cosmological Constant (part of understanding dynamic geometry.)

The path up the mountain is zig-zag. So I am always watching out for these surprise changes, that we have seen the Quantum Relativists make several times over the years.

Besides the particle theory of the "big bounce" (or whatever was the Beginning-of-Expansion) there is also the thermodynamics and statistical mechanics of the "big bounce" (or whatever was the Beginning-of-Expansion). Maybe that has tended to be overlooked, but it is a persistent interesting problem. I will set it aside for the moment and just think about the quantum particle relativist side.

This is why I think it is so important to review Marciano's May 2012 talk, and to hear Alexander's talk tomorrow (26 February 2013).

marcus

As I see it, LQG is a subfield of LQC. Much (perhaps most) Loop community work is now Cosmo-related. Papers by Engle and by Alesci show a good bridge, symmetry reduction can be done at the quantum level. And symmetry restrictions are gradually being relaxed--eg the work on Bianchi-One cosmologies.

If you think of this as "the tail wagging the dog" then as an aggregate research effort the tail is now bigger than the dog.

We tend to think of the main Loop research centers as Marseille, Perimeter, PennState, Erlangen, Warsaw...

But Agullo and Nelson are very important in cosmology and Agullo is at Cambridge and Nelson is at Nijmegen. And now suddenly I have realized that Dartmouth is an important place on the Loop map. That is where Marciano is--currently postdoc working with Alexander.

The Dartmouth people seem to start with particle theory and cosmology, and with unification at a classical level, and then move naturally into a spin foam quantization!

That makes me think that what Loop is depends on what you start with. It is a bunch of background-free lattice gauge theory techniques that have so far been explored using classic GR as a starting point. But the Dartmouth people show me that you do not have to be limited to starting with GR---you can start with more.

That is what tomorrow's talk by Alexander is about, and what the 7 May talk by Marciano will be about.

So this probably is a major revolution in Loop---another turning point in the zig-zag climb up the mountain.

Also it is a very necessary revolution, because to understand the Big Bounce one has to understand matter fields behavior in extreme dynamic geometry conditions. So one probably needs some BF-like extension of Plebanski action, and a background-free lattice quantization. Spinfoam in other words. This understanding is the mountain top that people are working towards, and we can think of Spinfoam work so far as practice for that ascent.

Anyway that is my two cents. It is how I see the general overall context: where LQG fits in.
I will try to assemble some kind of "progress report" for you on a more detailed level, although I'm no expert in the business.

EDIT: BTW Marciano's May 2012 talk is http://pirsa.org/12050079/
also BTW it would help me, if you have any comments on the above, to know your reactions.
It may be a while before I get to the job of assembling details of the picture and responses to this much, from you, could I think be very helpful.

EDIT: Reminder, the link to get slides PDF and audio for tomorrow's talk by Alexander is
http://relativity.phys.lsu.edu/ilqgs/
The title of the talk is Gravity Electroweak Unification

marcus

Although not well enough informed to give a professional level "progress report" for Loop research, in view of Tom's question I'll give some opinions and impressions. The following two papers tend to EMBED Loop cosmology in the full theory, thus making the full theory astrophysically testable.
I think these two represent some of the most important recent progress.

http://arxiv.org/abs/1301.2245
Quantum-Reduced Loop Gravity: Cosmology
Emanuele Alesci, Francesco Cianfrani
(Submitted on 10 Jan 2013)
We introduce a new framework for loop quantum gravity: mimicking the spinfoam quantization procedure we propose to study the symmetric sectors of the theory imposing the reduction weakly on the full kinematical Hilbert space of the canonical theory. As a first application of Quantum-Reduced Loop Gravity we study the inhomogeneous Bianchi I model. The emerging quantum cosmological model represents a simplified arena on which the complete canonical quantization program can be tested. The achievements of this analysis could elucidate the relationship between Loop Quantum Cosmology and the full theory.

http://arxiv.org/abs/1301.6210
Embedding loop quantum cosmology without piecewise linearity
Jonathan Engle
(Submitted on 26 Jan 2013)
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), directly at the quantum level. Such a firmer understanding would increase confidence in the reduced theory as a tool for formulating predictions of the full theory,...The present paper constructs an embedding of the usual state space of LQC into that of standard LQG, that is, LQG based on piecewise analytic paths. The embedding is well-defined even prior to solving the diffeomorphism constraint, at no point is a graph fixed, and at no point is the piecewise linear category used. ...

The most important progress any QG theory can make is progress towards testability and this can be of two kinds, IMHO:
1) Observable consequences in early universe astrophysics.
2) LHC-testable consequences of unification of gravity with particle physics.

As to point 1), there has been substantial progress towards deriving observable consequences of Loop cosmology--more than I can readily list or outline. Here is a recent example. See also papers by Barrau, Grain, and co-authors.

http://arxiv.org/abs/1302.0254
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations
Ivan Agullo, Abhay Ashtekar, William Nelson
(Submitted on 1 Feb 2013)
Using techniques from loop quantum gravity, the standard theory of cosmological perturbations was recently generalized to encompass the Planck era. We now apply this framework to explore pre-inflationary dynamics. The framework enables us to isolate and resolve the true trans-Planckian difficulties, with interesting lessons both for theory and observations. Specifically, for a large class of initial conditions at the bounce, we are led to a self consistent extension of the inflationary paradigm over the 11 orders of magnitude in density and curvature, from the big bounce to the onset of slow roll. In addition, for a narrow window of initial conditions, there are departures from the standard paradigm, with novel effects ---such as a modification of the consistency relation between the ratio of the tensor to scalar power spectrum and the tensor spectral index, as well as a new source for non-Gaussianities--- which could extend the reach of cosmological observations to the deep Planck regime of the early universe.
64 pages, 15 figures

Here are the quantum cosmology papers that the INSPIRE search engine identifies (appeared since 2009, ranked by cite count.) This includes Loop AND all the other kinds of quantum cosmology. So one can compare and get a sense of the relative importance.
http://inspirehep.net/search?ln=en&a...=50&sc=0&of=hb

As to point 2) there has, to my knowledge, been slight progress thus far. A beginning was made last year in the work of Alexander, Marciano, and Smolin. We'll have to see how that goes.

I suspect that any "progress report" for Loop should mention Wieland's recent paper. It addresses many issues---joining the Hamiltonian and Spinfoam approaches---understanding the various conditions and constraints. Basically learning how to put the theory in a nice form. Again we will have to see how this work continues.
http://arxiv.org/abs/1301.5859
Hamiltonian spinfoam gravity
Wolfgang M. Wieland
(Submitted on 24 Jan 2013)
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
28 pages, 2 figures

In one point I find I can't cover all the topics! Just in the past year there has also been remarkable progress in studying the Loop black hole.

I will have to redo this and try to organize it better.

tom.stoer

Marcus, my question was about LQG as the general framework, not about LQC.

marcus

I know. I don't think that is the best way to look at it.
I explained why in post #149

QC is the overall framework for quantum gravity.
It contains the big thing we want to understand.
It has a huge amount of relevant data.
It is the arena of testability.

So QC is the natural framework to consider.