Reuter takes hit, Hamber says Lambda can't run

[marcus]

As I see it, observational early universe cosmology is the main arena for testing quantum models of the start of expansion and the two main rival lines of research are Asym Safe QG and Loop.

In the Asym Safe safe approach to quantum geometry both G and Lambda run with scale.
In particular Lambda gets large, as k→∞ and the dimensionless version Λ/k²=λ→λ_* goes to a finite fixedpoint limit.

So it is of interest that Hamber says that Lambda cannot run unless you want to give up general covariance.

As I see it, if Hamber Toriumi's finding is sustained this effectively shoots Asymptotic Safety down in the quantum cosmology (QC) arena. This makes me a bit sad---I've harbored considerable hope and enthusiasm for it. AFAICS the quality of Hamber Toriumi's paper is high, maybe someone else will take a look and offer a second opinion.

http://arxiv.org/abs/1301.6259
Inconsistencies from a Running Cosmological Constant
Herbert W. Hamber, Reiko Toriumi
(Submitted on 26 Jan 2013)
We examine the general issue of whether a scale dependent cosmological constant can be consistent with general covariance, a problem that arises naturally in the treatment of quantum gravitation where coupling constants generally run as a consequence of renormalization group effects. The issue is approached from several points of view, which include the manifestly covariant functional integral formulation, covariant continuum perturbation theory about two dimensions, the lattice formulation of gravity, and the non-local effective action and effective field equation methods. In all cases we find that the cosmological constant cannot run with scale, unless general covariance is explicitly broken by the regularization procedure. Our results are expected to have some bearing on current quantum gravity calculations, but more generally should apply to phenomenological approaches to the cosmological vacuum energy problem.
34 pages.

 

[atyy]

That reminds me of another paper.

http://arxiv.org/abs/1111.2875
On the running of the gravitational constant
Mohamed M. Anber, John F. Donoghue
(Submitted on 11 Nov 2011 (v1), last revised 19 Feb 2012 (this version, v2))
We show that there is no useful and universal definition of a running gravitational constant, G(E), in the perturbative regime below the Planck scale. By consideration of the loop corrections to several physical processes, we show that the quantum corrections vary greatly, in both magnitude and sign, and do not exhibit the required properties of a running coupling constant. We comment on the potential challenges of these results for the Asymptotic Safety program.

 

[marcus]

The Hamber Toriumi paper is the main thing I want to discuss in this thread but a related development should be mentioned on the side. Just a week ago there appeared an attempt by Reuter et al to treat Einstein-Cartan gravity in an Asym Safe framework. It looked to me as if it did not work out very well.
9]http://arxiv.org/abs/1301.5135
Einstein-Cartan gravity, Asymptotic Safety, and the running Immirzi parameter
Jan-Eric Daum, Martin Reuter
(Submitted on 22 Jan 2013)
In this paper we analyze the functional renormalization group flow of quantum gravity on the Einstein-Cartan theory space. The latter consists of all action functionals depending on the spin connection and the vielbein field (co-frame) which are invariant under both spacetime diffeomorphisms and local frame rotations. In the first part of the paper we develop a general methodology and corresponding calculational tools which can be used to analyze the flow equation for the pertinent effective average action for any truncation of this theory space. In the second part we apply it to a specific three-dimensional truncated theory space which is parametrized by Newton's constant, the cosmological constant, and the Immirzi parameter. A comprehensive analysis of their scale dependences is performed, and the possibility of defining an asymptotically safe theory on this hitherto unexplored theory space is investigated. In principle Asymptotic Safety of metric gravity (at least at the level of the effective average action) is neither necessary nor sufficient for Asymptotic Safety on the Einstein-Cartan theory space which might accommodate different "universality classes" of microscopic quantum gravity theories. Nevertheless, we do find evidence for the existence of at least one non-Gaussian renormalization group fixed point which seems suitable for the Asymptotic Safety construction in a setting where the spin connection and the vielbein are the fundamental field variables.
121 pages, 8 figures

You must judge for yourself, if you are interested in Einstein-Cartan and in Asymptotic Safety. To me it looked like a mess (as if there was an awkward incompatibility with using the spin connection and tetrad instead of the metric, in AS) but I could be wrong.

When I saw the Daum Reuter paper last week it looked to me like a bad sign for AS. But it was nice they were trying to reach out in the E-C (and incidentally the Loop) direction.

