Understanding the Relation between LQG and NQC

[tom.stoer]

Hi,

unfortunatey I lost track. I do not understand much reagrding NCG, but I noticed that there seems to be a line of research that tries to harmonize the NCG and the LQG approach, right?

Can anybody here explain the relation between LQG and NQC, the "big picture", not so much focussed on technical details?

What is the intention? Is it something like unification of matter + geometry?

Is there some hint why certain special structures (like the specific NCG models and SU(2) spin networks) have to be used? Why not something else? Is this harmonization of NGC and LQG natural or just introduced by hand? Can one structure be explained via the other one?

Thanks in advance
Tom

 

[Careful]

Hi,

unfortunatey I lost track. I do not understand much reagrding NCG, but I noticed that there seems to be a line of research that tries to harmonize the NCG and the LQG approach, right?

Can anybody here explain the relation between LQG and NQC, the "big picture", not so much focussed on technical details?

What is the intention? Is it something like unification of matter + geometry?

Is there some hint why certain special structures (like the specific NCG models and SU(2) spin networks) have to be used? Why not something else? Is this harmonization of NGC and LQG natural or just introduced by hand? Can one structure be explained via the other one?

Thanks in advance
Tom

As far as I seem to remember, quantum groups do show up rigorously in 2+1 quantum gravity (see John Barrett (?)) - I never really looked into this. But nobody knows whether there is any connection between 3+1 quantum gravity and quantum groups - this is just a lot of speculation (for example in the context of doubly special relativity).

 

[tom.stoer]

As far as I seem to remember, quantum groups do show up rigorously in 2+1 quantum gravity (see John Barrett (?)) - I never really looked into this.

I didn't, either.

But nobody knows whether there is any connection between 3+1 quantum gravity and quantum groups - this is just a lot of speculation (for example in the context of doubly special relativity).

Especially DSR seems (seemed) to be wishful thinking of Smolin.

 

[Careful]

Especially DSR seems (seemed) to be wishful thinking of Smolin.

I is good to have dreams, but it is a nightmare not knowing how to realize them in practice

 

[MTd2]

Yes, there are quantum groups in 4 dimensions. According to John Baez, there is even exotic statistics in 4 dimension, contrary to the myth.

http://lanl.arxiv.org/abs/gr-qc/0603085

Exotic Statistics for Strings in 4d BF Theory

John C. Baez, Derek K. Wise, Alissa S. Crans
(Submitted on 21 Mar 2006 (v1), last revised 9 May 2006 (this version, v2))
After a review of exotic statistics for point particles in 3d BF theory, and especially 3d quantum gravity, we show that string-like defects in 4d BF theory obey exotic statistics governed by the 'loop braid group'. This group has a set of generators that switch two strings just as one would normally switch point particles, but also a set of generators that switch two strings by passing one through the other. The first set generates a copy of the symmetric group, while the second generates a copy of the braid group. Thanks to recent work of Xiao-Song Lin, we can give a presentation of the whole loop braid group, which turns out to be isomorphic to the 'braid permutation group' of Fenn, Rimanyi and Rourke. In the context 4d BF theory this group naturally acts on the moduli space of flat G-bundles on the complement of a collection of unlinked unknotted circles in R^3. When G is unimodular, this gives a unitary representation of the loop braid group. We also discuss 'quandle field theory', in which the gauge group G is replaced by a quandle.

http://lanl.arxiv.org/abs/gr-qc/0605087

Quantization of strings and branes coupled to BF theory

John C. Baez, Alejandro Perez
(Submitted on 15 May 2006)
BF theory is a topological theory that can be seen as a natural generalization of 3-dimensional gravity to arbitrary dimensions. Here we show that the coupling to point particles that is natural in three dimensions generalizes in a direct way to BF theory in d dimensions coupled to (d-3)-branes. In the resulting model, the connection is flat except along the membrane world-sheet, where it has a conical singularity whose strength is proportional to the membrane tension. As a step towards canonically quantizing these models, we show that a basis of kinematical states is given by `membrane spin networks', which are spin networks equipped with extra data where their edges end on a brane.

 

[tom.stoer]

Has this anything to do with NCG a la Connes?

