Implications of validating loop quantum cosmology

[kodama]

suppose, for example,

Pre-inflationary universe in loop quantum cosmology
Tao Zhu, Anzhong Wang, Gerald Cleaver, Klaus Kirsten, Qin Sheng
(Submitted on 22 May 2017 (v1), last revised 4 Jun 2017 (this version, v2))
The evolutions of the flat FLRW universe and its linear perturbations are studied systematically in the dressed metric approach of LQC. When it is dominated by the kinetic energy of the inflaton at the quantum bounce, the evolution of the background can be divided into three different phases prior to the preheating, {\em bouncing, transition and slow-roll inflation}. During the bouncing phase, the evolution is independent of not only the initial conditions, but also the inflationary potentials. In particular, the expansion factor can be well described by the same exact solution in all the cases considered. In contrast, in the potential dominated case such a universality is lost. It is because of this universality that the linear perturbations are also independent of the inflationary models and obtained exactly. During the transition phase, the evolution of the background is studied and matched to that given in other two phases, whereby the e-folds of the expansion in each of these three phases are obtained. In this phase the perturbation modes are all oscillating and can be easily matched to the ones given in other phases. Then, considering two different sets of initial conditions, one imposed during the contracting phase and the other at the bounce, we calculate the Bogoliubov coefficients and find that the two sets yield the same results and all lead to particle creations at the onset of the inflation. Due to the pre-inflationary dynamics, the scalar and tensor power spectra become scale-dependent. Comparing with the Planck 2015 data, we find constraints on the total e-folds that the universe must have expanded since the bounce, in order to be consistent with current observations.
Comments: revtex4, 24 figures, and 5 tables. Some typos were corrected
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1705.07544 [gr-qc]

and

Measuring the effects of Loop Quantum Cosmology in the CMB data
Spyros Basilakos, Vahid Kamali, Ahmad Mehrabi
(Submitted on 16 May 2017)
In this Essay we investigate the observational signatures of Loop Quantum Cosmology (LQC) in the CMB data. First, we concentrate on the dynamics of LQC and we provide the basic cosmological functions. We then obtain the power spectrum of scalar and tensor perturbations in order to study the performance of LQC against the latest CMB data. We find that LQC provides a robust prediction for the main slow-roll parameters, like the scalar spectral index and the tensor-to-scalar fluctuation ratio, which are in excellent agreement within 1σ with the values recently measured by the Planck collaboration. This result indicates that LQC can be seen as an alternative scenario with respect to that of standard inflation.
Comments: 7 pages, 1 figure. To appear in IJMPD. This essay received an honorable mention in the 2017 Essay Competition of the Gravity Research Foundation. For a comprehensive presentation of these results, see arXiv:1703.01409
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1705.05585 [gr-qc]
(or arXiv:1705.05585v1 [gr-qc] for this version)

and

Hybrid loop quantum cosmology and predictions for the cosmic microwave background
Laura Castelló Gomar, Daniel Martín de Blas, Guillermo A. Mena Marugán, Javier Olmedo
(Submitted on 20 Feb 2017 (v1), last revised 30 May 2017 (this version, v2))
We investigate the consequences of the hybrid quantization approach for primordial perturbations in loop quantum cosmology, obtaining predictions for the cosmic microwave background and comparing them with data collected by the Planck mission. In this work, we complete previous studies about the scalar perturbations and incorporate tensor modes. We compute their power spectrum for a variety of vacuum states. We then analyze the tensor-to-scalar ratio and the consistency relation between this quantity and the spectral index of the tensor power spectrum. We also compute the temperature-temperature, electric-electric, temperature-electric, and magnetic-magnetic correlation functions. Finally, we discuss the effects of the quantum geometry in these correlation functions and confront them with observations.
Comments: 34 pages, 23 figures, 1 table; v2: revised and minor improvements included
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Report number: IGC-17|2-1
Cite as: arXiv:1702.06036 [gr-qc]
(or arXiv:1702.06036v2 [gr-qc] for this version) Some Clarifications on the Duration of Inflation in Loop Quantum Cosmology
Boris Bolliet, Aurélien Barrau, Killian Martineau, Flora Moulin
(Submitted on 9 Jan 2017)
The prediction of a phase of inflation whose number of e-folds is constrained is an important feature of loop quantum cosmology. This work aims at giving some elementary clarifications on the role of the different hypotheses leading to this conclusion. We show that the duration of inflation does not depend significantly on the modified background dynamics in the quantum regime.
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph)
DOI: 10.1088/1361-6382/aa7779
Cite as: arXiv:1701.02282 [gr-qc]

these predictions were
1- validated by observation and experiment, survives peer review, and nobel prizes are awarded and these results become standard textbooks in the field and
2- only loop quantum cosmology makes these predictions, other frameworks, such as string theory are unable to reproduce these unique predictions from loop quantum cosmology - no other candidate theory of QG such as string theory can make the same predictions as LQC which are then validated by observation to 5-sigma levels significance.

what would be the implications to fundamental physics, quantum gravity, string theory, and cosmology if loop quantum cosmology predictions provided in the above papers and in other similar papers are validated by experiment and observation.

 

[mitchell porter]

Let's first revisit the relationship between loop quantum gravity and other quantum theories.

(In what follows, I am going to summarize a lot of things that I don't know firsthand - it's what I've gleaned from papers, and from the blog discussions about LQG that took place ten years ago. Hopefully, if there's someone out there who can clarify or correct a technical point, or who wants to challenge some broad statement that I make, they will speak up, and we can dig into the details.)