Anyway, back to the Hamber paper.

 

[member 11137]

That reminds me of another paper.

http://arxiv.org/abs/1111.2875
On the running of the gravitational constant
Mohamed M. Anber, John F. Donoghue
(Submitted on 11 Nov 2011 (v1), last revised 19 Feb 2012 (this version, v2))
We show that there is no useful and universal definition of a running gravitational constant, G(E), in the perturbative regime below the Planck scale. By consideration of the loop corrections to several physical processes, we show that the quantum corrections vary greatly, in both magnitude and sign, and do not exhibit the required properties of a running coupling constant. We comment on the potential challenges of these results for the Asymptotic Safety program.

More on the gravitational constant - APOLLO (link wikipedia)

 

[MTd2]

So it is of interest that Hamber says that Lambda cannot run unless you want to give up general covariance.

Quantization procedures for QG fixes a hypersurface slice, so, that is not surprising. In fact that is expected. What about Tomita time? What's the problem, then? Aren't we talking about a Quantum Einstein Gravity within the context of Asymptotic Safety?

If this is the case, then that paper is a big straw man.

BTW, isn't this related to the fact that quantization schemes breaks down background independence? These theories may be background independent in terms of its wavefunctions but its corresponding eigenfunctions tend not to be independent, isn't that what happens in general (are there any exceptions btw)?

 

[marcus]

Quantization procedures for QG fixes a hypersurface slice, so, that is not surprising. In fact that is expected. What about Tomita time? What's the problem, then? Aren't we talking about a Quantum Einstein Gravity within the context of Asymptotic Safety?

Indeed Reuter named his AS approach "Quantum Einstein Gravity" (abbreviated QEG) as you say. But it does not fix a hypersurface slice.
So I am a bit confused by your post. Are you saying that Hamber et al paper is trivial?

You may need to spell things out for us in more detail, to be understood. I will get a link to Hamber's work so that people can get better acquainted if they want.
http://inspirehep.net/author/H.W.Hamber.1/
Only 62 published papers so far. But those papers each got, on average, 35 citations, which is pretty good. His main institution affiliations so far have been Princeton IAS and UC-Irvine, but it looks like he recently got an appointment at AEI-Potsdam (that would be Hermann Nicolai's QG bunch).
Total number of cites so far: around 2200.
I recall being impressed by the talk he gave at Perimeter Institute a few years back. I'll get a link to whatever PIRSA video talks are online.

MTd2, this may not be directly relevant to your comment (which I don't fully understand). But it's probably good in general for people to have an easy way--a few links--to check who the author is.

I think it is an important paper because I've been aware of Reuter AS approach for some 10 years now and as I recall, in every AS paper, Lambda always runs. No one has ever objected to this. In fact the dimensional Lambda gets ever larger, in the UV. This has always been fine with everybody. Now Hamber is saying this cannot be, if the theory is to be general covariant, as Einstein would want :-)

 

[marcus]

Here is the PIRSA video talk I was remembering. It was back in 2009.
http://pirsa.org/09050006/
Quantum Gravitation and the Renormalization Group
Herbert Hamber
Abstract: In my talk I will provide an overview of the applications of Wilson's modern renormalization group (RG) to problems in quantum gravity. I will first discuss the development of the RG for continuum gravity within the framework of Feynman's covariant path integral approach. Then I will discuss a number of issues that arise when implementing the path integral approach with an explicit lattice UV regulator, and later how non-perturbative RG flows and universal non-trivial scaling dimensions can in principle be extracted from these calculations. Towards the end I will discuss recent attempts at formulating RG flows for gravitational couplings within the framework of a set of manifestly covariant, but non-local, effective field equations suitable for quantum cosmology.
13 May 2009.

Springer published a book of his in 2009:
https://www.amazon.com/dp/3540852921/?tag=pfamazon01-20
Quantum Gravitation: the Feynman Path Integral Approach
I have not looked at it but in case it has some helpful information here is the publisher's description:
==quote==

"Quantum Gravitation" approaches the subject from the point of view of Feynman path integrals, which provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. It is shown that the path integral method is suitable for both perturbative as well as non-perturbative studies, and is already known to offer a framework for the theoretical investigation of non-Abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman’s formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The renormalization group for gravity and the existence of non-trivial ultraviolet fixed points are investigated, stressing a close correspondence with well understood statistical field theory models. The final chapter addresses contemporary issues in quantum cosmology such as scale dependent gravitational constants and quantum effects in the early universe.
==endquote==

 

[MTd2]

So I am a bit confused by your post. Are you saying that Hamber et al paper is trivial?

