Reinforcing the Loop Program: 3 New Papers

[marcus]

Three new papers appeared this week which strongly reinforce the Loop program.

1. The Ashtekar Sloan paper shows inflation favors the Loop early universe. Loop cosmology makes an adequate (60 e-folds) inflation episode overwhelmingly more likely, without special tuning, than is classically the case.

2. The Barrett Fairbairn Hellmann paper is the third this year from Barrett's group at Nottingham, establishing the classical GR limit for Loop's new covariant version. Page 15:

"...The question of whether the Regge equations of motion appear correctly from the state sum models is an important question...For the Lorentzian theory however, the situation is much simpler and clearer... Thus the Lorentzian gravity configurations can only be perturbed to other Lorentzian gravity configurations. This means that the correct Regge-like gluing of 4-simplexes is preserved under perturbations. Thus perturbations can lead only to the Regge equations of motion. Thus the state sum model does indeed contain asymptotic terms which approximate general relativity."

3. In the paper by Bianchi Magliaro Perini, it looks like they have hit on a satisfactory way to define coherent semiclassical Loop states. This has been a focus of considerable effort by several groups. Page 9:

"...A surprising property of the states we have discussed is that they bring together so many (apparently conflicting) ideas that have been proposed in the search for semiclassical states in Loop Quantum Gravity. We consider this convergence to be a measure of the robustness of the theory."

 

[marcus]

Loop stronger: Ashtekar Sloan; Barrett Fairbairn Hellmann; Bianchi Magliaro Perin

MTd2 spotted one or more of these and entered them in our bibliography thread. I am going to copy the abstracts here just to have something definite to refer to, and then comment on the first of the three---the one by Ashtekar and Sloan. The result seems to have been something of a surprise. One did not expect such a stark difference, since outside the quantum regime (the very high density early universe) Loop cosmology behaves very much like that specified by general relativity---the context in which inflation scenarios are normally constructed. Why should there be a sharp contrast in the way inflation proceeds? Why should Loop cause an extended duration of inflation, adequate to bring about the conditions which we observe today and which motivate the inflationary assumption?

http://arxiv.org/abs/0912.4093
Loop quantum cosmology and slow roll inflation
Abhay Ashtekar, David Sloan
8 pages, 1 table
(Submitted on 21 Dec 2009)
"In loop quantum cosmology the big bang is replaced by a quantum bounce which is followed by a robust phase of super-inflation. We show that this phase has an unforeseen implication: in presence of suitable inflationary potentials it funnels all dynamical trajectories to conditions which virtually guarantee a slow roll inflation with more than 68 e-foldings, without any input from the pre-big bang regime. This is in striking contrast to the situation in general relativity where it has been argued that the a priori probability of obtaining a slow roll inflation with N e-foldings is suppressed by a factor Exp(-3N)."

http://arxiv.org/abs/0912.4907
Quantum gravity asymptotics from the SU(2) 15j symbol
John W. Barrett, Winston J. Fairbairn, Frank Hellmann
17 pages
(Submitted on 24 Dec 2009)
The asymptotics of the SU(2) 15j symbol are obtained using coherent states for the boundary data. The geometry of all non-suppressed boundary data is given. For some boundary data, the resulting formula is interpreted in terms of the Regge action of the geometry of a 4-simplex in 4-dimensional Euclidean space. This asymptotic formula can be used to derive and extend the asymptotics of the spin foam amplitudes for quantum gravity models. The relation of the SU(2) Ooguri model to these quantum gravity models and their continuum Lagrangians is discussed.

http://arxiv.org/abs/0912.4054
Coherent spin-networks
Eugenio Bianchi, Elena Magliaro, Claudio Perini
11 pages
(Submitted on 20 Dec 2009)
"In this paper we discuss a proposal of coherent states for Loop Quantum Gravity. These states are labeled by a point in the phase space of General Relativity as captured by a spin-network graph. They are defined as the gauge invariant projection of a product over links of Hall's heat-kernels for the cotangent bundle of SU(2). The labels of the state are written in terms of two unit-vectors, a spin and an angle for each link of the graph. The heat-kernel time is chosen to be a function of the spin. These labels are the ones used in the Spin Foam setting and admit a clear geometric interpretation. Moreover, the set of labels per link can be written as an element of SL(2,C). Therefore, these states coincide with Thiemann's coherent states with the area operator as complexifier. We study the properties of semiclassicality of these states and show that, for large spins, they reproduce a superposition over spins of spin-networks with nodes labeled by Livine-Speziale coherent intertwiners. Moreover, the weight associated to spins on links turns out to be given by a Gaussian times a phase as originally proposed by Rovelli."