There is a well-trodden path in constructing the quantum mechanics of a harmonic oscillator, other finite-dimensional systems, field theories, gauge field theories in particular. At each stage, there are multiple ways to "quantize" (associated with names like Schrodinger, Heisenberg, Dirac, Feynman), but in the end, you want to arrive at the same quantum theory, the one which explains the observed phenomena.

Then we have gravity, described by general relativity, and we want to make a quantum theory of it. Loop quantum gravity proposes a procedure. Unfortunately, this procedure - if you examine its implications for those simpler physical systems - does not give you back the familiar quantum theory.

The most obviously serious case concerns gauge field theories. In the real world, it is important that symmetries of the classical theory can sometimes be broken by quantum effects (in anomalies), because we actually see those effects. However, the "canonical" quantization procedure employed by loop quantum gravity guarantees, by its very construction, that the symmetries will be exactly obeyed by the quantum theory. (I put "canonical" in quotes because this LQG procedure is not canonical quantization as normally understood in quantum field theory. It's called canonical because it involves canonical variables, but as I just mentioned, what's done with them is quite different.)

This means that anomalies are impossible. But anomalies are observed!

Even when applied to something as simple and basic as the harmonic oscillator, the LQG procedure does not give back the usual quantum theory. People have named the procedure "polymer quantization"; apparently this refers to a kind of discretization of space that emerges (polymers in chemistry are chain molecules like DNA, that consist of a series of discrete subunits)... These properties of polymer quantization do not sound as immediately fatal to the theory's prospects (compared to the lack of anomalies), because one might hope that in some continuum limit, the familiar quantum theory is restored (whereas there seems to be no way that anomalies can reappear).

The familiar quantum theory had better be restored, because that familiar quantum theory is what describes e.g. atoms. But I have no idea if that restoration looks likely, plausible, or even possible.

To reiterate, the "canonical" quantization procedure employed in loop quantum gravity appears to go fatally wrong when applied to gauge field theories, because it cannot reproduce anomalies. Meanwhile, if we quantize gauge field theories in the standard way, we get - the standard model, with all its successes. If we try to apply those same standard methods to quantizing general relativity, we get some extra complications, and a theory that looks to be incomplete, but it's still a theory that works for weak gravitational fields, and which is consistent with the black hole thermodynamics deduced by Bekenstein and Hawking.

Some further comments:

Loop quantum gravity starts with the new variables of Ashtekar, in which classical general relativity is expressed in terms of a connection rather than a metric. Those variables have become associated with loop quantum gravity and with "polymer quantization", but they can be quantized in a more orthodox way, and when you do that, you get something consistent with standard QFT and "orthodox" quantum gravity.

One of the attractions of string theory is that it provides a viable completion of the "quantum gravity that works". But most people outside of loop quantum gravity, that are still trying to make quantum gravity work as a field theory rather than a string theory, are using the standard methods of quantization. I mean people working on asymptotic safety, conformal gravity, and so on.

Along with its "canonical" quantization, loop quantum gravity also gave rise to research on spin foams. This is LQG's version of the path integral - Feynman's method of quantization, the sum over histories. They call it covariant quantization. It seems that, in general, they have not shown that it is equivalent to their canonical quantization, and in practice the research into covariant quantization proceeds somewhat independently.

Its problems and maybe its prospects are different to those of canonical LQG. The main "problem", as I understand it, is just that there are infinitely many possible elementary spin-network transitions, each with its own amplitude or coupling constant, and so the situation is analogous to perturbative quantum gravity, with its infinitely many higher-order terms.

This leads me to think that there might be a type of spin foam which does actually converge on the "orthodox" quantum gravity, and perhaps even on some type of string theory. My best guess is that there might be a twistor spin foam that is equivalent to an Ashtekar-like version of general relativity that has been quantized in the orthodox way.

Now - what about loop quantum cosmology? I don't know much about it, but I do know that it involves describing gravitational systems in a radically simplified way. Specifically, instead of the infinitely many degrees of freedom possessed by a field theory, one uses simplified models which only have finitely many degrees of freedom. This is standard practice in quantum cosmology, it's not just LQG. (Confusingly for a modern reader, these are called minisuperspace models. It's confusing because it has nothing to do with supersymmetry. Superspace was also a 1960s name for the space of possible geometries in general relativity, and minisuperspace is the space of possible geometries in one of these highly simplified models with a finite number of variables.)

So I would expect that LQC is more like the polymer-quantized harmonic oscillator than the "canonically" quantized LQG field theory. The latter seems to be doomed because it cannot reproduce anomalies, whereas the former should just be a deformation of the minisuperspace dynamics you get from orthodox quantum gravity. LQC may therefore not be so obviously implausible. But even if it made a correct prediction, one still might be better off looking for an alternative way to obtain that deformation.

 

[kodama]

Now - what about loop quantum cosmology? I don't know much about it, .

you and Urs were 2 i wanted to hear from.

