# Tests of LQG in cosmology (proposals, prospects etc)

1. Feb 22, 2009

### marcus

In the last couple of years there'v been several papers on this, often by people I hadn't heard of before. The question came up in another thread "can you summarize in a single post" the various ideas being discussed? Personally I couldn't but I can dig up some links. Toss them out for you to look at. Maybe I can evaluate and organize some later. Busy this afternoon with other stuff, though.

I only want 2007-2009 stuff. Here's one that was accepted by Physical Review Letters:
http://arxiv.org/abs/0902.0928
Chaplygin inflation in loop quantum cosmology
Xin Zhang, Jingfei Zhang, Jinglei Cui, Li Zhang
6 pages, accepted for publication in Mod. Phys. Lett. A
(Submitted on 5 Feb 2009)
"In this paper we discuss the inflationary universe in the context of a Chaplygin gas equation of state within the framework of the effective theory of loop quantum cosmology. Under the slow-roll approximation, we calculate the primordial perturbations for this model. We give the general expressions of the scalar spectral index, its running, and the tensor-to-scalar ratio, etc. For the chaotic inflation with a quadratic potential, using the WMAP 5-year results, we determine the parameters of the Chaplygin inflation model in loop quantum cosmology. The results are consistent with the WMAP observations."

Here's one by Jack Mielczarek of whom I have a good impression from past work
http://arxiv.org/abs/0902.2490
Tensor power spectrum with holonomy corrections in LQC
Jakub Mielczarek
13 pages, 13 figures
(Submitted on 14 Feb 2009)
"In this paper we consider tensor perturbations produced at a bounce phase in presence of the holonomy corrections. Here bounce phase and holonomy corrections originate from Loop Quantum Cosmology. We re-derive formulas for the of the corrections for the model with a scalar field content. Background dynamics with a free scalar field and multi-fluid potential are considered. Both analytical approximations as well as numerical investigations were performed. We have found analytical solutions on super-horizontal and sub-horizontal regimes and derived corresponding power spectra. Also occupation number $$n_{\bf k}$$ and parameter $$\Omega_{\text{gw}}$$ were derived in sub-horizontal limit, leading to its extremely low present value. Final results are numerical power spectra of the gravitational waves produced in the presence of quantum holonomy corrections. In the super-horizontal limit the obtained spectrum behaves like $$\mathcal{P}_T \propto k^3(C_1+\log^2(k))$$ while on sub-horizontal scales it exhibits oscillations around $$\mathcal{P}_T \propto k^2$$. These results can be directly applied as initial conditions for the inflationary modes. We mention possible resulting observational features of the CMB in particular BB spectrum of polarization."

http://arxiv.org/abs/0810.0104
The gravitational wave background from super-inflation in Loop Quantum Cosmology
E. J. Copeland, D. J. Mulryne, N. J. Nunes, M. Shaeri
8 pages, 3 figures
(Submitted on 1 Oct 2008)

"We investigate the behaviour of tensor fluctuations in Loop Quantum Cosmology, focusing on a class of scaling solutions which admit a near scale-invariant scalar field power spectrum. We obtain the spectral index of the gravitational field perturbations, and find a strong blue tilt in the power spectrum with $$n_t \approx 2$$. The amplitude of tensor modes are, therefore, suppressed by many orders of magnitude on large scales compared to those predicted by the standard inflationary scenario where $$n_t \approx 0$$."

Sorry, there's a bunch more but I've other things I have to do. Will try to add to this later...

Last edited: Feb 22, 2009
2. Feb 22, 2009

### Haelfix

Hmm, these are all model specific. Also cosmology oriented, which have the general drawback that they have yet to be embedded into the standard theories precisely. Instead they're mostly LQG "inspired".

I am unaware of a generic universal prediction across all models. Even something like the constant in front of the black hole area-entropy law seems to be in dispute in the literature.

