Reformulation of Loop gravity in progress, comment?

tom.stoer

Marcus, I disagree. QG is the basis, QC is an application.

Cosmology is an application of GR which provides the fundamental framework - not the other way round.

marcus

Progress in QG can only be understood in the larger QC context.
Cosmology is what gives scientific meaning and urgency to the study of geometry at planck scale.

Cosmology is what gives us the questions:
dark matter
expansion of distances between stationary observers
the fact that geometry is dynamic
the fact that there is another gravitational constant Lambda which Newton didn't know about
how does matter behave in extreme dynamic geometry?
etc.

And Cosmology is where the great bulk of observational data is, that is relevant
to quantum gravity.

So to me it seems inevitable to conclude that QC provides the larger context in which LQG progress
must be assessed. If one is to make a meaningful assessment, that is.

tom.stoer

Cosmology is relevant as one application and as 'experimental setup'. But the develoment of a theory like QG focusses on a sound mathematical construction, of course to be tested in a larger context.

The development of GR was focussed on symmetry principles, field equations etc., not on expanding universes. The construction of QM was focussed on matrix and wave mechanics, not on spectroscopy.

Of course you have to apply a theory in larger context, and you have to have quantitative predictions and means to falsify the model. But first you have to have a model (or a class of models) passing basic tests like mathematical consistency, absence of anomalies, GR as semiclassical limit, ...

Looking at the current status of LQG most astrophysical data do not help much. They have to get the math right (and the latest spinor/twistor papers indicate that the celebrated Rovellian models are still incomplete). Assume we have a new deep space survey providing revolutionary results regarding CMB, galaxy superclusters or even the topology of our universe. This wouldn't change the status of LQG, unfortunately. They are not (yet) in the situation to select from a class of well-defined models based on experimental input. They are still in the construction phase.

marcus

You have some good points here. Let me try to say my idea in a different way. LQG is thought of as a pure gravity program---the quantum dynamics of pure matterless geometry.
I watch the research closely (as closely as I, as non-expert, can) and I see a trend. You could think of it as the emergence of a new field of research called LQGM ("loop quantum geometry-and-matter").

I can try to make a general statement about this. Let's see if this is right: LQGM arises from the application of principles of loop quantum gravity (LQG) to general relativity and standard matter theory. The goal is to quantize Plebanskian action containing GR and the local symmetries of standard matter, by following the physical ideas and mathematical tools underlying LQG.

Basically this involves building a more general theory, of which some version of the old LQG might turn out to be a special case. The important thing is that the new theoretical program follows the physical ideas and applies the mathematical tools developed in the more specialized earlier program.

Does this make sense to you? Many of the leading people I can think of who used to be working on the more limited specialized LQG program I now see to be working on combining geometry with matter in one way or another---creating, in effect, a broader more general program (undoubtably with some new mathematical tools and possibly with some new principles besides those developed in the earlier program.)

If you would like, I will try to enumerate the people involved in this move, and some of the papers. Let me know what you think, and what (if any) additional information you require.

tom.stoer

I can't see this big move and I think that incorporating matter has something to do with the key issues like definition of Dirac-observables, physical observers, gauge fixing/unfixing etc. And I think it's a new line of research, but not a paradigm shift.

But besides these details, responding to your question whether it makes sense to me: yes, it does.

marcus

Your question about progress of the purely QG part of the program also makes sense to me, although I take a broader view of the program. On the SPINORIAL formulation front, Etera Livine offers this as a review.
http://arxiv.org/abs/1201.2120
It's a paper by Dupuis Speziale Tambornino called
Spinors and Twistors in Loop Gravity and Spin Foams
"Spinorial tools have recently come back to fashion in loop gravity and spin foams. They provide an elegant tool relating the standard holonomy-flux algebra to the twisted geometry picture of the classical phase space on a fixed graph, and to twistors. In these lectures we provide a brief and technical introduction to the formalism and some of its applications."

Here's a recent paper by Livine himself:
http://arxiv.org/abs/1302.7142
Holonomy Operator and Quantization Ambiguities on Spinor Space
Etera R. Livine
(Submitted on 28 Feb 2013)
"We construct the holonomy-flux operator algebra in the recently developed spinor formulation of loop gravity. We show that, when restricting to SU(2)-gauge invariant operators, the familiar grasping and Wilson loop operators are written as composite operators built from the gauge-invariant 'generalized ladder operators' recently introduced in the U(N) approach to intertwiners and spin networks. We comment on quantization ambiguities that appear in the definition of the holonomy operator and use these ambiguities as a toy model to test a class of quantization ambiguities which is present in the standard regularization and definition of the Hamiltonian constraint operator in loop quantum gravity."