 

[MTd2]

I don't know. I am not even aware if anyone tried...

 

[Careful]

I don't know. I am not even aware if anyone tried...

These exotic statistics are just mental masturbation excercises ... Baez has no idea which physical principles he has to use to derive the statistics. The same goes for Majid and company, it's all just mathematical play based upon the Yang Baxter equation: it's what I teach my 6 year old kid, before he is ready to see the world in its full complexity. :-))

 

[MTd2]

It's really hard to have a nice discussion if you are trolling. Please, tone down.

 

[Careful]

It's really hard to have a nice discussion if you are trolling. Please, tone down.

I thought the discussion was already over, since all answers which are currently known to humanity have been given. And what's wrong with a good pun in these days?

 

[MTd2]

You said those were masturbation exercises and says he is clueless. This must be a joke, right? But a bad one. I raised a discussion point and you come with that.

 

[Careful]

You said those were masturbation exercises and says he is clueless. This must be a joke, right? But a bad one. I raised a discussion point and you come with that.

Ohw this is NO joke, any kid can understand that when you assume (closed) strings to be fundamental degrees of freedom, that the relevant statistics is given by irreducible representations of the braid group - which are again linked to the Yang-Baxter equation. I don't need to work out the mathematics to understand that, so these papers are just formal excercises. However, assuming that strings are fundamental constituents of nature is NOT a physical principle, that's just one particular realization of a theory which you are still looking for which might be appropriate at some energy scales. As far as I am aware, string theorists in those days do not really talk about strings anymore but about some non-perturbative meta construction nobody knows the appropriate mathematical language for.

So yeah, my comments were way justified and correct, but you just don't like them for political reasons.

 

[MTd2]

You seems to be paranoid and trolling. I am out of this thread.

 

[Careful]

You seems to be paranoid and trolling. I am out of this thread.

Bye bye Your intellectual omnipresence shall be missed.

Let me ask a silly question : what type of statistics is according to you commensurable with Lorentz invariance ?

 

[ensabah6]

Hi,

unfortunatey I lost track. I do not understand much reagrding NCG, but I noticed that there seems to be a line of research that tries to harmonize the NCG and the LQG approach, right?

Can anybody here explain the relation between LQG and NQC, the "big picture", not so much focussed on technical details?

What is the intention? Is it something like unification of matter + geometry?

Is there some hint why certain special structures (like the specific NCG models and SU(2) spin networks) have to be used? Why not something else? Is this harmonization of NGC and LQG natural or just introduced by hand? Can one structure be explained via the other one?

Thanks in advance
Tom

http://arxiv.org/abs/1012.0713
Quantum Gravity coupled to Matter via Noncommutative Geometry
Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke
15 pages, 1 figure
(Submitted on 3 Dec 2010)
"We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construction which encodes the kinematics of quantum gravity. The construction is a spectral triple over a configuration space of connections. It involves an algebra of holonomy loops represented as bounded operators on a separable Hilbert space and a Dirac type operator. Semi-classical states, which involve an averaging over points at which the product between loops is defined, are constructed and it is shown that the Dirac Hamiltonian emerges as the expectation value of the Dirac type operator on these states in a semi-classical approximation."

On a Derivation of the Dirac Hamiltonian From a Construction of Quantum Gravity
Authors: Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke
(Submitted on 19 Mar 2010)

Abstract: The structure of the Dirac Hamiltonian in 3+1 dimensions is shown to emerge in a semi-classical approximation from a abstract spectral triple construction. The spectral triple is constructed over an algebra of holonomy loops, corresponding to a configuration space of connections, and encodes information of the kinematics of General Relativity. The emergence of the Dirac Hamiltonian follows from the observation that the algebra of loops comes with a dependency on a choice of base-point. The elimination of this dependency entails spinor fields and, in the semi-classical approximation, the structure of the Dirac Hamiltonian.