3. Feb 22, 2009

### BenTheMan

I also think that using inflation as a test is a bit shaky, seeing as how you're only predicting 2 numbers, and the potentials are pretty well-tuned.

4. Feb 23, 2009

### cristo

Staff Emeritus
Well, the title of the thread is "Tests of LQG in cosmology"!

I don't know much about this, but the third paper doesn't seem to really be a test; at least not of LQG. A blue tensor spectrum means we shouldn't see any gravitational waves. If we do, then it presumably only rules out this model of superinflation in LQC. Of course, if all inflationary models in LQC generically predict a blue tensor spectrum, then this is a much stronger test but I'm not sure whether that's true or not. Perhaps marcus or others have more of an idea?

5. Feb 23, 2009

### marcus

My aim here is to educate us about the different ideas for testing LQG (and other QG) by observation of stuff at cosmological scale. In other words, proposals, ideas, prospects. It is a new growing area of phenomenology research (phenomenology means investigating potential ways of testing models---before the actual hardware is committed.)

The question came up "can you summarize this stuff in one post"? Well no, there are too many things going on, too many ideas on the table. But for starters I can lay out some papers, and then hopefully we can look them over and see what are the interesting ideas for testing. Judge what the good prospects are and then summarize.

http://arxiv.org/abs/0806.0339
Quantum Gravity Phenomenology
Giovanni Amelino-Camelia
82 pages
(Submitted on 2 Jun 2008)
"I review the present status of the development of Quantum Gravity Phenomenology. Among the accomplishments of this young research area I stress in particular the significance of studies which established that some appropriate data analyses provide sensitivity to effects introduced genuinely at the Planck scale. The objective of testing/falsifying theories that provide comprehensive solutions to the quantum-gravity problem appears to be still rather far, but we might soon be in a position to investigate some 'falsifiable quantum-gravity theories of not everything'."

I hope this review article will be useful to anyone who is actually interested in potential ways to test LQG.

Here are some more papers:

http://arxiv.org/abs/0807.0160
Loop Quantum Cosmology corrections to inflationary models
Michal Artymowski, Zygmunt Lalak, Lukasz Szulc
16 pages, 1 figure
(Submitted on 1 Jul 2008)

"In the recent years the quantization methods of Loop Quantum Gravity have been successfully applied to the homogeneous and isotropic Friedmann-Robertson-Walker space-times. The resulting theory, called Loop Quantum Cosmology (LQC), resolves the Big Bang singularity by replacing it with the Big Bounce. We argue that LQC generates also certain corrections to field theoretical inflationary scenarios. These corrections imply that in the LQC the effective sonic horizon becomes infinite at some point after the bounce and that the scale of the inflationary potential implied by the COBE normalisation increases. The evolution of scalar fields immediately after the Bounce becomes modified in an interesting way. We point out that one can use COBE normalisation to establish an upper bound on the quantum of length of LQG."

http://arxiv.org/abs/0807.0712
Gravitational waves from the Big Bounce
Jakub Mielczarek
19 pages, 9 figures
(Submitted on 4 Jul 2008)

"In this paper we investigate gravitational waves production during the Big Bounce phase inspired by the Loop Quantum Cosmology. We consider the influence of the holonomy corrections to the equation for tensor modes. We show that they act like additional effective graviton mass, suppressing gravitational waves creation. However, this effects can be treated perturbatively. We investigate the simplified model without these corrections and find its exact analytical solution. For this model we calculate a spectrum of the gravitational waves from the Big Bounce phase. The obtained spectrum decreases to zero for the low energy modes. Based on this observation we indicate that this effect can lead to the low CMB multipoles suppression and gives a potential way to test Loop Quantum Cosmology models. We also consider a scenario with a post-bounce inflationary phase. The obtained power spectrum gives qualitative explanation of the CMB spectra, including low multipoles suppression. This result is a challenge to construct a consistent bounce+inflation model in the Loop Quantum Cosmology."