despite all the issues you raise, and the earlier points you made in an another thread, that loop quantization makes no contact with established physics

in one paper,
Measuring the effects of Loop Quantum Cosmology in the CMB data
Spyros Basilakos, Vahid Kamali, Ahmad Mehrabi
[URL='https://arxiv.org/abs/1705.05585']arXiv:1705.05585[/URL]
[URL='https://arxiv.org/abs/1705.05585'][/URL]
and
[URL='https://arxiv.org/abs/1705.05585'][/URL]
Hybrid loop quantum cosmology and predictions for the cosmic microwave background
[URL='https://arxiv.org/find/gr-qc/1/au:+Gomar_L/0/1/0/all/0/1']Laura Castelló Gomar, Daniel Martín de Blas, Guillermo A. Mena Marugán, Javier Olmedo[/URL]
[URL='https://arxiv.org/find/gr-qc/1/au:+Olmedo_J/0/1/0/all/0/1'][URL='https://arxiv.org/abs/1702.06036v2']arXiv:1702.06036v2[/URL][/URL]
[URL='https://arxiv.org/find/gr-qc/1/au:+Olmedo_J/0/1/0/all/0/1'][URL='https://arxiv.org/abs/1702.06036v2'][/URL][/URL]
these and similar papers predictions are verified in future precision measurements in CMB, and only LQC is the only framework makes these predictions - they are unique to LQC and cannot be reproduced by any rival theory such as string theory
https://arxiv.org/find/gr-qc/1/au:+Mehrabi_A/0/1/0/all/0/1
what conclusions would you draw?https://arxiv.org/find/gr-qc/1/au:+Mehrabi_A/0/1/0/all/0/1

isn't making predictions for CMB - which could be validated by future experiments - an example of making contact with established physics

 

[mitchell porter]

isn't making predictions for CMB - which could be validated by future experiments - an example of making contact with established physics

It just means that you have a calculation which produces a number. It doesn't mean that the assumptions behind the calculation are consistent with the rest of physics.

 

[kodama]

It just means that you have a calculation which produces a number. It doesn't mean that the assumptions behind the calculation are consistent with the rest of physics.

what you say sounds perfectly reasonable,I agree that just 1 calculation that produces a number that comes out right is just 1 calculation and 1 number

here's another paper

Some Clarifications on the Duration of Inflation in Loop Quantum Cosmology
Boris Bolliet, Aurélien Barrau, Killian Martineau, Flora Moulin
arXiv:1701.02282

suppose both the duration of inflation in LQC and LQC prediction of CMB are both verified?
two separate issues, two different predictions from the same LQC theory.

if these and other papers which produces predictions in LQC framework are verified by experiment and observation, how many would lend support assumptions behind the calculation are consistent with the rest of physics? i.e how many different calculations and diverse predictions covering a wide range of phenomena are necessary before the LQC is said to be successful?

Testing loop quantum cosmology
Edward Wilson-Ewing
(Submitted on 14 Dec 2016 (v1), last revised 28 Feb 2017 (this version, v2))
Loop quantum cosmology predicts that quantum gravity effects resolve the big-bang singularity and replace it by a cosmic bounce. Furthermore, loop quantum cosmology can also modify the form of primordial cosmological perturbations, for example by reducing power at large scales in inflationary models or by suppressing the tensor-to-scalar ratio in the matter bounce scenario; these two effects are potential observational tests for loop quantum cosmology. In this article, I review these predictions and others, and also briefly discuss three open problems in loop quantum cosmology: its relation to loop quantum gravity, the trans-Planckian problem, and a possible transition from a Lorentzian to a Euclidean space-time around the bounce point.
Comments: 20 pages. Invited review for special edition "Testing quantum gravity with cosmology" of Comptes Rendus Physique
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Journal reference: Comptes Rendus Physique 18 (2017) 207-225
DOI: 10.1016/j.crhy.2017.02.004
Cite as: arXiv:1612.04551 [gr-qc]

Loop Quantum Cosmology Gravitational Baryogenesis
S.D. Odintsov, V.K. Oikonomou
(Submitted on 8 Oct 2016)
Loop Quantum Cosmology is an appealing quantum completion of classical cosmology, which brings along various theoretical features which in many cases offer remedy or modify various classical cosmology aspects. In this paper we address the gravitational baryogenesis mechanism in the context of Loop Quantum Cosmology. As we demonstrate, when Loop Quantum Cosmology effects are taken into account in the resulting Friedmann equations for a flat Friedmann-Robertson-Walker Universe, then even for a radiation dominated Universe, the predicted baryon-to-entropy ratio from the gravitational baryogenesis mechanism is non-zero, in contrast to the Einstein-Hilbert case, in which case the baryon-to-entropy ratio is zero. We also discuss various other cases apart from the radiation domination case, and we discuss how the baryon-to-entropy ratio is affected from the parameters of the quantum theory. In addition, we use illustrative exact solutions of Loop Quantum Cosmology and we investigate under which circumstances the baryon-to-entropy ratio can be compatible with the observational constraints.
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Theory (hep-th)
DOI: 10.1209/0295-5075/116/49001
Cite as: arXiv:1610.02533 [gr-qc]

 

[mitchell porter]

how many different calculations and diverse predictions covering a wide range of phenomena are necessary before the LQC is said to be successful?

From the purely empirical perspective of observational cosmology, loop quantum cosmology is just one more theory that can mimic standard cosmology, whose details can keep being modified to produce slightly different predictions. The LQC theorists can change the matter content of the theory, they can add extra dimensions, they can make other technical choices. There are a lot of other unorthodox theories which have a similar flexibility - holographic dark energy, running vacuum energy, various modified gravities - and standard cosmology has this freedom of choice too.

I'm not saying that these theories can be made to predict anything you want; but each of them is an adjustable paradigm rather than a theory giving unique predictions. The attempt to say which is favored by the data, depends on subtle choices of cosmological data set, statistical criteria, and allowed theoretical variations. There is no indication that LQC will stand out from the crowd in this way.

So LQC can probably do OK, so long as everyone sticks to the minisuperspace approximations. The real problems are going to return when you try to reconnect it to the rest of physics. Already, some of the papers you mention talk about a "hybrid" approach, in which gravity is "loop-quantized" but the matter fields are quantized in the usual way. Since canonical LQG cannot contain anomalies, this surely means that gravitational and mixed anomalies can't occur - and that ought to have astrophysical consequences.