Yes, they are trivial. When you quantize anything, you work with eigenfunctions of differential equations. But, you are working with variables that do not have a contravariant base in GR, that is G and Lambda. So, it will break covariance.

But, this is not an issue, since at least the coupling constant G is used in the usual perturbation expansion.

 

[marcus]

...But, this is not an issue, since at least the coupling constant G ...

I agree that what you have been talking about is not an issue. Hamber has a nontrivial and surprising result which (if it's right) does change the landscape for us.

Lambda and G are both treated as coupling constants. Steven Weinberg originally proposed AS and was still working on it in 2011. It has always been seen as a GENERAL COVARIANT approach. Besides Weinberg a number of smart people have worked on AS over the years, especially after 1998, having both G and Lambda run.

Wetterich and Shaposhnikov have both taken AS seriously---an important minimalist extension of the Standard Model, and a notable prediction of Higgs mass have been based on AS. Percacci has been a major proponent. No one said anything about AS failing general covariance.

You have to read pretty far into Hamber's paper (to around equation #85) to get to where he finally shows that Lambda cannot run, although G can. I'm inclined to wait for the fall-out from this. It will have to be checked and commented by other people. If it turns out to be upheld then some smart and prominent people will have been taken by surprise.

 

[MTd2]

It seems their result is not only restricted to AS. Any theory that makes the lambda running, including those based on a phantom field or holographic models. In fact, it affects all quantum theories of gravity, even string theoretical models since lambda should be an effective parameter in 4d.

But again, this is not surprising since you are trying to vary a parameter which is not not an index of a tensor against others which are. Plus, in a quantum theory, you break covariance since there is no scale of symmetry (except in theories trivial dimensions, like in 2, of string theory world sheet).

He actually uses this result to advocate for a quantum gravity model based on quantum condensate at the last lines of the paper. What I take from the end of the paper it is that AS is a king good example among theories of quantum gravity.

 

[marcus]

Since you refer to other approaches to QG, I should observe that Lambda has been included in LQG in such a way that it does NOT run, and LQG retains general covariance.

So there is a sharp contrast with AS, where Lambda is included in such a way that it MUST run and according to the Hamber result AS must lose general covariance.

 

[John86]

Could anyone sum up the consequences of the Hamber-Toriumi results, for AS in the future in relation with the Cosmological constant.

 

[marcus]

Could anyone sum up the consequences of the Hamber-Toriumi results, for AS in the future in relation with the Cosmological constant.

John, I can only give you my very personal assessment. It's a bit early to give a confident summary--there may be a flaw in Hamber-Toriumi's argument, or a special assumption that limits its applicability.

Otherwise things don't look so good for AS---that is, the Asymptotic Safe approach as developed by Reuter, Percacci, Litim and others.

The reason is that Einstein gravity has two main coupling constants G and Λ. In all the AS papers I have seen, both are allowed to run and the fixed point shows up as the destination of renormalization flow trajectories on the (G,Λ) plane.

The flow spirals into a certain (G,Λ) point. The reason Reuter-style AS has attracted attention is that this behavior persists even if other terms are included in the truncation.
Steven Weinberg, who had the original asymptotic safety idea in 1979, has commented to this effect. This numerical behavior, which involves the cosmological constant running in an essential way, is what has impressed people.

You've probably seen the same flow trajectory pictures that I have, many times. So you know what I mean.

 

[Finbar]

I want to make some comments on the Hamber-Toriumi but haven't got much time at the moment. I think in the end in the effective average action approach only the limits k->0 and k-> infinity really contain universal information which is not dependent on the RG scheme used. Also Hamber-Toriumi are saying that the bare cosmological constant is equal to one in units of the UV cut-off which is in agreement I would say with the AS prediction that Lambda -> Infinity in the UV. In the IR Hamber-Toriumi claim that the effective cosmological constant emerges in some way I don't understand. In the EAA set-up one is computing the full effective action in the limit k ->0 which must contain the effective cosmological constant in this limit.

