# Running Newton Constant (no dark matter)

1. Oct 11, 2004

### marcus

I admit that dark matter is apple pie and motherhood. I love Dark Matter just like you. But this paper has been accepted for publication in Physical Review Series D

they did not post the preprint at arxiv until it had passed peer review and been accepted.

this is a 72 page paper. we cannot ignore the possibility that what we think is the consequence of dark matter results at least in part from something else, something not as yet known in the law of gravitation (which may be related to quantizing it)

M. Reuter, H. Weyer
Running Newton Constant, Improved Gravitational Actions, and Galaxy Rotation Curves
http://arxiv.org/abs/hep-th/0410117

here is a followup paper by the same authors
M. Reuter, H. Weyer
Quantum Gravity at Astrophysical Distances?
http://arxiv.org/abs/hep-th/0410119

---abstract of /hep-th/0410117---
A renormalization group (RG) improvement of the Einstein-Hilbert action is performed which promotes Newton's constant and the cosmological constant to scalar functions on spacetime. They arise from solutions of an exact RG equation by means of a cutoff identification'' which associates RG scales to the points of spacetime. The resulting modified Einstein equations for spherically symmetric, static spacetimes are derived and analyzed in detail. The modifications of the Newtonian limit due to the RG evolution are obtained for the general case. As an application, the viability of a scenario is investigated where strong quantum effects in the infrared cause Newton's constant to grow at large (astrophysical) distances. For two specific RG trajectories exact vacuum spacetimes modifying the Schwarzschild metric are obtained by means of a solution-generating Weyl transformation. Their possible relevance to the problem of the observed approximately flat galaxy rotation curves is discussed. It is found that a power law running of Newton's constant with a small exponent of the order $10^{-6}$ would account for their non-Keplerian behavior without having to postulate the presence of any dark matter in the galactic halo.
---end quote---

The followup paper, Quantum Gravity at Astrophysical Distances?, is 43 pages. Here is the abstract.

---abstract of hep-th/0410119---
Assuming that Quantum Einstein Gravity (QEG) is the correct theory of gravity on all length scales we use analytical results from nonperturbative renormalization group (RG) equations as well as experimental input in order to characterize the special RG trajectory of QEG which is realized in Nature and to determine its parameters. On this trajectory, we identify a regime of scales where gravitational physics is well described by classical General Relativity. Strong renormalization effects occur at both larger and smaller momentum scales. The latter lead to a growth of Newton's constant at large distances. We argue that this effect becomes visible at the scale of galaxies and could provide a solution to the astrophysical missing mass problem which does not require any dark matter. We show that an extremely weak power law running of Newton's constant leads to flat galaxy rotation curves similar to those observed in Nature. Furthermore, a possible resolution of the cosmological constant problem is proposed by noting that all RG trajectories admitting a long classical regime automatically give rise to a small cosmological constant.
---end quote---

Last edited: Oct 11, 2004
2. Oct 11, 2004

### marcus

Martin Reuter has 33 papers going back to 1994
he has published several times with Christof Wetterich
and others whose names may ring a bell.
I like the range of things he has published articles about.
I am trying to form a superficial impression.
Even if you are sure that dark matter exists and they have
taken silhouette photographs of it and are almost on the point
of telling you what the particle is that comprises it, i still
think maybe you pay attention to martin reuter.
have to see. this is a first impression.

I see on page two of
Quantum Gravity at Astrophysical Distances?
http://arxiv.org/abs/hep-th/0410119
they refer to the "AJL" paper, Ambjorn Jurkiewicz, Loll
"Emergence of a 4D World from Causal Quantum Gravity"
http://arxiv.org/abs/hep-th/0404156
only a light reference but helps complete their comparison between what they are doing as regards gravity on the one hand and QCD on the other.

Last edited: Oct 11, 2004
3. Oct 11, 2004

### Mike2

from which the first sentence is:
"Assuming that Quantum Einstein Gravity (QEG) is the correct theory of gravity
on all length scales we use analytical results from nonperturbative renormalization
group (RG) equations..."

My question is 1) Assuming quantum Einstein gravity???... how can you assume what you're trying to prove.
and 2) "nonperturbative renormalization"??? Since when does one exist without the other?

4. Oct 11, 2004

Staff Emeritus
This work is a follow-on to one about a year ago, which characterized what they call QEG as a "safe" theory. Their quantization is the same one that was abandoned by field theorists because it was unrenormalizable, but newer theory says it could be safe in spite of this; the infinities could be controlled. This is certainly a fascinatig research program.

5. Oct 11, 2004

Staff Emeritus
Read further on in the paper. They aren't trying to justify their QEG in this paper; that was done in earlier papers. What they are trying to do here is deduce the RG flow equations in the non-pertubative sector of the theory. To do that, they have to assume "for the sake of argument" that the QEG theory is the correct one, so that you can feed your equations into the RG flows just as if you were Mother Nature herself. This is a delicate point and they motivate it by showing a similar strategy applied to QCD.