And I suspect I am still very much underestimating the problems of canonical LQG. I emphasize the issue of anomalies because it's a very straightforward problem, even a falsification: anomalies involve violations of classical symmetries in the quantum theory, but canonical LQG by construction ensures that the classical symmetries are exact in the quantum theory. Meanwhile, the impression I get, from people who have studied LQG in a far more serious way, is that canonical LQG hasn't even demonstrated the existence of a semiclassical limit. That would mean, not that it gives us a weird modified version of QFT, but that it doesn't give us anything like fields in space-time at all.

Covariant LQG (spin foams) is a different story, but again, it will need to somehow come out looking much more like an ordinary QFT than canonical LQG does. Also, LQC is based on canonical LQG.

 

[kodama]

From the purely empirical perspective of observational cosmology, loop quantum cosmology is just one more theory that can mimic standard cosmology, whose details can keep being modified to produce slightly different predictions. The LQC theorists can change the matter content of the theory, they can add extra dimensions, they can make other technical choices. There are a lot of other unorthodox theories which have a similar flexibility - holographic dark energy, running vacuum energy, various modified gravities - and standard cosmology has this freedom of choice too.

I'm not saying that these theories can be made to predict anything you want; but each of them is an adjustable paradigm rather than a theory giving unique predictions. The attempt to say which is favored by the data, depends on subtle choices of cosmological data set, statistical criteria, and allowed theoretical variations. There is no indication that LQC will stand out from the crowd in this way.
/QUOTE]

focusing on this, what sort of theoretical or empirical results would be persuasive evidence of one theory over the others? i understand that there has been recent controversy of standard inflation, as it predicts a flat smooth universe, and everything else.

 

[mitchell porter]

what sort of theoretical or empirical results would be persuasive evidence of one theory over the others?

That is far too broad a question for me, given the variety of theories and the variety of observations. I suggest you ask the cosmology forum.

 

[kodama]

That is far too broad a question for me, given the variety of theories and the variety of observations. I suggest you ask the cosmology forum.

specifically
does string theory offer a concrete prediction and calculation for CMB similar to what LQC papers i provided above, using similar assumptions that the LQC paper makes?

 

[mitchell porter]

does string theory offer a concrete prediction and calculation for CMB similar to what LQC papers i provided above, using similar assumptions that the LQC paper makes?

There are certainly calculations. I don't have a perfect complement to the papers you selected because both observational cosmology and string cosmology are somewhat unfamiliar to me, but I have dug up some papers for comparison.

Ferrara and Kallosh seems to be about implications of M-theory for "α-attractor" models of inflation. As field theories, the α parameter of the α-attractor models is a free quantity, but in their M-theory realization, only certain values of α are possible. They get to actual predictions in the final paragraph.

Gruppuso et al discusses an extension to the cosmological standard model Lambda-CDM, that adds a new parameter Delta (∆) quantifying (I think) a suppression of lower-energy modes in the CMB spectrum. This is meant to be indicative of a transition in inflation (from "fast roll" to "slow roll"), and again there is a string theory model in which this occurs ("brane supersymmetry breaking").

Of these two, Ferrara and Kallosh seems to be more about aiming at the simplest model that fits the data; whereas Gruppuso et al is more of a what-if (what would be the visible effect, if brane susy breaking occurs), though it is inspired by some anomalies in the data.

 

[kodama]

this is interesting thanks.

so what about say standard inflation, is it just a calculation which produces a number. It doesn't mean that the assumptions behind the calculation are consistent with the rest of physics, since in part it can produce an infinite number of universes radically different from the observed universe, and the simplest predictions are infinite inflation which is radically different from the observed universe.

Steinhardt et al, for example, points out it most commonly leads to infinite inflation

 

[mitchell porter]

Inflation is completely consistent with the rest of physics! If you have general relativity, and you have a scalar field moving slowly towards its minimum, you get inflation. The main question is just whether or not it occurred.

 

[kodama]

Inflation is completely consistent with the rest of physics! If you have general relativity, and you have a scalar field moving slowly towards its minimum, you get inflation. The main question is just whether or not it occurred.

is there any experimental evidence or observational evidence that spacetime can travel faster than c?

wouldn't spacetime expanding faster than c allow for faster than light communication?

 

[mitchell porter]

is there any experimental evidence or observational evidence that spacetime can travel faster than c?

wouldn't spacetime expanding faster than c allow for faster than light communication?

Imagine a ruler, one meter long, where each centimeter segment doubles in length. A mark one centimeter away is now two centimeters away, but a mark one meter away is now two meters away because there were 100 segments in between, and each of them grew by one centimeter.

In the same way, because every part of space between us and a distant galaxy is expanding, the distance to the galaxy can be increasing faster than light can travel, because every part of the "space-time ruler" is getting longer.

In other words, faster-than-light expansion is already a feature of today's universe - see "misconceptions #1 and #2" here. As before, this is orthodox general relativity.

 

[Urs Schreiber]

(Back from vacation.)

Everything that Mitchell Porter says above is right to the point. This here just to add one aspect:

Despite the naming, it is a wild speculation that the difference equation of LQC follows in any way from LQG.

This speculation is entirely based on prejudice: Some people expect that quantum gravity will reveal space and time to consist of discrete buildung blocks, and the difference equation of LQC is nothing but a simple discretizaton of the FRW differential equation. That's all there is to the foundations of LQC.