http://arxiv.org/abs/0810.4330
Loop quantum cosmology and tensor perturbations in the early universe
Gianluca Calcagni, Golam Mortuza Hossain
12 pages. Invited contribution to the special issue of Advanced Science Letters on "Quantum gravity, Cosmology and Black Holes"
(Submitted on 23 Oct 2008)

"We study the tensor modes of linear metric perturbations within an effective framework of loop quantum cosmology. After a review of inverse-volume and holonomy corrections in the background equations of motion, we solve the linearized tensor modes equations and extract their spectrum. Ignoring holonomy corrections, the tensor spectrum is blue tilted in the near-Planckian superinflationary regime and may be observationally disfavoured. However, in this case background dynamics is highly nonperturbative, hence the use of standard perturbative techniques may not be very reliable. On the other hand, in the quasi-classical regime the tensor index receives a small negative quantum correction, slightly enhancing the standard red tilt in slow-roll inflation. We discuss possible interpretations of this correction, which depends on the choice of semiclassical state."

Last edited: Feb 23, 2009
6. Feb 23, 2009

### marcus

Hi cristo! That's an interesting idea. In fact I had noticed that several of the papers mentioned this. But I don't know about all.

Maybe it would help if I gave some general perspective.

What I am seeing are not yet concrete proposals---e.g. requests for telescope time etc, instruments to be put in orbit. What I'm seeing is a bunch of papers exploring preliminary ideas for detecting quantum gravity effects by cosmo observations---observations of the early universe essentially.

I look over these papers. I see a lot of new people have entered the field and are thinking about this. And the lesson I'm tending to draw is (not that some one of these ideas is the answer and will test some particular class of models but) that the proverbial wisdom that you can't see quantum gravity effects without building a stupendous accelerator the size of a....whatever, is simply wrong. You CAN expect to see quantum gravity effects in cosmology basically because cosmo scale approaches or is reciprocal to planck scale.
There are opportunities. That's the first message I get from this, and probably the most important one. There may be other things we can uncover by looking over this bunch of research.

Last edited: Feb 23, 2009
7. Feb 23, 2009

### BenTheMan

You seem to be telling me basically the same statement that people working on string inflation make---we can find lots of models which predict specific things, but non-observation of those specific things is not a falsification of the theory, because we also have lots of models which predict lots of other things. In other words, like Haelfix said, every abstract you post makes model dependent statements.

Of course this is the case, this was well known probably to the first people who wrote down the temperature fluctuation prediction from inflation in the CMB. The problem is that experiments like WMAP and Planck can only give you a very small set of observables (usually 2 numbers). Considering the freedom that you have to tune potentials and initial conditions, it's not surprising that you can fit such a small set of observables.

8. Feb 23, 2009

### Coin

Can you clarify... would these be tests of "LQG in cosmology", or would these be tests of "Loop Quantum Cosmology"?

I have been told in the past that Loop Quantum Gravity and Loop Quantum Cosmology are decoupled, something along the lines that they are different theories that apply similar methods from different starting points, and that although they are believed to be linked this has not yet been shown. Is this correct?

It also seems to me that if we treat LQG and LQC as different, that all of these papers so far here concern LQC, not necessarily LQG, with the exception of the general quantum gravity review from Amelino-Camelia. Is this correct?

Last edited: Feb 23, 2009
9. Feb 23, 2009

### marcus

It is correct! One is heuristically but not logically derived from the other. LQC was developed in an attempt to implement a isotropic and homogeneous (a symmetry-reduced) version of LQG. Aiming to stand in relation to the full LQG theory much as the Friedmann equations cosmo model stands to GR.

As you suggest there are several research papers working out the relation. Also LQC researchers are gradually opening up, relaxing the requirements of homogeneity and isotropy! So LQC is getting more like full LQG as time goes by. This is probably the most interesting development----a LQG-LQC middle ground. We should probably have a thread to track this gradual bridging and merging.