 

[marcus]

A significant background factor to the Ashtekar Sloan paper is a 2006 result by Gary Gibbons and Neil Turok, both at Cambridge at the time. Turok is an eminent cosmologist who recently took over the directorship of Perimeter Institute. Gibbons was Hawking's student and collaborator. He is known both for his work in relativity (black hole radiation, etc) and later in string theory.

There is a long history of worry by some in the string community that inflation might be incompatible with string's compact extra dimensions, and of attempts to find alternatives, so that inflation could be dispensed with. In other words, to find other ways of addressing cosmic puzzles that inflation was intended (or just happens) to resolve. Steinhardt and Turok have a series of papers describing a speculative clashing brane scenario which some think might fit reality without inflation.

Research arising in this context, and separately from Loop concerns, has spotlighted potentially severe problems with inflation. Here's one. Essentially it says getting inflation to last for the required 60 e-foldings is incredibly improbable and requires an incredible degree of fine-tuning.

http://arxiv.org/abs/hep-th/0609095
The Measure Problem in Cosmology
G.W. Gibbons, Neil Turok
22 pages, 6 figures
(Submitted on 13 Sep 2006, last revised 2 Jan 2007)
"The Hamiltonian structure of general relativity provides a natural canonical measure on the space of all classical universes,...One such quantity is the probability of inflation in simple scalar field models. We find that, according to our implementation of the canonical measure, the probability for N e-folds of inflation in single-field, slow-roll models is suppressed by of order exp(-3N) and we discuss the implications of this result."

Inflation scenarios require at least N = 60 e-foldings to produce satisfactory results, so 3N=180 and the probability of a satisfactory inflation comes out to be a ridiculously tiny number like e^-180.

On the other hand, Loop cosmology involves an extremely brief "quantum regime" episode right around the bounce, when geometry and gravity behave non-classically. Ashtekar and Sloan discovered the surprising result that this brief quantum episode makes all the difference! Unexpectedly it causes the single-field graviton to be set up for protracted expansion.

So Ashtekar and Sloan basically took off from Gary Gibbons and Neil Turok's 2006 result.

 

[ensabah6]

Can we be sure that the results of LQC will carry over to full LQG?

 

[marcus]

No. Nothing like that is absolutely certain. In order to judge the probability you need to have been paying attention to the work that appeared in the past year connecting LQG with LQC.
Relaxing LQC assumptions of isotropy and homogeneity (to make it more like LQG) and then lately reformulating LQC using spinfoam. The connection between the two is an area where progress is being made. You have to be prepared to watch how that effort is proceeding and draw your own conclusions.

Let me know if you want links to recent research connecting LQC with LQG.

 

[ensabah6]

No. Nothing like that is absolutely certain. In order to judge the probability you need to have been paying attention to the work that appeared in the past year connecting LQG with LQC.
Relaxing LQC assumptions of isotropy and homogeneity (to make it more like LQG) and then lately reformulating LQC using spinfoam. The connection between the two is an area where progress is being made. You have to be prepared to watch how that effort is proceeding and draw your own conclusions.

Let me know if you want links to recent research connecting LQC with LQG.

Might change dramatically in the next year :)

BTW I did see Sabin "bee" Hoss.. new LQC & BH -- I knew she worked in physics but not in LQG (as opposed to strings or particles)

Did Rovelli ever publish that Spinfoam in 4D semiclassical analysis you predicted way back when? :)

 

[marcus]

...Did Rovelli ever publish that Spinfoam in 4D semiclassical analysis you predicted way back when? :)

I'm not sure exactly what that was but apparently he didn't have to! Bianchi, Magliaro, and Perini are his current PhD students. They are working for Rovelli and obviously taking care of business

3. In the paper by Bianchi Magliaro Perini, it looks like they have hit on a satisfactory way to define coherent semiclassical Loop states. This has been a focus of considerable effort by several groups. Page 9:

"...A surprising property of the states we have discussed is that they bring together so many (apparently conflicting) ideas that have been proposed in the search for semiclassical states in Loop Quantum Gravity. We consider this convergence to be a measure of the robustness of the theory."