Livine is to be one of the invited speakers at Loops 2013 and my guess is he will summarize what is going on in this area. At this point I can't do better than simply refer to what he indicates is the review paper of choice (Dupuis, Speziale, Tambornino).

marcus

The earlier interesting discussion with Tom helped me to clarify my view that the hallmark of any QG theory is how it deals with cosmology (and the start of expansion in particular.)
The robust identifying feature of Loop Quantum Geometry has been that it leads back to a bounce with a period of natural faster-than-exponential expansion ("superinflation") due to quantum effects at high density. To summarize:Now something I did not expect has happened. The Group Field Theory (GFT) program has come out with a way to do GFT cosmology. This could have a significant effect on the Loop program.

http://arxiv.org/abs/1303.3576
Cosmology from Group Field Theory
Steffen Gielen, Daniele Oriti, Lorenzo Sindoni
(Submitted on 14 Mar 2013)
We identify a class of condensate states in the group field theory (GFT) approach to quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a non-linear and non-local extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semi-classical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.
5 pages

marcus

Since I last posted on this thread two important papers have come out, one by Ashtekar and the other by George Ellis, Reza Tavakol, Tim Clifton. Both have to do with cosmology which is pretty clearly turning out to be the main arena for QG theory. Early universe cosmology, in particular, is a kind of testing ground for Loop gravity. Several of the recent posts on this thread have been on the general them of LQG and cosmology.

What Ashtekar here calls "Planck regime" is in other papers he cites specified to be "pre-inflationary" expansion history arising from the LQG bounce.
The George Ellis paper is interesting because of the whole gravitational entropy issue.
there are conceptual difficulties with defining the entropy of the gravitational field---IOW geometric entropy. There is in fact no agreed on idea of gravitational entropy. So one cannot say what happens to the entropy during the LQG bounce. the concept (which is probably observer-dependent and scale-dependent) fails to be defined. So Ellis paper is much needed:it attacks this problem of defining entropy.

http://arxiv.org/abs/1303.5612
A Gravitational Entropy Proposal
Timothy Clifton, George F R Ellis, Reza Tavakol
(Submitted on 22 Mar 2013)
We propose a thermodynamically motivated measure of gravitational entropy based on the Bel-Robinson tensor, which has a natural interpretation as the effective super-energy-momentum tensor of free gravitational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein-Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson-Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein's field equations. It is also in keeping with Penrose's Weyl curvature hypothesis.
17 pages

Ashtekar's paper is more of a review of recent progress in pre-inflation LQG cosmology and consequent opportunities to make testable predictions about features of the cosmic microwave background.

http://arxiv.org/abs/1303.4989
Loop Quantum Gravity and the The Planck Regime of Cosmology
Abhay Ashtekar
(Submitted on 20 Mar 2013)
The very early universe provides the best arena we currently have to test quantum gravity theories. The success of the inflationary paradigm in accounting for the observed inhomogeneities in the cosmic microwave background already illustrates this point to a certain extent because the paradigm is based on quantum field theory on the curved cosmological space-times. However, this analysis excludes the Planck era because the background space-time satisfies Einstein's equations all the way back to the big bang singularity. Using techniques from loop quantum gravity, the paradigm has now been extended to a self-consistent theory from the Planck regime to the onset of inflation, covering some 11 orders of magnitude in curvature. 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 involving the scalar and tensor power spectra and a new source for non-Gaussianities. Thus, the genesis of the large scale structure of the universe can be traced back to quantum gravity fluctuations in the Planck regime. This report provides a bird's eye view of these developments for the general relativity community.
23 pages, 4 figures. Plenary talk at the Conference: Relativity and Gravitation: 100 Years after Einstein in Prague. To appear in the Proceedings to be published by Edition Open Access. Summarizes results that appeared in journal articles [2-13]

torsten

Yes, I totally agree that the falsification of a quantum gravity theory can be done by using cosmology. But also I agree with Tom that the grounded principles are not based on experimental results. During the birth of quantum mechanics, there was a close relationship between teory and experiment. One part of interpretational problems are caused by this history. Another part is reflected in the trial to define quantum geometry. Simple questions like: does the quantum geometrical state (for instance the superposition of spin networks) actually exists? are not answered. But an aswer would be important to go on.
But back to this topic....
In particular, a quantum gravity theory should explain the exponential increase of inflation. But I don't say any really good result in this direction (which satisfied me).
BTW, we formulated an inflation scenario (which purely geometrical roots) which is able to explain the exponential increase. In particular, the factor can be explicitly calculated using topological invaraints of the three manifold only. Maybe a beginning?

marcus

That sounds intriguing! Maybe you should give a link to the paper. I cannot remember all the papers and the interesting results that come out of your alternative smooth structures approach.