Finally I think Marcus has made claims that Lambda always runs in the AS approach. Maybe you missed this paper?

http://arxiv.org/abs/1301.0879


On unimodular quantum gravity

Astrid Eichhorn
(Submitted on 5 Jan 2013)
Unimodular gravity is classically equivalent to standard Einstein gravity, but differs when it comes to the quantum theory: The conformal factor is non-dynamical, and the gauge symmetry consists of transverse diffeomorphisms only. Furthermore, the cosmological constant is not renormalized. Thus the quantum theory is distinct from a quantization of standard Einstein gravity. Here we show that within a truncation of the full Renormalization Group flow of unimodular quantum gravity, there is a non-trivial ultraviolet-attractive fixed point, yielding a UV completion for unimodular gravity. We discuss important differences to the standard asymptotic-safety scenario for gravity, and provide further evidence for this scenario by investigating a new form of the gauge-fixing and ghost sector.

 

[marcus]

Fascinating idea! Going over to unimodular gravity, instead of ordinary Einstein gravity. Thanks for pointing out Eichhorn's paper. Lee Smolin was interested in unimodular gravity a few years back and wrote several papers--offering it as a solution to the cosmological constant problem.
Correct me if I am wrong---as I recall in unimodular gravity the vacuum energy does not gravitate. A constant energy density can be treated as "weightless".

If you look back to post #13, I was talking about AS as developed by Reuter, Percacci, Litim (ordinary Einstein gravity, not the unimodular variant) and said that in all the AS papers I had seen Lambda runs. I had indeed missed Eichhorn's paper. Maybe the Hamber-Toriumi result will help to get more people interested in unimodular gravity.

 

[marcus]

Here is Lee Smolin's 2009 paper on unimodular gravity.
http://arxiv.org/abs/0904.4841
The quantization of unimodular gravity and the cosmological constant problem
Lee Smolin
(Submitted on 30 Apr 2009)
A quantization of unimodular gravity is described, which results in a quantum effective action which is also unimodular, ie a function of a metric with fixed determinant. A consequence is that contributions to the energy momentum tensor of the form of the metric times a spacetime constant, whether classical or quantum, are not sources of curvature in the equations of motion derived from the quantum effective action. This solves the first cosmological constant problem, which is suppressing the enormous contributions to the cosmological constant coming from quantum corrections. We discuss several forms of uniodular gravity and put two of them, including one proposed by Henneaux and Teitelboim, in constrained Hamiltonian form. The path integral is constructed from the latter. Furthermore, the second cosmological constant problem, which is why the measured value is so small, is also addressed by this theory. We argue that a mechanism first proposed by Ng and van Dam for suppressing the cosmological constant by quantum effects obtains at the semiclassical level.
22 pages
(http://inspirehep.net/search?p=find+eprint+0904.4841)

Besides Smolin, there is also Enrique Alvarez, who has shown a long-standing interest in this modification of GR. Here are a couple of recent paper of his.
http://inspirehep.net/search?p=find+eprint+1209.6223
http://inspirehep.net/record/1215628?ln=en

 

[atyy]

Do Hamber and Toriumi say anywhere that the non-running of lambda argues against AS? I thought Hamber had written papers supporting the general idea of AS, eg. http://arxiv.org/abs/0901.0964.

Hamber and Toriumi seem to assume AS at some parts of their paper. http://arxiv.org/abs/1301.6259, eg. p7 "Furthermore, the existence of a non-trivial ultraviolet fixed point for quantum gravity in four dimensions is entirely controlled by this dimensionless parameter only, both on the lattice [4, 5] and in the continuum [6]."

It looks like he is saying the lattice approach to AS is more reliable wrt running of lambda than the Reuter method (his reference 26).

 

[marcus]

Do Hamber and Toriumi say anywhere that the non-running of lambda argues against AS? ...

Yes. Look on page 30 where they devote a paragraph to critiquing Reuter AS. Leading up to page 30 they cite Reuter and Litim papers: references [25], [26], [27]. They describe salient features of the approach. Then on page 30 they say there are two problems with it. But they actually give three problems. The second problem is that (according to them) it is inconsistent with general covariance, for the reason discussed in this thread.

 

[Haelfix]

One has to be a little bit careful here. The definitions of lambda(k) and G(k) in general differ substantially between the classical theory, the usual quantum gravity procedure utilized by eg , 'T Hooft, Donaghue and Hamber, the functional renormalization group approach utilized by Reuter and older asymptotic safety proposals and methods from the 90s.