10. Feb 23, 2009

### BenTheMan

marcus---I don't know if you're ignoring me or not, but can you answer this question.

Succinctly (i.e. without reading an 80 page paper), what observation or non-observation would rule out the loop quantum gravity paradigm?

I can't decide if you can't tell me, or if you won't tell me.

11. Feb 23, 2009

### marcus

Well obviously the observation of extra dimensions!
LQG is quantum theory of 4D geometry. All the results so far depend on that.
If there turned out to be more they'd have to start all over again from scratch

12. Feb 23, 2009

### marcus

I think everybody who wants to talk about LQG should first listen to the 35 minute talk that Carlo Rovelli gave to several hundred string theorists at the Strings 2008 conference.
It would save us a considerable amount of bother, misunderstanding and wasted effort.

It's not hard to understand, he makes it accessible to suit the knowledge and comprehension of the bulk of the audience. Afterwards he gets some 6 or 7 interesting questions. His replies are worth listening to as well, if you have time.

2008 LQG invited survey talk to the Strings '08 conference, video:
http://cdsweb.cern.ch/record/1121957?ln=en
and slides:
http://indico.cern.ch/getFile.py/access?contribId=30&resId=0&materialId=slides&confId=21917

It's a great talk. And easy to understand. You especially should listen to it. Get us all much more on the same page.
It makes a point or two that I think your questions show you are missing. Maybe I should excerpt some slides here for you. But the most efficient thing would be if you would just watch the video of Rovelli's talk. It's well-tailored to the string audience.

Here's an excerpt from the talk around slides #3 and #4 that's relevant to the questions you'v been asking:
==quote==
Goal: How to describe the elementary degrees of freedom of a quantum field theory when there is no ﬁxed background spacetime.

Requirements: Consistency with quantum mechanics and (in the low-energy limit) General Relativity, and full diff-invariance are extremely strong constraints on the theory.

(side comment to the effect that our problem is not to choose among several possible theories, it is first of all to find just one!)

Main result: Definition of diffeomorphism-invariant quantum ﬁeld theory (for gauge ﬁelds plus fermions), in canonical and in covariant form.
==endquote==

I'd like to get exactly what he said---which was different and more than what's on the slides. This is only approximate.

By coincidence at about the same time starting in 2006 there's been a revolution and convergence in both LQC and LQG. In LQC Ashtekar et al introduced the socalled improved dynamics, which is now the basis for pretty much everything in LQC. (Solvable equation models and effective models have to match the new standard.) This is one reason that new people are entering LQC research in substantial numbers. There is now a standard recipe, a standard quantum universe model (Ashtekar-approved) that they can pick up without too much trouble and start deriving results from.

At the same time, around 2006-2007 there was a revolution and convergence in the full LQG theory. Basically everybody moved over to what's called EPRL gamma < 1.
Rovelli has christened it "Covariant LQG" which sounds better and makes more sense.

The wall between the covariant (4D) version and the canonical (3D) formalism came down. The old Barrett-Crane model was abandoned. The new one was proven to be satisfactory in several ways. So by 2008 that was the LQG that pretty much everybody was working on, or meant when they said LQG.

That's a reason it is good to listen to Rovelli's talk to Strings 2008. He is talking about EPRL, or Covariant LQG, and describing it in simple terms suitable to his audience. So it is a good way to get up to date.

What to expect:
They will work using the now-standard models of LQC and LQG until and if some hangup or inconsistency appears. If trouble develops they fix it and move on.
There has to be a way to define quantum field theories without any background spacetime to define them ON.

I expect by September 2009 the low energy limit will be proven. It will be shown that Covariant LQG (or EPRL) gives GR at large scale. If it hasn't already been completely.
There are already a lot of positive partial results. That's just my expectation, anything could happen of course.

(It was a negative result in 2006 that triggered all the present activity. Certain terms in Barrett-Crane didn't reproduce classical gravity.)