But it is a wild speculation that LQG yields this difference equation. The problems with this idea are heavy: Not the least, there is still no consensus on what the "Hamiltonian constraint" in LQG actually is, and whether it has any solution at all. But the FRW equation would be just that Hamiltonian constrain equation, in the appropriate cosmological limit. The problem with dealing with the Hamiltonian constraint in LQG was "dealt with" by jumping ahead to a wild guess as to what its cosmological limit should be, and then naming that guess "loop quantum cosmology". Hier war der Wunsch der Vater des Gedanken.

Due to the foundational problems with LQG it may in the end be regarded as a benefit of LQC that it is connected to LQG only by speculation: Because it is logically possible that some quantum gravity effects in the very early universe are fitted well by the difference equation of LQC, by chance, while I suppose it is not logically possible that LQG is correct.

 

[kodama]

Urs, suppose that both SUSY and KK are ruled out on experimental grounds i.e experimentalists at colliders say not only is there no evidence for SUSY but they have been able to rule out the entire framework, say from precision measurements of rare decays in combination with electron, neutron EDM and possibly other tests.

In the event that both SUSY and KK are ruled out on experimental grounds, what approach to 4D QG would you think is most promising?

 

[Urs Schreiber]

Kodama,

I see that your questions are motivated from the desire to see how one could reduce the theoretical uncertainty concerning the nature of BSM physics by hunting for experimental hints or at least near future potential hints. I think this is a ood cause and worthy of some thoughts.

Nevertheless, by the nature of the problem, this is an elusive business. If we are unlucky, mankind just has to wait a bunch of decades before anything of certainty can be said. Observe that we had to wait 60 years from the proposal of the Higgs mechanism to its experimental detection. The next BSM physics is plausibly at least as elusive as the Higgs used to be, so that it might plausibly take way over a century until anything definite is found. The universe is large, and as we are after the next deep mysteries of the universe, a human life span may not be an appropriate unit of time anymore.

That said, I have been wondering whether certain non-LHC experimental results that are available should get more attention as possible hints for BSM physics:

• The Planck satellite data consistently favours Plateau-type inflationary models, which look like Starobinsky inflation, see here. While these models are experimentally favored, they have a problem: the initial homogenous patch in these models has to be of the order of some 10^3 Planck lengths on the onset of inflation, in order to yield the observed results, among them the large scale homogenity of the observable universe. Since there is no reason to expect initial homogenity across more than some 10^0 Planck lengths, this begs part of question that inflation was meant to answer. Hence something is missing.
  
  But now in Starobinsky inflation the inflaton arises from pure gravity (higher curvarture corrections.) Hence this class of models lends itself to embedding into supergravity (aka high energy supersymmetry, as opposed to the low energy supersymmetry that used to be popular and is being ruled out by experiment more and more).. An obvious question is: Might such an embedding reduce the required size of the initial homogenous patch? Dalianis and Farakos claim that is does, see here
  
  I don't know how robust the computation is. Probably it needs to be taken with a good grain of salt. But maybe there is an interesting possibility here that one could see hints of supergravity by close analysis of the Planck satellite data.
• One of the big conundrums of our time is that the assumption of dark matter works extremely well on large scales for explaining the structure of the cosmos, but seems to fail to work on the scale of galaxies. One interesting idea how to fix this (without giving up on the established theory of gravity as MOND does) is to assume that dark matter consists of massive but extremely light particles, whose de Broglie wavelength is of the order of thousands of parsecs (called "fuzzy dark matter", "FDM", see here). This has the consequence that at around the scale of that wavelength the behaviour of this dark matter changes.
  
  Now Edward Witten et al. have argued in more detail that this works really well:
  
  Lam Hui, Jeremiah P. Ostriker, Scott Tremaine, Edward Witten,
  "On the hypothesis that cosmological dark matter is composed of ultra-light bosons"
  https://arxiv.org/abs/1610.08297
  
  There is a natural candidate for such massive but extremely light particles: "axions". They arise in abundance in string theory, as the low dimensional shadows of higher gauge fields, see here .
  
  I wonder if one should turn this around: Perturbative string theory always has axions in its spectrum -- the B-field in the NS-NS sector, along with the graviton. I am unsure as to whether standard string phenomenology models argue that this "model independent axion", as it is sometimes called, should somehow become unobservable. Maybe this is a blind spot of all string model building? (I am not an expert on this. Any expert reading this here, please set me straight). So I am thinking: Maybe the most immediate stringy BSM signature is axions. And there are good arguments that we are already seeing them in the form of fuzzy dark matter.
  This speculation is in fact getting more and more attention since Witten's article above. I have collected some references here . But there have appeared many more articles very recently.

 

[kodama]

Urs,

inflation is a pretty flexible framework, and LQC researchers have also offered predictions, which may or may not be verified. Paul J. Steinhardt's et argued inflation predicts everything, and he favors cosmic bounce. LQC also offers bounce scenarios.

axions have not yet been verified.

Verlinde's paper
Emergent Gravity and the Dark Universe
https://arxiv.org › hep-th
by EP Verlinde - ‎2016 - ‎Cited by 59 - ‎Related articles
Nov 7, 2016 - The emergent laws of gravity contain an additional `dark' gravitational force describing the `elastic' ... From: Erik Verlinde P [view email]
has 59 citations and is premised that "MOND" is an effect of dark energy without need for axions.

Smolin also observe that MOND seemingly works well on the galaxy level, and proposes MOND is an effect of QG without the need of axions.

You are right about reducing risk in theoretical uncertainty.
Let me put it another way, since neither SUSY nor KK have been verified, you and Mitchell aver since loop quantization is the wrong way to do it what would you propose is a more promising way to directly quantize GR field equations in 4D and without SUSY.