Just to review, Loop bounce cosmology does have a brief period of faster than exponential expansion, which happens inevitably as a consequence of the bounce. It naturally occurs and then naturally ends as the density declines. It is called "super-inflation" because the scale factor goes as e^Ht with H increasing.

In ordinary inflation the scale factor goes as e^Ht with H approximately constant or slowly decreasing.

But this period of super-inflation does not continue long enough, according to the LQC calculations. So the researchers have had to assume the existence of a scalar field which could take over from the naturally occurring super-inflation and serve as an "inflaton" field, to finish the job.

A recent paper about that:

http://arxiv.org/abs/1301.1264
Inflation as a prediction of loop quantum cosmology
Linda Linsefors, Aurelien Barrau
(Submitted on 7 Jan 2013)
Loop quantum cosmology is known to be closely linked with an inflationary phase. In this article, we study quantitatively the probability for a long enough stage of slow-roll inflation to occur, by assuming a minimalist massive scalar field as the main content of the universe. The phase of the field in its "pre-bounce" oscillatory state is taken as a natural random parameter. We find that the probability for a given number of inflationary e-folds is quite sharply peaked around 145, which is indeed more than enough to solve all the standard cosmological problems. In this precise sense, a satisfactory inflation is therefore a clear prediction of loop gravity. In addition, we derive an original and stringent upper limit on the Barbero-Immirzi parameter. The general picture about inflation, super-inflation, deflation and super-deflation is also much clarified in the framework of bouncing cosmologies.
6 pages, 4 figures

torsten

Thanks for the paper. I understand the necessarity to introduce this scalar field but this field is not an output of the model.
Here is the link:
http://arxiv.org/abs/1301.3628
of the paper "On the origin of inflation by using exotic smoothness". It also explained the reason to introduce the scalar field.

marcus

It is an intriguing paper. Can you give me the most basic intuition of how a transition to an alternative differential structure can cause inflation? Intuitively what causes the inflation and then what causes it to stop?

torsten

In this paper we consider an exotic [itex]S^3 \times \mathbb{R}[/itex]. This differential structure is characterized by a topological transition from a 3-sphere to another homology 3-sphere (for instance Poincare sphere) and back. Here we choose a homology 3-sphere [itex]\Sigma[/itex] with a hyperbolic structure (i.e. negative scalar curvature). Then we have a change from a positive curvature (3-sphere) to a 3-manifold with negative curvature (looking like a 3-sphere).
This transition leads to an accelaerated expansion. But we were able to show more. The 4-manifold representing the transition also carries a hyperbolic structure leading to an exponential increase (two geodesics in a hyperbolic geometry diverge exponentially). This exponential increase can be also expressed explicitly: there is a tree with an exponential number of states.
We obtained also an effective picture for this transition: it can be described by a SU(2)-valued scalar field (inflanton).
Again: [itex]S^3 \rightarrow\Sigma \rightarrow S^3[/itex] are the transitions, the first transition leads to an accelerated expansion whereas the second transition stops it.
I hope it helps. My view is more geometrically.

marcus

Thanks Torsten! That does help.

I should mention in connection with new developments in LQG that the ILQGS blog has a wide-audience article by Mano Alesci and Francesco Cianfrani about their (quantum) Reduced LQG
approach to cosmology.
http://ilqgs.blogspot.com/2013/03/re...m-gravity.html

It makes a bridge between the full LQG theory and cosmology because the reduction to the homogeneous and isotropic case is done within LQG
In conventional LQC the reduction is done first, and then this is reduced model is quantized, so the connection with the full theory is not so direct.

As I recall Jon Engle also has some recent work along these lines. It is very important because cosmology is the main testing ground for QG. We have to know what the full LQG theory has to say about the CMB power spectrum, conditions around the start of expansion, and the subsequent inflation.

The blog post by Alesci Cianfrani gives motivation and intuitive understanding of their new (reduced) version of Loop gravity.

marcus

In four days Wolfgang Wieland will give an ILQGS talk (available online) on a Hamiltonian approach to Spin Foam QG. This has been an important outstanding problem, how to unite the covariant Spin Foam approach with the older canonical LQG Hamiltonian approach.

Revised ILQGS Spring 2013 Schedule
http://relativity.phys.lsu.edu/ilqgs/
Wolfgang's paper of the same title, that the talk will be based on, is currently the leading paper on our first quarter 2013 MIP poll. http://www.physicsforums.com/showthread.php?t=681598

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. ... 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

Wolfgang Wieland's talk at ILQGS was given today and both the slides PDF and the audio are already online.
http://relativity.phys.lsu.edu/ilqgs/
I still do not see any one single clear direction in how LQG+Spinfoam theory is developing. It seems necessary to keep alert to several possible directions. To me personally the line taken by Wieland and Speziale and others (see the short bibliography at the end of Wolfgang's talk) looks very promising. It is aimed directly at showing the CONSISTENCY of the theory and they seem to have made good progress.