If the low energy limit checks out then the first part of program will have succeeded. The next thing will, I expect, be to derive LQC from the standard version of the full theory, and extract predictions of cosmo stuff to look for in the CMB etc. (Planck and Herschel observatories to be launched April 16 2009.)

Last edited: Feb 24, 2009
13. Feb 24, 2009

### BenTheMan

So, is this tongue in cheek, or is this a serious response?

14. Feb 24, 2009

### BenTheMan

Look---either you understand the physics or you don't. If you don't, then maybe you shouldn't start threads like this. Any monkey can do a google search and find the papers.

So I'll ask again---can you condense this in something that is easy to read, or do you have no idea what you're talking about?

15. Feb 24, 2009

### cristo

Staff Emeritus
There was a paper on the arxiv yesterday (http://arxiv.org/abs/0902.3605) which seems to suggest that a period of slow roll inflation, which is apparently required in LQC after a period of superinflation, can provide a red spectrum of tensor perturbations. Thus, it seems that the tensor spectrum cannot be used as 'test' of LQC, at least not in the sense I suggested above.

Thanks, I'll have a listen to this talk later.

Have you got a reference to either this paper, or a review paper?

16. Feb 24, 2009

### cristo

Staff Emeritus
I think the point of this thread is to document the areas in which LQG could feasibly be tested in Cosmology, not any test of LQG. Also, as marcus mentions above, I don't think there are any standard observations or non-observations at this stage, however I could be wrong.

17. Feb 24, 2009

### Coin

You're asking if he can condense a 15-year multifarous differential geometry research program into something which is short and easy to read?

18. Feb 24, 2009

### Coin

I mean, I may or may not understand what Ben is asking.

It seems like Ben is asking for a consequence or prediction of LQG which is experimentally falsifiable.

But I don't think anyone here has an answer to that question. As far as I know there do not exist any unambiguous falsifiable predictions from LQG. I believe LQG has some ground assumptions which in principle experiment could invalidate and rule out the whole paradigm, but I also imagine that if this ever happened LQG could continue with modified assumptions-- as I understand, it has already happened more than once that some variant of LQG has produced a prediction which was not only falsifiable, but false, and research just continued on different variants of LQG. So is there no way to rule out LQG through observation? Well, I'm not sure. Nobody here seems to be able to specifically name one. But given the level of relative immaturity of LQG, the existence of multiple LQG variants, and the fact that LQG does exist wholly in the experiment-unfriendly realm of QG, I don't think it's entirely reasonable to expect people working at the level of this forum to even clearly know whether an answer to this question exists.

Marcus, etc seem to be trying to provide the closest thing to an answer to Ben's question that they have, saying, here at least are some references on current attempts to link the LQG paradigm with experiment.

Ben is getting frustrated because that isn't the question he asked. But I'm not sure the question he asked has an answer.

19. Feb 24, 2009

### BenTheMan

Well, yes. Is that too much to offer from someone who keeps abreast of the field, as marcus (supposedly) does? Does it have to be complete? I wouldn't expect that, but I also would appreciate more than just a bunch of cutting and pasting of abstracts of preprints.

The point is that, because of the multiverse, people like to claim that string theory isn't science. But I can give you an unambiguous test of string theory---Kaluza Klein modes with planck scale mass splittings. That may not be a realistic test, but it is a test in principle---it is a test of string theory.

So, if it IS the case that LQC or LQG (or whatever) has no experimental predictions (even as of yet), then the situation is the same as it is in string theory.

Note---Coin, in your second post, you can replace LQG everywhere with String Theory.

20. Feb 24, 2009

### atyy

I've read that LQG predicts a minimum measurable area. Eg. section 7 of Rovelli's http://relativity.livingreviews.org/Articles/lrr-2008-5/ [Broken]

However, Dittrich and Thiemann have challenged this, and I don't know if the matter is resolved. http://arxiv.org/abs/0708.1721

Last edited by a moderator: May 4, 2017