Could you describe a research program in 4D QG that involves directly quantizing GR in 4D and without SUSY, that is both mathematically consistent and physically plausible. If rewriting GR in Ashketar's variables is mistake, what would you propose is a better way to succeed in a program of directly quantizing standard non-SUSY non-KK GR for those theorists who find this promising.

I'm listening

 

[Urs Schreiber]

axions have not yet been verified.

As I said, if you are after fully verified effects, it's not unplausible that you may have to wait a few decades. Therefore if you care about the question right now, you should settle for a little less than full verification and take interest in plausible hints, carefully investigated.

There are two experimental hints for axions: One is that they are a plausible solution to the strong CP problem, the other is that there is a decent argument that the shift of behaviour of dark matter on the scale of galaxies is due to unltralight axions.

Both of these are just hints, not proofs of anything. But they are interesting hints.

Verlinde [...] Smolin [...] MOND

The reason that I don't find this plausible is that these ideas don't have any comprehensive theory, no mathematics behind them, they are vague, wild ad-hoc informal modifications of basic established physics theory, dreamed up for the sole purpose of fitting one single effect while silently breaking established physics. If we allow ourselves that level of unrestrained wild speculation then we are lost, back at the level of story-telling. It may be fun for camp-fire discussion, late at night, after three beer, though.

Notice that high energy supersymmetry and KK-reduction are, while also speculative, quite different. They are not dreamed up by story-telling, but they happen to drop out by mathematical derivation from a systematic, mathematically formalized process within established physical theory: One first proves that the Feynman rules are equivalently given by the worldline correlators of a 1d field theory on the graphs (the worldline formulation of quantum field theory), then one explores the mathematically well-motivated question of regarding these graph correlators as limits of surface correlators of a 2d QFT, and then one derives that this works precisely if that 2d QFT is a 2d super-conformal field theory of the same central charge as a non-linear sigma-model on a 10d supergravity background (but it need no be such a geometric sigma-model, the compact dimensions may degenerate to a purely algebraic non-classical point geometry, as we discussed recently in another thread). Nobody ordered all this. No human dreamed this up in order to fit some effects. Instead, this is what mathematical physics delivers from established input patterns. As a consequence, speculative as this still is, it has the advantage that by construction it is compatible with all principle of established physics, such as conservation laws, gauge symmetry, anomalies etc. pp.

At the level of Planck scale physics, if not way before that, human intuition is no good anymore. We need to be guided by formalism, by the mathematics of established physical theory.

That's the huge advantage of, say, axion models over unconstrained speculation about alternative laws of physics: Axion models fit established theory.

If rewriting GR in Ashketar's variables is mistake,

No change of variables can ever be a "mistake", if it really is a change of variables. Ashtekar variables are an honest set of variables. The technical mistake of LQG is to actually abandon the Ashtekar variables when passing from connections to "generalized connections". While Ashtekar variables are still an equivalent description of the phase space of 4d-gravity, these "generalized connections" are not, not even classically. And their "polymer quantization" is a wild dream unrelated to anything known as physics.

Could you describe a research program in 4D QG that involves directly quantizing GR in 4D and without SUSY, that is both mathematically consistent and physically plausible.

As I said before, perturbative quantum gravity exists as a mathematically consistent theory (see here). It is non-renormalizable, but that just means you have to keep measuring counter-terms as the energy scale increases. Still, at each energy scale, after having measured the finite number of counter-terms up to that scale, the remaining observables of the theory are predictions. Check out the references behind the above link for some such prediction, such as the modification to the 1/r^2 law to first non-trivial order. That is the first effect that may be computed in perturbative quantum gravity. Still, it is way beyond present experimental detectability. Therefore for many decades or centuries to come, perturbative quantum gravity may completely suffice to describe all measurable quantum gravity effects.

The big open question is for the non-perturbative and background free version of this. String theory offers a bunch of hints (not dreamed up, but derived, if at some rough level of rigour, from mathematical physics formalism), and it seems to me that these hints are pretty interesting. But as long as they are just hints, there is no way that I can prove this to you, and so all we can do on this front is to wait for experiment and theory to develop. My hunch is that if we develop theory far enough in mathematically precise form, we will eventually see the light. The theory will guide us. It is smarter than us.

 

[kodama]

The reason that I don't find this plausible is that these ideas don't have any comprehensive theory, no mathematics behind them, they are vague, wild ad-hoc informal modifications of basic established physics theory, dreamed up for the sole purpose of fitting one single effect while silently breaking established physics. If we allow ourselves that level of unrestrained wild speculation then we are lost, back at the level of story-telling. It may be fun for camp-fire discussion, late at night, after three beer, though.
.

The wild speculation you speak of is an attempt to provide an explanation to Renzo’s rule Baryonic Tully-Fisher relation, and the Radial Acceleration Relation which strongly disfavors cold dark matter and is predicted by MOND.