On the other hand we saw in fourth quarter 2012 a lot of work being done with TENSOR models. Some ILQGS talks were given on tensorial QG. And today a relevant paper by Razvan Gurau appeared on arxiv. So I should post that as instance of either a closely related rival approach (GFT) or as a reformulation that is brewing.

http://arxiv.org/abs/1304.2666
The 1/N Expansion of Tensor Models Beyond Perturbation Theory
Razvan Gurau
(Submitted on 9 Apr 2013)
We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges.
As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N to infinity limit, in the universality class of Gaussian tensor models.
45 pages

Gurau's paper is entirely technical. He refers to application in Quantum Gravity (e.g. via GFT) but does not give any detail. He proves many theorems. Past experience of both Gurau and Rivasseau work makes me expect that this may have significance for QG applications but I cannot foresee the specifics. Maybe some other people can.

marcus

A propos the preceding post, Razvan Gurau is to be one of the invited plenary speakers at the upcoming Loops conference, as is also Vincent Rivasseau. Loops 2013 will be held at Perimeter in latter half of July, just three months off, and I still have only a very rough notion of what the current state of LQG is that will appear at the biennial conference. There seem to be an unusually large number of different currents. We can watch the seminar talks at Perimeter, and at the ILQGS, during the run-up to the conference, for hints as to what the main developments are. Here are a couple of April talks scheduled at Perimeter:

The first of these seems unusual. An imaginary part of the action?
April 18, Yasha Neiman:
http://www.perimeterinstitute.ca/sem...k-hole-entropy
THE IMAGINARY PART OF THE GRAVITATIONAL ACTION AND BLACK HOLE ENTROPY
I present a candidate for a new derivation of black hole entropy. The key observation is that the action of General Relativity in bounded regions has an imaginary part, arising from the boundary term. The formula for this imaginary part is closely related to the Bekenstein-Hawking entropy formula, and coincides with it for certain classes of regions. This remains true in the presence of matter, and generalizes appropriately to Lovelock gravity. The imaginary part of the action is a versatile notion, requiring neither stationarity nor any knowledge about asymptotic infinity. Thus, it may provide a handle on quantum gravity in finite and dynamical regions. I derive the above results, make connections with standard approaches to black hole entropy, and speculate on the meaning of it all. Implications for loop quantum gravity are also discussed.

April 25, Casey Tomlin:
http://www.perimeterinstitute.ca/sem...lidean-gravity
LOOP QUANTIZATION OF A WEAK-COUPLING LIMIT OF EUCLIDEAN GRAVITY
I will describe recent work in collaboration with Adam Henderson, Alok Laddha, and Madhavan Varadarajan on the loop quantization of a certain G_N→ 0 limit of Euclidean gravity, introduced by Smolin. The model allows one to test various quantization choices one is faced with in loop quantum gravity, but in a simplified setting. The main results are the construction of finite-triangulation Hamiltonian and diffeomorphism constraint operators whose continuum limits can be evaluated in a precise sense, such that the quantum Dirac algebra of constraints closes nontrivially and free of anomalies. The construction relies heavily on techniques of Thiemann's QSD treatment, and lessons learned applying such techniques to the loop quantization of parameterized scalar field theory and the diffeomorphism constraint in loop quantum gravity. I will also briefly discuss the status of the quantum constraint algebra in full LQG, and how some of the lessons learned from the present model may guide us in that setting.

http://www.perimeterinstitute.ca/eve...entific-events

The Yasha Neiman talk relates to this March 2013 paper:
http://arxiv.org/abs/1303.4752
Imaginary action, spinfoam asymptotics and the 'transplanckian' regime of loop quantum gravity
Norbert Bodendorfer, Yasha Neiman
(Both authors recently took postdocs at Penn State.)

The Casey Tomlin talk relates to several recent papers:
http://arxiv.org/abs/1204.0211
Constraint algebra in LQG reloaded : Toy model of a U(1)^{3} Gauge Theory I
Adam Henderson, Alok Laddha, Casey Tomlin

http://arxiv.org/abs/1210.3960
Constraint algebra in LQG reloaded : Toy model of an Abelian gauge theory - II Spatial Diffeomorphisms
Adam Henderson, Alok Laddha, Casey Tomlin

http://arxiv.org/abs/1210.6869
Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity
Casey Tomlin, Madhavan Varadarajan
(Again for the most part the authors are full or part-time connected with Ashtekar's institute at Penn State, but also have ties with MPI-Potsdam, RRI-Bangalore, CMI-Chennai.)