In general, these terms are regularization and renormalization scheme dependant, even before truncation approximations are utilized.

This of course makes perfect sense, b/c G is dimensionful, so people organize the energy expansion in such a way as to find some (any) dimensionless coupling to expand about. This of course requires G and two powers of mass, so something like G(k^2). So it is something like G (cutoff)^2 that could *potentially* run, never the actual bare Newton's constant. Of course the details will differ up to field redefinitions.

Now, the actual running and renormalization of these quantities is very subtle business, and different authors organize the problem in mathematically different ways. Which leads to a problem with making a naive comparison between quantities that are no longer trivially related.

Also there have always been technical issues with the functional renormalization group approach (incompatibility between the IR and UV cutoffs, the violence of the truncation to the divergence structure of the theory, how terms are absorbed into the definition of the running coupling constant etc etc). Anyway all of this is far from settled. So there is not necessarily a disagreement (although Hamber does think that there is) in principle, but it does require more careful work.

Anyway, these are all technical problems, perhaps in principle fixable. There are much more serious physical problems with the theory. Namely the fact that conformal field theories dof and entropy counting scales as the volume, and not as the area (as you would expect a general theory of quantum gravity in the deep UV to behave as). This violent clash with Black hole thermodynamics is not fixable and is a prediction of the theory (one that seems violently at odds with how we understand black hole physics). Likewise, locality is always manifest in AS and not broken. This is also at odds with the black hole information loss

 

[atyy]

Is the Hamber/Reuter difference something like a renormalization scheme dependence (ignoring the truncation issue)?

Edit: Yes, it seems from Haelfix's post just above this.

I remember seeing another interesting paper about renormalization scheme dependence in quantum gravity recently http://arxiv.org/abs/1211.1729

 

[marcus]

Is the Hamber/Reuter difference something like a renormalization scheme dependence (ignoring the truncation issue)?

Let me see if I can spell it out. Hamber specifically targets Reuter AS and refers to several representative Reuter papers. Let's study what he actually says. That should answer your question in the least vague least interpretational way.

Look on page 30 where they devote a paragraph to critiquing Reuter AS. Leading up to page 30 they cite Reuter and Litim papers: references [25], [26], [27]. They describe salient features of the approach. Then on page 30 they say there are two problems with it. But they actually give three problems. The second problem is that (according to them) it is inconsistent with general covariance, for the reason discussed in this thread.

Here is the relevant paragraph.
==quote Hamber Toriumi p. 30==
...A nontrivial fixed point in both couplings (G∗,λ∗) is then found in four dimensions, generally with complex relevant eigenvalues ν−1, with some dependence on the gauge parameters [26].
There seem to be two problems with the above approach (apart from the reliability and convergence of the truncation procedure, which is an entirely separate issue). The first problem is an explicit violation of the scaling properties of the gravitational functional integral, see Eqs. (6),(7) and (8) in the continuum, and of the corresponding result in the lattice theory of gravity, Eq. (53). As a result of this conflict, it seems now possible to find spurious gauge-dependent separate renormalization group trajectories for G(k) and λ(k), in disagreement with the arguments presented previously in this paper, including the explicit gauge-independence of the perturbative result of Eq. (36). In light of these issues, it would seem that the RG trajectory for the dimensionless combination G(k)λ(k) should be regarded as more trustworthy. The second problem is that the running of λ(k) claimed in this approach seems accidental, presumably due to the diffeomorphism violating cutoff, which allows such a running in spite of the fact that, as we have shown, the latter is inconsistent with general covariance. One additional and somewhat unrelated problem is the fact that the above method, at least in its present implementation, is essentially perturbative and still relies on the weak field expansion. It is therefore unclear how such a method could possibly give rise to an explicit nonperturbative correlation length ξ [see Eq. (40)], which after all is non-analytic in G.
==endquote==

 

[atyy]

Honestly, seems like no big deal. Hasn't Hamber's AS has differed from Reuter AS for many years? I believe the lambda issue is already mentioned in passing in the old Hamber papers.