Comments: 13 pages, two figures.
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1003.3802v1 [hep-th]

Emergent Dirac Hamiltonians in Quantum Gravity
Authors: Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke
(Submitted on 12 Nov 2009)

Abstract: We modify the construction of the spectral triple over an algebra of holonomy loops by introducing additional parameters in form of families of matrices. These matrices generalize the already constructed Euler-Dirac type operator over a space of connections. We show that these families of matrices can naturally be interpreted as parameterizing foliations of 4-manifolds. The corresponding Euler-Dirac type operators then induce Dirac Hamiltonians associated to the corresponding foliation, in the previously constructed semi-classical states.

Comments: one figure
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:0911.2404v1 [hep-th]

On Semi-Classical States of Quantum Gravity and Noncommutative Geometry
Authors: Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke, Ryszard Nest
(Submitted on 31 Jul 2009)

Abstract: We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated as a spectral triple over holonomy loops. The semi-classical limit of the spectral triple gives the Dirac Hamiltonian in 3+1 dimensions. Also, time-independent lapse and shift fields emerge from the semi-classical states. Our analysis shows that the model might contain fermionic matter degrees of freedom.
The semi-classical analysis presented in this paper does away with most of the ambiguities found in the initial semi-finite spectral triple construction. The cubic lattices play the role of a coordinate system and a divergent sequence of free parameters found in the Dirac type operator is identified as a certain inverse infinitesimal volume element.

Comments: 31 pages, 10 figures
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:0907.5510v1 [hep-th]

Holonomy Loops, Spectral Triples & Quantum Gravity
Authors: Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest
(Submitted on 24 Feb 2009)

Abstract: We review the motivation, construction and physical interpretation of a semi-finite spectral triple obtained through a rearrangement of central elements of loop quantum gravity. The triple is based on a countable set of oriented graphs and the algebra consists of generalized holonomy loops in this set. The Dirac type operator resembles a global functional derivation operator and the interaction between the algebra of holonomy loops and the Dirac type operator reproduces the structure of a quantized Poisson bracket of general relativity. Finally we give a heuristic argument as to how a natural candidate for a quantized Hamiltonian might emerge from this spectral triple construction.

Comments: 24 pages, 7 figures, based on talk given by J.M.G. at the QG2 conference, Nottingham, juli 2008; at the QSTNG conference in Rome in sept/oct 2008; at the AONCG conference, Canberra, dec. 2008
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
Journal reference: Class.Quant.Grav.26:165001,2009
DOI: 10.1088/0264-9381/26/16/165001
Cite as: arXiv:0902.4191v1 [hep-th]

On Spectral Triples in Quantum Gravity I
Authors: Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest
(Submitted on 13 Feb 2008)

Abstract: This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator. The interaction between the Dirac operator and the algebra reproduces the Poisson structure of General Relativity. Moreover, the associated Hilbert space corresponds, up to a discrete symmetry group, to the Hilbert space of diffeomorphism invariant states known from Loop Quantum Gravity. Correspondingly, the square of the Dirac operator has, in terms of canonical quantum gravity, the form of a global area-squared operator. Furthermore, the spectral action resembles a partition function of Quantum Gravity. The construction is background independent and is based on an inductive system of triangulations. This paper is the first of two papers on the subject.

Comments: 84 pages, 8 figures
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
DOI: 10.1088/0264-9381/26/6/065011
Cite as: arXiv:0802.1783v1 [hep-th]


Intersecting Connes Noncommutative Geometry with Quantum Gravity
Authors: Johannes Aastrup, Jesper M. Grimstrup
(Submitted on 18 Jan 2006)

Abstract: An intersection of Noncommutative Geometry and Loop Quantum Gravity is proposed. Alain Connes' Noncommutative Geometry provides a framework in which the Standard Model of particle physics coupled to general relativity is formulated as a unified, gravitational theory. However, to this day no quantization procedure compatible with this framework is known. In this paper we consider the noncommutative algebra of holonomy loops on a functional space of certain spin-connections. The construction of a spectral triple is outlined and ideas on interpretation and classical limit are presented.