My guess is that his series of lectures at the September Corfu School (which I believe is what I was talking about) covered results obtained with his PhD students and also results by Barrett's group tending to confirm the classical limit like this by Barrett Fairbairn Hellmann.

http://arxiv.org/abs/0912.4907
Quantum gravity asymptotics from the SU(2) 15j symbol
John W. Barrett, Winston J. Fairbairn, Frank Hellmann
17 pages
(Submitted on 24 Dec 2009)...

http://arxiv.org/abs/0912.4054
Coherent spin-networks
Eugenio Bianchi, Elena Magliaro, Claudio Perini
11 pages
(Submitted on 20 Dec 2009)
"In this paper we discuss a proposal of coherent states for Loop Quantum Gravity. These states are labeled by a point in the phase space of General Relativity as captured by a spin-network graph. ... We study the properties of semiclassicality of these states and show that, for large spins, they reproduce a superposition over spins of spin-networks with nodes labeled by Livine-Speziale coherent intertwiners. Moreover, the weight associated to spins on links turns out to be given by a Gaussian times a phase as originally proposed by Rovelli."

BTW Fairbairn and Hellmann are former students of Rovelli at Marseille, who then went on to join Barrett's group in the UK. At this point it looks like all one enterprise, so it doesn't matter greatly who signs the papers.

You reminded me to check the predictions made as of the end of last year, and to make some new ones for 2010! I remember back a while, early this year, we had a thread called something like "What to expect from Loop in 2009." We should post something comparable now.

Here is the old "what to expect thread":
https://www.physicsforums.com/showthread.php?t=296341

 

[ensabah6]

I would say it is reasonable to expect at a minimum the graviton two-point function to be calculated by September, but actually I expect considerably more to have happened by then. And I don't expect the papers appearing between now and then to be all by Rovelli

Was what I was alluding to.

Given that LHC is online and is capable of collisions energies higher than TEV and may discover SUSY a couple years from now (or may not...) I'm surprised there aren't more SUSY-LQG papers. I'm well aware that LQG can incorporate SUSY, still, it's not clear why researchers should prefer LQG-SUSY over strings should LHC find evidence of SUSY. Perhaps LQG'r are gambling SUSY won't be found at LHC. I infer that the non-observation of SUSY or higher dimensions has been a major impetus for LQG research.

I wonder how SUSY, if it does exist, and its breaking, affect the results of LQG and LQC.

 

[marcus]

Was what I was alluding to.
...

As far as that goes (graviton propagator, two-point function...) see already the paper that appeared in May 2009:

http://arxiv.org/abs/0905.4082

That took care of my minimum prediction. But as you saw, they went on beyond that.

Here are some interesting quotes from page 24:

"9. The LQG propagator can be compared to the graviton propagator. This is done in section 8. We find that the LQG propagator has the correct scaling behaviour. The three parameters α_k appearing in the semiclassical boundary state can be chosen so that the tensorial structure of the LQG propagator matches with the one of the graviton propagator.

The matching is obtained in the limit γ → 0 with γ j₀ fixed.

Now we would like to put these results in perspective with respect to the problem of extracting the low energy regime of loop quantum gravity and spin foams (see in particular [50]). Deriving the LQG propagator at the level of a single spin foam vertex is certainly only a first step. Within the setting of a vertex expansion, an analysis of the LQG propagator for a finite number of spinfoam vertices is needed. Some of the techniques developed in this paper generalize to this more general case. In particular superpositions of coherent spin networks can be used to build semiclassical states peaked on the intrinsic and the extrinsic curvature of an arbitrary boundary Regge geometry..."

Here they are looking ahead to what they have now done in their most recent paper, mentioned in the title of this thread.
==================

Their May 2009 paper is kind of nice, so I will paste the abstract in case anyone wants to take a look:

http://arxiv.org/abs/0905.4082
LQG propagator from the new spin foams
Eugenio Bianchi, Elena Magliaro, Claudio Perini
28 pages; Nuclear Physics B822:245-269,2009
(Submitted on 25 May 2009)
"We compute metric correlations in loop quantum gravity with the dynamics defined by the new spin foam models. The analysis is done at the lowest order in a vertex expansion and at the leading order in a large spin expansion. The result is compared to the graviton propagator of perturbative quantum gravity."

We probably should take the two papers together, this one and also the December 2009 one that I already noted at the beginning of the thread. The work of Barrett's group is also important to establishing the proper large-scale limit.

 

[MTd2]

Just a reminder. Do not forget about a thread about the best papers of Q4 and the year.

 

[marcus]

Thanks for the reminder! I expect there might be something coming out on the 30th, so I plan to wait until then to do the Q4 poll.
The poll for the whole year is going to be interesting! there were so many outstanding papers in 2009.