Eg. in the new paper "The same is found to be true in the lattice formulation of gravity, where again the bare cosmological can be scaled out, and thus set equal to one in units of the ultraviolet cutoff without any loss of generality. One concludes therefore that a running of lambda is meaningless in either formulation." http://arxiv.org/abs/1301.6259 p2

In the old paper "by a suitable rescaling of the metric, or the edge lengths in the discrete case, one can set the cosmological constant to unity in units of the cutoff. The remaining coupling G should then be viewed more appropriately as the gravitational constant in units of the cosmological constant λ." http://arxiv.org/abs/0901.0964 p55

 

[marcus]

Honestly, seems like no big deal. ... I believe the lambda issue is already mentioned in passing in the old Hamber papers...

That's your interpretation based on your sense of proportion. For you Hamber's persistence makes his objection less significant. For me, more.

It looks to me as if he has raised the ante by devoting a paper to proving that having the two couplings run separately is inconsistent with general covariance. He apparently is convinced that it is the dimensionless product λG that should do the running, if anything does.

If you like, call that "G in units of one over λ". One over λ is an area, and if you set c and hbar equal to one then G is naturally an area quantity---so can be expressed in terms of 1/λ. You quoted Hamber saying something to that effect.

Anyway you may be paying too much attention to the "politics" of who is pro-this and con-that. I've long been a fan of Shaposhnikov, and minimalist approaches, and of AsymSafe QG particularly as presented by Percacci, and occasionally by Saueressig, and Reuter. I've never been an enthusiast for Hamber's work. But I think Hamber may have proved something and I have to take the possibility seriously.

It may turn out to be a false alarm and be dismissed. But if not, if it is confirmed, then I expect some kind of tectonic shift in AS---maybe a move in the direction Finbar suggested:
AS with Unimodular rather than standard AS---viz the paper by Astrid Eichhorn. And I would also expect (if this critique of standard AS is upheld) for Shaposhnikov to modify what he says and take a somewhat different tack.

So at this point I won't dismiss the paper as you do, and say it is "no big deal"
I'll probably wait and see a little on this one.

 

[atyy]

I don't think it will move it towards unimodular AS, since Hamber has been saying this a long time. I have felt the same respect for Hamber as for Percacci, Reuter, Litim etc.

Anyway, maybe it'd for me be better to say no new deal, rather than no big deal.

What's unclear to me is whether Hamber's method gets any closer to showing AS than eg. Percacci. It seems to me all the AS papers have problems, OTOH there are also no non-handwavy arguments against AS.

 

[John86]

Anyway you may be paying too much attention to the "politics" of who is pro-this and con-that. I've long been a fan of Shaposhnikov, and minimalist approaches, and of AsymSafe QG particularly as presented by Percacci, and occasionally by Saueressig, and Reuter. I've never been an enthusiast for Hamber's work. But I think Hamber may have proved something and I have to take the possibility seriously.

Will this in one way or another mean that the AS framework will be les minimalist

 

[atyy]

Will this in one way or another mean that the AS framework will be les minimalist

I don't think so. Hamber is a proponent of AS. He's been having a non-running "cosmological constant" since at least 2007. http://arxiv.org/abs/0704.2895 "The remaining coupling G should then be viewed more appropriately as the gravitational constant in units of the cosmological constant λ". In that paper he also discusses the "non-trivial fixed point" that is characeristic of the simplest versions of AS.

I think the question of minimal or non-minimal within AS has to be about the matter content. It's not clear whether any version of AS exists at all, or whether there are many versions of AS each with different matter. The Shaposhnikov and Wetterich proposal assumes AS and is minimalist in matter content - one could discuss whether Hamber's conclusions affect that proposal. I think one should be careful in comparing Hamber's scheme and Shaposhnikov's, and whether the operational definitions of the various quantities having the same name are also the same. I believe this is what Haelfix's post #19 is also saying.

Eg. Shaposhinkov and Wetterich's footnote 1 says "We would like to stress that the definition of the running couplings here is based on the gauge-invariant high energy physical scattering amplitudes [1], rather than on the minimal subtraction (MS) scheme of the dimensional regularization. In the MS scheme perturbative Einstein gravity does not contribute to the β functions of the Standard Model couplings [13]" Ref [13] is http://arxiv.org/abs/0710.1002 .