Comments: 19 pages, 4 figures
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Journal reference: Int.J.Mod.Phys.A22:1589-1603,2007
DOI: 10.1142/S0217751X07035306
Report number: NORDITA-2006-1
Cite as: arXiv:hep-th/0601127v1


Spectral triples of holonomy loops
Authors: Johannes Aastrup, Jesper M. Grimstrup
(Submitted on 31 Mar 2005 (v1), last revised 18 Jan 2006 (this version, v2))

Abstract: The machinery of noncommutative geometry is applied to a space of connections. A noncommutative function algebra of loops closely related to holonomy loops is investigated. The space of connections is identified as a projective limit of Lie-groups composed of copies of the gauge group. A spectral triple over the space of connections is obtained by factoring out the diffeomorphism group. The triple consist of equivalence classes of loops acting on a separable hilbert space of sections in an infinite dimensional Clifford bundle. We find that the Dirac operator acting on this hilbert space does not fully comply with the axioms of a spectral triple.

Comments: 36 pages, material added, references added, version accepted for publication in Communications in Mathematical Physics
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Journal reference: Commun.Math.Phys. 264 (2006) 657-681
DOI: 10.1007/s00220-006-1552-5
Cite as: arXiv:hep-th/0503246v2

 

[tom.stoer]

Thanks for searching arxiv! Any recommendation from your side where to start reading?

 

[ensabah6]

Thanks for searching arxiv! Any recommendation from your side where to start reading?

http://arxiv.org/abs/hep-th/0601127

Intersecting Connes Noncommutative Geometry with Quantum Gravity
Authors: Johannes Aastrup, Jesper M. Grimstrup
(Submitted on 18 Jan 2006)

Abstract: An intersection of Noncommutative Geometry and Loop Quantum Gravity is proposed. Alain Connes' Noncommutative Geometry provides a framework in which the Standard Model of particle physics coupled to general relativity is formulated as a unified, gravitational theory. However, to this day no quantization procedure compatible with this framework is known. In this paper we consider the noncommutative algebra of holonomy loops on a functional space of certain spin-connections. The construction of a spectral triple is outlined and ideas on interpretation and classical limit are presented.

Comments: 19 pages, 4 figures
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Journal reference: Int.J.Mod.Phys.A22:1589-1603,2007
DOI: 10.1142/S0217751X07035306
Report number: NORDITA-2006-1
Cite as: arXiv:hep-th/0601127v1


On Spectral Triples in Quantum Gravity I
Authors: Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest
(Submitted on 13 Feb 2008)

Abstract: This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator. The interaction between the Dirac operator and the algebra reproduces the Poisson structure of General Relativity. Moreover, the associated Hilbert space corresponds, up to a discrete symmetry group, to the Hilbert space of diffeomorphism invariant states known from Loop Quantum Gravity. Correspondingly, the square of the Dirac operator has, in terms of canonical quantum gravity, the form of a global area-squared operator. Furthermore, the spectral action resembles a partition function of Quantum Gravity. The construction is background independent and is based on an inductive system of triangulations. This paper is the first of two papers on the subject.

Comments: 84 pages, 8 figures
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
DOI: 10.1088/0264-9381/26/6/065011
Cite as: arXiv:0802.1783v1 [hep-th]

 

[Careful]

As far a I remember, similar ideas have been worked out way before by Ioannis Raptis. My memory tells me that all these constructions are just quite ad hoc and not very deep at all. The major problem is that you have to work with regular lattices in order to make sense of this : by this I mean the following, for an irregular graph (just like happens in causal set theory for example) one just does not even know what the ''local dimension'' is precisely. Dimension is a dynamical variable in graph theories and therefore, one does not predispose of the right dimension of the clifford algebra at any vertex either. This is one serious problem or such theories: I am pretty sure the authors do not adress this issue, I wonder whether they even thought about this. So, apart from even this issue, one has to be extremely careful about chosing the right Dirac operator such that no severe non-local effects arise. I presume that what these authors do is work on something they imagine to be an euclidean lattice and they brutally violate Lorentz invariance, so their Dirac operator is an euclidean one. Even the construction of something like a good d'Alembertian on causal sets is a daunting task and seems to depend upon some notion of dimension. So yeah, I am pretty sure these things are just unphysical, mathematical excercises. I still could utter other objections against this kind of ideas but this is quite sufficient for now.

It looks pretty, but it most likely ain't very good.

 

[atyy]

There is very little published relationship between LQG in any form and NCG.