The observational physics that needs to be explained -

One Law To Rule Them All: The Radial Acceleration Relation of Galaxies
Federico Lelli (1, 2), Stacy S. McGaugh (1), James M. Schombert (3), Marcel S. Pawlowski (1, 4) ((1) Case Western Reserve University, (2) European Southern Observatory, (3) University of Oregon, (4) University of California, Irvine)
(Submitted on 27 Oct 2016 (v1), last revised 23 Jan 2017 (this version, v2))
We study the link between baryons and dark matter in 240 galaxies with spatially resolved kinematic data. Our sample spans 9 dex in stellar mass and includes all morphological types. We consider (i) 153 late-type galaxies (LTGs; spirals and irregulars) with gas rotation curves from the SPARC database; (ii) 25 early-type galaxies (ETGs; ellipticals and lenticulars) with stellar and HI data from ATLAS^3D or X-ray data from Chandra; and (iii) 62 dwarf spheroidals (dSphs) with individual-star spectroscopy. We find that LTGs, ETGs, and "classical" dSphs follow the same radial acceleration relation: the observed acceleration (gobs) correlates with that expected from the distribution of baryons (gbar) over 4 dex. The relation coincides with the 1:1 line (no dark matter) at high accelerations but systematically deviates from unity below a critical scale of ~10^-10 m/s^2. The observed scatter is remarkably small (<0.13 dex) and largely driven by observational uncertainties. The residuals do not correlate with any global or local galaxy property (baryonic mass, gas fraction, radius, etc.). The radial acceleration relation is tantamount to a Natural Law: when the baryonic contribution is measured, the rotation curve follows, and vice versa. Including ultrafaint dSphs, the relation may extend by another 2 dex and possibly flatten at gbar<10^-12 m/s^2, but these data are significantly more uncertain. The radial acceleration relation subsumes and generalizes several well-known dynamical properties of galaxies, like the Tully-Fisher and Faber-Jackson relations, the "baryon-halo" conspiracies, and Renzo's rule.
Comments: Accepted for publication in ApJ (23 pages, 14 figures, 4 tables). Added discussion on recent claims from numerical simulations
Subjects: Astrophysics of Galaxies (astro-ph.GA)
DOI: 10.3847/1538-4357/836/2/152
Cite as: arXiv:1610.08981 [astro-ph.GA]

Stacy S. McGaugh on his blog and articles is highly skeptical of dark matter models (including Witten's proposals) and shows how the predictions of dark matter models on such issues as dwarf galaxies is inconsistent with what is actually observed. So it is possible Witten's ideas, while plausible, might be wrong.

Urs, since radial acceleration relation along with Renzo’s rule Baryonic Tully-Fisher relation is based on actual observation of real galaxies, it is actual real physics, and it is at odds with cold dark matter theories for galaxy curves, what physical principles concepts and theories would you propose to modify gravity - GR - to reproduce these relations that can easily be derived from MOND, in the event that Witten's proposal of ultra light scalar bosons like axions is an incorrect explanation (even if it takes decades to fully rule out)?

Smolin, Verlinde et al proposal that MOND is a quantum gravity modification of GR seems entirely plausible.

 

[Urs Schreiber]

The HOTW-paper explicitly discusses that FDM does fit "core aspects" of dwarf galaxies (search the article for this keyword). That's the point.

The trouble with MOND is that while it is an equation that gives an excellent fit for a class of phenomena in a small range, it is completely inconsistent if promoted to a fundamental law of nature. As such it breaks relativity, conservation laws (besides giving ridiculous predictions outside that small range, as highlighted in Dodelson's "The real problem with MOND" ). If faced with this problem, people usually point out that MOND may be embedded into Bekenstein's tensor-vector-scalar gravity theory. But as the name suggests, "tensor-vector-scalar gravity" is standard gravity with... extra fields added, which must be argued to be otherwise unobserved. So it's just another kind of "dark stuff" theory, after all.

A good historical analogue of the MOND formula is the Rydberg formula. At the time when it was proposed, it was the best formula in fitting certain atomic spectra while existing physical theory could not explain any of this. Still, the Rydberg formula is not a fundamental law of nature, instead it is an effect of a more fundamental theory, even if that fundamental theory was discovered only much later.

While it may be fun to speculate that for the MOND formula that more fundamental theory is a de Sitter version of AdS/CFT, this argument is almost as hand-wavy as the argument for LQC from LQG. As long as there is no argument with a minimum of mathematical decency, something living up to the standards of 20th century theoretical physics, we can have endless speculation, but no conclusion.

 

[mitchell porter]

I have been very interested in Justin Khoury's attempt to obtain MOND from "axion-like particles" that form a galactic superfluid. In Berezhiani and Khoury 2015, the MOND law comes from phonons in the superfluid that couple to baryons, while in Khoury 2016, it just comes from the gravity of the superfluid.

 

[Urs Schreiber]

I have been very interested in Justin Khoury's attempt to obtain MOND from "axion-like particles" that form a galactic superfluid. In Berezhiani and Khoury 2015, the MOND law comes from phonons in the superfluid that couple to baryons, while in Khoury 2016, it just comes from the gravity of the superfluid.

Thanks for the pointers. I hadn't looked at these. That's of course another example of a fuzzy dark matter model that I was referring to above (there is a plethora of more or less synonymous terms for this idea, also "BEC dark matter" or "wave dark matter"). Lee's recent review mentions them all, though he does not seem to cite Khoury.

 

[kodama]

No change of variables can ever be a "mistake", if it really is a change of variables. Ashtekar variables are an honest set of variables. The technical mistake of LQG is to actually abandon the Ashtekar variables when passing from connections to "generalized connections". While Ashtekar variables are still an equivalent description of the phase space of 4d-gravity, these "generalized connections" are not, not even classically. And their "polymer quantization" is a wild dream unrelated to anything known as physics. .

do you have any theoretical objections then to a research program in which researchers stay with Ashtekar variable, then quantize them in a way you find acceptable. If "polymer quantization" is the wrong way to quantize Ashtekar variables, what would be the "correct" way to nonpertubative quantize Ashtekar variables? Is there a way to nonpertubatively quantize Ashtekar variables that is related to known physics.

or formulating a theory of gravity say in terms of a gauge theory that reproduces GR in 4D, then quantizing that, quantizing in a way that is physically related to known physics.