In another but similar context, http://arxiv.org/abs/1209.3511 says "Despite having a pre-history[32], recent activity stems from the work of Robinson and Wilczek[33], who suggested that the beta function of a gauge theory could have the form ... While this correction is tiny for most energies, the negative sign suggests that all couplings could be asymptotically free if naively extrapolated past the Planck scale. Subsequent work by several authors, all using dimensional regularization, found that the gravitational correction to the running coupling vanishes[34]. Further work, including some of the same authors, using variations of cutoff (Λ) regularization then found that it does run[35], ... Papers trying to clarify this muddle include[36, 37, 38, 39]. My treatment here most naturally follows the ones of my collaborators and myself[36, 37]"

http://arxiv.org/abs/1111.2875 and http://arxiv.org/abs/1209.3511 are probably the most problematic for AS, since it seems to contradict all versions of AS, even Hamber's. However, the authors stop short of this conclusion, and says it deserves further study. I believe Anber and Donoghue do not rule out AS, but show that its ability to predict will be very restricted unless the exact matter content is known. The problem with AS being non-predictive without knowing matter is established and discussed by Percacci.

In http://arxiv.org/abs/0910.5390 Gurain and Percacci discuss renormalization scheme dependence.

In http://arxiv.org/abs/0910.5167 Percacci says "Of course I am not claiming here that equations (64) are to be taken literally as the correct predictions: there is too much that we are neglecting in the calculations. However it seems possible that with more effort the asymptotic safety program will eventually produce realistic predictions."

I think Anber and Donoghue suggest the problem may be much worse than Percacci had hoped.

 

[MTd2]

Well, the Hamber - Toriumi hasn't gotten any citations so far...

 

[Haelfix]

No but similar ideas have actually generated some discussion in the field. See for instance
http://pirsa.org/13050003/

 

[MTd2]

Has anyone thought about the phantom field of CCC which sort of runs the coupling constants?

 

[ohwilleke]

You have to read pretty far into Hamber's paper (to around equation #85) to get to where he finally shows that Lambda cannot run, although G can.

A running G without a running lambda still leaves a lot of room for innovative AS type theories. And, evidence from the APOLLO experiment, e.g., doesn't necessarily mean much if the running of G is non-linear.

Isn't Lambda more or less analogous to the Higgs vev in electroweak theory, which also doesn't run?

 

[marcus]

A running G without a running lambda still leaves a lot of room for innovative AS type theories. And, evidence from the APOLLO experiment, e.g., doesn't necessarily mean much if the running of G is non-linear.

Isn't Lambda more or less analogous to the Higgs vev in electroweak theory, which also doesn't run?

I imagine some of the others will have more of an opinion about that analogy. It makes sense to me that it would not run or vary with scale/energy, but not necessarily for the reason you gave.

I don't think of Lambda as "dark energy" but simply as a one of two gravitational constants that must appear in the Einstein equation because they are allowed by the symmetry of the theory (invariance under diffeomorphisms). So in a rough sense it's analogous to a "constant of integration" that you have to put into have a correct answer in calculus. It has to appear. Einstein wrote it on LHS as a constant CURVATURE. People had no reason to expect it to be zero and when it was finally measured it turned out not to be zero. Based on Planck report, the estimate is:
1.007 x 10^-35 seconds^-2

A curvature is reciprocal area or reciprocal length squared. It just turns out to be convenient to say in reciprocal square seconds. One can convert to a possible fictitious energy by multiplying by c^2/(8 pi G)

I think the associated "dark" energy density may just be a fiction. IOW it is just a "vacuum curvature" or intrinsic curvature constant. Maybe there is a quantum geometric explanation for it. So I have no reason to expect it to run.

(Of course I could be wrong. Maybe there is some actual real energy field associated with it! Just so far no evidence of that has appeared. So far it behaves exactly like Einstein's cosmological curvature constant.)
====================

However, Ohwilleke, it looked to me like in Reuter's context it HAD to run. The dimensionless version of Lambda is a coupling constant λ, and the rules of the game are you solve the renormalization group equations and let the couplings (out to a certain order) run if they want to.
He did that, both dimensionless versions of G and Lambda wanted to run, and he got some very nice results on the (g, λ) plane.

To me it looks like his approach would have considerably less integrity/credibility if he artificially restricted one of the two main coupling constants. So either Hamber is wrong or this disables Reuter's approach.

Anyway that's how it looks to me. You may know differently and if so I'd be glad to hear an explanation. For the time being I'm tending to discount Asymptotic Safety QG and take more interest in Causal Sets, CDT, and some variants of LQG (tensor networks, spinorial Lqg, holonomy spinfoam ).