There is some relationship between LQG and some form of NCFT. This is still being explored.
http://arxiv.org/abs/hep-th/0512113
http://arxiv.org/abs/0903.3475

However, marcus pointed out that John Barrett is working on LQG and NCG. (I don't understand a word of this!)
http://johnwbarrett.wordpress.com/talks/

 

[Careful]

However, marcus pointed out that John Barrett is working on LQG and NCG. (I don't understand a word of this!)
http://johnwbarrett.wordpress.com/talks/

I watched the first 25 minutes of the video of his talk ... nothing I didn't know. These people just look for motivations to introduce abstract structures like braided monodial categories into physics because some interpretation of phenomena allows them to do so. The whole difference between the 3-d case which he shows around minut 20 and the 4-d case is that in 4-d the geometry has local degrees of freedom. In 3-d you can still calculate the physics using these pretty diagrams (and still understand what you are doing because you only have a finite number of physical degrees of freedom) but in 4-d you can pray to god and look at the heavens, but that is not going to help you.

 

[atyy]

I watched the first 25 minutes of the video of his talk ... nothing I didn't know. These people just look for motivations to introduce abstract structures like braided monodial categories into physics because some interpretation of phenomena allows them to do so. The whole difference between the 3-d case which he shows around minut 20 and the 4-d case is that in 4-d the geometry has local degrees of freedom. In 3-d you can still calculate the physics using these pretty diagrams (and still understand what you are doing because you only have a finite number of physical degrees of freedom) but in 4-d you can pray to god and look at the heavens, but that is not going to help you.

But who's to say the devil won't help?

 

[Careful]

But who's to say the devil won't help?

 

[marcus]

Hi,

unfortunately I lost track. I do not understand much regarding NCG, but I noticed that there seems to be a line of research that tries to harmonize the NCG and the LQG approach, right?

Can anybody here explain the relation between LQG and NQC, the "big picture", not so much focussed on technical details?

What is the intention? Is it something like unification of matter + geometry?

Is there some hint why certain special structures (like the specific NCG models and SU(2) spin networks) have to be used? Why not something else? Is this harmonization of NGC and LQG natural or just introduced by hand? Can one structure be explained via the other one?

Thanks in advance
Tom

IMHO it's good to know something about current developments in NCG. You are right that a number of people are thinking how to connect NCG with LQG, but this should probably not be one's immediate focus.

I think one should at first approach NCG a little bit by itself. One way to get an overview is to look at this recent paper by Mairi Sakellariadou (King's College London):

http://arxiv.org/abs/1010.4518
Cosmological consequences of the noncommutative spectral geometry as an approach to unification
Mairi Sakellariadou
8 pages, Invited talk at the 14th Conference on recent Developments in gravity (NEB 14), Ioannina, Greece, 8-11 June 2010
(Submitted on 21 Oct 2010)
"Noncommutative spectral geometry succeeds in explaining the physics of the Standard Model of electroweak and strong interactions in all its details as determined by experimental data. Moreover, by construction the theory lives at very high energy scales, offering a natural framework to address early universe cosmological issues. After introducing the main elements of noncommutative spectral geometry, I will summarise some of its cosmological consequences and discuss constraints on the gravitational sector of the theory."

In this way one is introduced to NCG, better called "spectral geometry", in a practical empirical light---or anyway more so that way to the extent possible, not merely seen abstractly.

===The rest is just background. Not suggested reading. I only suggest glancing at 1010.4518 as a start==

Here is the researcher's webpage:
http://www.kcl.ac.uk/schools/nms/physics/people/academic/sakellariadou/

It seems to me that Sakellariadou is not specifically a NCG or Loop person, she has published about string and brane, she has taken a critical approach to Loop in #11 here, more the broad scope phenomenologist with an EU (early universe) focus. Some sample recent papers:

5. arXiv:1005.4279
Constraining the Noncommutative Spectral Action via Astrophysical Observations
William Nelson, Joseph Ochoa, Mairi Sakellariadou
Comments: 5 pages; slightly shorter version to match the one will appear in Phys. Rev. Lett
Journal-ref: Phys.Rev.Lett.105:101602,2010