 

[Urs Schreiber]

what would be the "correct" way to nonpertubative quantize Ashtekar variables?

That's the right question!

Remember, as I mentioned a few times before, that not a single interacting field theory in dimensions 4 or higher has been non-perturbatively quantized yet. It's a major open problem. For the case of gauge theory (Yang-Mills theory) this problem is one of the "Millenium Problems" of the Clay Institute. So the same question for gravity might well be a "10^4 year problem". But every journey starts with the first step in the right direction, and so it's good to at least ask the right question.

At least the problem description is understood:

The usual perturbative quantum field theory in terms of formal power series of Feynman graphs is now known (due to Collini 16) to be the (Fedosov) formal deformation quantization of the covariant phase space induced by the given Lagrangian density (at least under favorable circumstances).

This suggests that the non-perturbative quantization is what is called the "strict deformation quantization" of this covariant phase space (with gauge invariance etc. properly taken into account).

This may or may not exist. If string theory is right, it probably does not exist for gravity, because in this case non-perturbative gravity is not a local field theory (possibly some string field theory, though). But it would be good to prove a theorem that this does or does not exist.

Presently essentially nothing is known about this. It's a hard problem, but also essentially nobody has really looked into it. (LQG drew loads of attention away from the real problem.)

There is one hint: Hawkins 06 has shown that plausible candiates of strict deformation quantizations of finite-dimensional phase spaces are nothing but the convolution algebras of the higher pre-quantized symplectic groupoids induced by the covariant phase space. My students Bongers and Nuiten have shown that this, in turn, is equivalently holography for the non-perturbative PSM topological string (master thesis Bongers and master thesis Nuiten). There is a subtlety with defining the symplectic groupoid relevant in field theory. If that could be solved, there would be a road towards non-perturbative quantization of field theory.

 

[kodama]

Urs
ever thought about writing a resesarch paper to this effect?

if a research group were to successfully strict deformation quantizations of gravity expressed as Ashketar variables,
1- what would be some qualitative features you would expect to see in a strict deformation quantizations of gravity expressed as Ashketar variables
2- would you take it as a serious candidate theory of Planck scale physics
3- would certain issues such as resolving the semiclassical limit be easier to arrive at?
4- how would strict deformation quantizations qualitative features be similar or different from the current polymer quantization?

would you prefer LQC to also be done as a strict deformation quantizations?

 

[Urs Schreiber]

Urs
ever thought about writing a resesarch paper to this effect?

Sure, when it's done I am going to claim the million dollar prize money ;-)

Regarding your other questions: Beware, as I said, that it is not clear that strict deformation quantization of gravity will exist as an "non-perturbative effective field theory", but it would be very interesting to investigate the existence in its correct and precise form, something which has received almost no attention yet. If it exists, it should be independent of which variables are used to describe the phase space, though it might have more convenient expressions in one choice of variables or the other.

would you take it as a serious candidate theory of Planck scale physics

You seem to be asking whether quantum gravity could be a serious candidate theory of Planck scale physics. This sounds like a tautology to me, or else I am misunderstanding what you are after here.

would certain issues such as resolving the semiclassical limit be easier to arrive at?

That's built into the very definition of "strict deformation quantization": This is a continuous deformation, parameterized by the value of Planck's constant, which interpolates continuously between the classical theory and the non-perturbative quantum theory at some finite value of Planck's constant (if it exists, that is).

how would strict deformation quantizations qualitative features be similar or different from the current polymer quantization?

The concept of strict deformation quantization is a mathematically precise formalization of ordinary/standard/established/observed quantum theory. It's standard established physics, just phrased in precise enough terms to guarantee that everything makes sense and we don't trick ourselves into thinking we have found a quantization while in reality we didn't. That "polymer quantization" instead is an example of the latter error.

would you prefer LQC to also be done as a strict deformation quantizations?

What is called LQC is nothing but the proposal that the differential equation that describes FRW-like cosmological models is to be replaced by a finite difference equation. That this is the quantization of anything is a conjecture without any evidence.

While we are waiting for non-perturbative quantization theory to develop, the next thing that should be done in quantum cosmology is probably clean discussion of perturbation theory of quantum fields (gravity plus other fields) on a classical curved background, as in BFHPR 16 . For instance I am being told that presently there is still a gap in the derivation of the nature of Hawking radiation of gravitons themselves.

 

[kodama]

You seem to be asking whether quantum gravity could be a serious candidate theory of Planck scale physics. This sounds like a tautology to me, or else I am misunderstanding what you are after here.
.

In context, i was asking if a "strict deformation quantization" of Ashketar variables could be a serious candidate theory of Planck scale physics, since the discussion was that you regard polymer quantization to be unrelated to known physics, and that if Ashketar variables could be successfully quantized using "strict deformation quantization" instead of polymer quantization, what would be its qualitative features.

would there still be spin networks, area and volume operators in "strict deformation quantization" of Ashketar variables?

 

[Urs Schreiber]

would there still be spin networks, area and volume operators in "strict deformation quantization" of Ashketar variables?

Regarding the area operators in LQG polymer quantization: Their specific nature is directly connected to the polymer-style prescription, with a disconnected copy of SU(2) associated wiith each edge of a spin network, each being quantized separately.

If you are looking for solid results that support the wide-spread intuition that quantum gravity will reveal that the nature of spacetime itself becomes fuzzy/quantized on small scales, I recommend

• Theodore G. Erler, David J. Gross, Locality, Causality, and an Initial Value Formulation for Open String Field Theory (arXiv:hep-th/0406199)

which works out in technical detail how string field theory retains causal locality macroscopically albeit this being manifestly broken on the string scale.