 

[ensabah6]

http://arxiv.org/abs/0912.4093
Loop quantum cosmology and slow roll inflation
Abhay Ashtekar, David Sloan
8 pages, 1 table
(Submitted on 21 Dec 2009)
"In loop quantum cosmology the big bang is replaced by a quantum bounce which is followed by a robust phase of super-inflation. We show that this phase has an unforeseen implication: in presence of suitable inflationary potentials it funnels all dynamical trajectories to conditions which virtually guarantee a slow roll inflation with more than 68 e-foldings, without any input from the pre-big bang regime. This is in striking contrast to the situation in general relativity where it has been argued that the a priori probability of obtaining a slow roll inflation with N e-foldings is suppressed by a factor Exp(-3N)."

You might be interested in something by Princeton's Paul Steinhardt (who has contributed both to string, back in its boom years, and to inflation, and to the ekpyrotic alternative.
He concluded that inflation wasn't really very compatible with compactified extra dimensions and has started proving a kind of "no-go". Either inflation is no-go, or else rolled up extra dimensions are a no-go.
http://arxiv.org/abs/0811.1614
Dark Energy, Inflation and Extra Dimensions
Paul J. Steinhardt, Daniel Wesley
26 pages, Physical Review D
(Submitted on 11 Nov 2008 )
"We consider how accelerated expansion, whether due to inflation or dark energy, imposes strong constraints on fundamental theories obtained by compactification from higher dimensions. For theories that obey the null energy condition (NEC), we find that inflationary cosmology is impossible for a wide range of compactifications; and a dark energy phase consistent with observations is only possible if both Newton's gravitational constant and the dark energy equation-of-state vary with time. If the theory violates the NEC, inflation and dark energy are only possible if the NEC-violating elements are inhomogeneously distributed in the compact dimensions and vary with time in precise synchrony with the matter and energy density in the non-compact dimensions. Although our proofs are derived assuming general relativity applies in both four and higher dimensions and certain forms of metrics, we argue that similar constraints must apply for more general compactifications."

He works both in the NEC case and in the NEC-violating case. Gets interesting results either way.

What are the relative implications of Paul J. Steinhardt, Daniel Wesley on string and inflation vs Abhay Ashtekar, David Sloan loop and inflation?

 

[marcus]

'Sabah said, but then edited out:

We have a string theorist arguing that inflation is strongly disfavored by string theory, and loop theorist arguing that slow roll inflation, consistent with known observation, is a generic feature of LQC.​

At present I wouldn't call Steinhardt a string theorist. He strikes me as being part of the recent exodus of top people---those who gradually lost interest after 2003, or whose attention is shifting.

As I said, Steinhardt used to be very interested in string. Back in the 1990s he did string research and worked on string-inspired cosmology. In the early 2000s, he and Turok set forth the brane-clash (ekpyrotic) alternative to inflation, which was a string-friendly project since they suspected string extra dimensions couldn't gracefully handle inflation.

But now I would expect that Steinhardt willing to consider inflation as a real possibility. So I would put it differently. His paper means that string is disfavored by inflation.

Certainly extra dimensions are not completely ruled out, but thanks to his theorems they become more awkward to assume, more problematical, in the context of either inflation or dark energy.

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

About LQC and inflation. We've known for years that an inflation episode was generic in Loop cosmology. Even without any "inflaton" field, or any exotic physics you inevitably get a brief period of exponential expansion.

As I recall there were papers about this as early as 2004. But the natural LQC inflation did not necessarily achieve 60 efolds. It didn't last long enough. It was not enough to explain the puzzles that inflation was invented to explain.

So what Ashtekar did recently was to say "OK let's take over a inflaton field from the inflation scenarios. If they can do it, so can we." So in effect he took the simplest most basic inflaton available and put it into the LQC picture and studied the result.

 

[ensabah6]

No. Nothing like that is absolutely certain. In order to judge the probability you need to have been paying attention to the work that appeared in the past year connecting LQG with LQC.
Relaxing LQC assumptions of isotropy and homogeneity (to make it more like LQG) and then lately reformulating LQC using spinfoam. The connection between the two is an area where progress is being made. You have to be prepared to watch how that effort is proceeding and draw your own conclusions.

Let me know if you want links to recent research connecting LQC with LQG.

I do have one ?
If we take the full LQG, make assumptions of isotropy and homogeneity, add matter, does it behave like LQC?