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Reuter takes hit, Hamber says Lambda can't run

by marcus
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marcus
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Feb1-13, 12:46 PM
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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.
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atyy
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Feb1-13, 01:03 PM
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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
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Feb1-13, 01:12 PM
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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.

Blackforest
#4
Feb1-13, 03:23 PM
P: 450
Reuter takes hit, Hamber says Lambda can't run

Quote Quote by atyy View Post
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
#5
Feb1-13, 09:00 PM
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Quote Quote by marcus View Post
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
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Feb1-13, 09:15 PM
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Quote Quote by MTd2 View Post
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
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Feb1-13, 09:37 PM
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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:
http://www.amazon.com/Quantum-Gravit.../dp/3540852921
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
#8
Feb1-13, 09:39 PM
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Quote Quote by marcus View Post
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
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Feb3-13, 02:16 PM
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Quote Quote by MTd2 View Post
...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
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Feb3-13, 02:48 PM
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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
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Feb3-13, 06:41 PM
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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
#12
Feb8-13, 07:20 AM
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Could anyone sum up the consequences of the Hamber-Toriumi results, for AS in the future in relation with the Cosmological constant.
marcus
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Feb8-13, 07:58 AM
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Quote Quote by John86 View Post
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 in to 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
#14
Feb13-13, 07:11 AM
P: 343
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
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Feb13-13, 07:47 AM
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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
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Feb13-13, 09:09 AM
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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
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Feb13-13, 09:18 AM
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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
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Feb13-13, 09:41 AM
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Quote Quote by atyy View Post
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.


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