6. arXiv:1005.4276
Gravitational Waves in the Spectral Action of Noncommutative Geometry
William Nelson, Joseph Ochoa, Mairi Sakellariadou
Comments: 15 pages, 3 figures
Journal-ref: Phys.Rev.D82:085021,2010

7. arXiv:1005.1188
Inflation in models with Conformally Coupled Scalar fields: An application to the Noncommutative Spectral Action
Michel Buck, Malcolm Fairbairn, Mairi Sakellariadou
Comments: 14 pages, 3 figures Slightly modified version to match the one will appear in Phys.Rev.D
Journal-ref: Phys.Rev.D82:043509,2010

9. arXiv:1001.0161
Phenomenology of loop quantum cosmology
Mairi Sakellariadou
Comments: 16 pages, 3 figures; Invited talk in the First Mediterranean Conference on Classical and Quantum Gravity (Crete, Greece)
Journal-ref: J. Phys.: Conf. Ser. Vol.222:012027, 2010

10. arXiv:0910.0181
Cosmological consequences of the NonCommutative Geometry Spectral Action
Mairi Sakellariadou
Comments: 7 pages, LaTeX. Invited talk at the XXV Max Bonn Symposium "Physics at the Planck Scale", in Wroclaw (Poland), 29th June-3rd July 2009. To appear in the Conference Proceedings

11. arXiv:0907.4057
Unstable Anisotropic Loop Quantum Cosmology
William Nelson, Mairi Sakellariadou
Comments: 13 pages, 2 figures
Journal-ref: Phys.Rev.D80:063521,2009

If she thinks she sees a flaw or an instability in your model she will point it out forcefully. She does not have brand loyalty. Certainly this can be constructive if not always comfortable.

 

[marcus]

... I noticed that there seems to be a line of research that tries to harmonize the NCG and the LQG approach...

That's certainly right---there was a workshop at Oberwolfach in 2010 about that, organized by one of Alain Connes' main collaborators. But it is early days---too early to guess what shape that might take.

If I remember right, Tom Krajewski (one of the Luminy LQG group) was at that workshop.

I see the situation as still very amorphous. What suggests itself to me is that if NCG and LQG are going to meet, they will meet in the early universe. (Sakellariadou calls it the EU, five syllables is too much for such a busy person )

Both LQG and NCG say things about the EU, and both seem to have gotten the interest of phenomenologists----like Aurelien Barrau, like Wen Zhao, like Mairi Sakellariadou.

The EU begins to look like the main empirical arena for QG---the place where theories mean something.

So far what we think of as LQG could be called "LQG-Lite". The version where matter is at best rudimentary---scalar field matter. Nevertheless it seems to be an efficient, even powerful, theory---able to make predictions and get the attention of the EU phenomenology people.

We already see Rovelli working on applying the full "LQG-Lite" theory to cosmology---so it is no longer dependent on the symmetry-reduced old version of "LQC". We see spinfoam cosmology. Now we should be looking out for spinfoam cosmology with matter.

Matter will probably be added incrementally, step by step----a gradual approach to unification rather than attempting it in a single blow or "in one fell swoop" as the expression goes. Lewandowski already discussed this incremental way of proceeding towards unification---in one of his 2010 papers.

Barrau has proposed to work on understanding LQG and inflation jointly. Loop gives inflation the naturalness it needs and inflation gives loop the testability it needs. Each can help illuminate the other.

So one should look back and see what Sakellariadou has said about NCG and inflation---that is, if one is interested in comprehending how NCG and LQG might eventually relate.

Just risky speculations on my part. But I don't know how else to answer the original question about LQG and NCG. Maybe I will think of something more helpful later and add it on here.

Wen Zhao's page:
http://www.astro.cardiff.ac.uk/contactsandpeople/?page=full&id=455

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

More about early universe phenomenology (as it relates to qg):
https://www.physicsforums.com/showthread.php?p=3028777#post3028777

 

[Careful]

(Sakellariadou calls it the EU, five syllables is too much for such a busy person )

Nobody is that busy (although many people want to give the impression they are) More likely it is just a marketing devise to ''compare'' the early universe to the european union, gives an important edge to it.