6. Oct 12, 2004

### Chronos

If this makes DM gravitational lensing go away, I will yield.

7. Oct 12, 2004

### marcus

dont let's anybody yield quite yet!
it is a really interesting idea
(also one Smolin was discussing a lot in February---the possibility of getting
MOND results out of LQG and triply special relativity as its flat limit---

In this case I dont see any reason the DM gravitational lensing wouldnt be included with the rotation curve.

that is, Reuter has a thing that curves space just a tad different
so if the curvature is OK to account for the galaxy rotation
it would automatically be OK to account for the bending of light from other more distant objects (lensing).

since lensing and rotation are consistent, the same tweaked spacetime curvature that accounts for one should account for the other.

so if you promised to yield, then you should yield but it is way too early.

if this thing is right then one should be able to get it from a fundamental quantum gravity theory like Loop or Simplicial or whatever (not just from an effective theory). It is nice that Reuter mentions Renate Loll's simplicial gravity.

Last edited: Oct 12, 2004
8. Oct 12, 2004

Staff Emeritus
The AJL paper is getting a lot of play. In the latest Physics Today it gets a section in the Physics Update feature. Almost unheard-of for a quantum gravity paper. BTW Frank Wilczec has a great riff on force in this issue. He says it's like using a higher level programming language instead of machine language (QED-QCD being machine language).

9. Oct 12, 2004

### marcus

Happily, although most of the current Physics Today is not accessible unless one subscribes, the Frank Wilczek is FREE. they always put out some goodies on the free shelf.

thanks for the tip, he is a great writer for putting it in clear memorable simple-as-possible terms. enjoy folks!

http://www.physicstoday.org/vol-57/iss-10/p11.html [Broken]

SelfAdjoint, I'm glad AJL got their notice, but I believe I will have to go to the library to have a look----it is in the locked part of the online issue

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10. Oct 16, 2004

### Chronos

Er, safe from what? There are a number of theories that would benefit from infinities that could be controlled without renormalization.

11. Oct 16, 2004

Staff Emeritus
Asymptotic Safety

Asymptotically safe. Lauscher & Reuter discuss it in their paper http://www.arxiv.org/PS_cache/hep-th/pdf/0108/0108040.pdf [Broken], where they say:

This paper is one of several referenced in the current paper which concerns this thread.

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12. Nov 8, 2004

### marcus

I would appreciate any explanation of what QEG is about, that anybody wants to give. "Quantum Einstein Gravity" is new to me. It would help to have some explanation in basic not-too-technical terms, if that is possible.

AFAIKS it is Reuter's name for what he does. And it seems to be an alternative to Loop approach, and to parallel LQG in the sense that it starts at the base-camp of Wheeler DeWitt equation (a quantization of GR which didnt quite make it) and sets on up the mountain by a different path.

Maybe this is a faulty characterization. The reason I'm thinking of it is that a straightforward quantization of Gen Rel was, at one point in history, recognized to be unrenormalizable (and according to tradition this motivated String research) and now it looks as if Reuter et al are saying no, maybe it is renormalizable in some sense after all.

Since it may help, I will list the recent Reuter et al papers on QEG. Hoping we can get a little introductory-level light shed here, if people think it's an interesting gambit.

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13. Nov 8, 2004

### marcus

Have we had threads about Martin Reuter papers, and QEG, here at PF before? Any links to prior discussion? (I have been having trouble with with PF search engine and have temporarily given up on it, except for very recent stuff). Here is the paper selfAdjoint cited:

Oliver Lauscher, Martin Reuter
Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity
99 pages, 11 figures,
http://arxiv.org/hep-th/0108040 [Broken]

here is a link to all Martin Reuter's papers on arxiv
http://arxiv.org/find/hep-th/1/au:+Reuter_M/0/1/0/all/0/1
http://lanl.arxiv.org/find/hep-th/1/au:+Reuter_M/0/1/0/all/0/1

I will see how far back the ones go that sound like they might have to do with "Quantum Einstein Gravity"

this one seems to be near the beginning of the sequence. Correct me if you see earlier stuff:
Martin Reuter
Newton's Constant isn't constant
8 pages
http://lanl.arxiv.org/abs/hep-th/0012069

Abstract: "This article contains a brief pedagogical introduction to various renormalization group related aspects of quantum gravity with an emphasis on the scale dependence of Newton's constant and on black hole physics."

From my standpoint, "pedagogical" sounds like a plus, as does the only 8 pages.

After that, in 2001, came very quickly a lot of papers from Martin Reuter:

Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity (40 pages)
http://arxiv.org/hep-th/0106133 [Broken]

Cosmology with Self-Adjusting Vacuum Energy Density from a Renormalization Group Fixed Point (8 pages)
http://arxiv.org/astro-ph/0106468 [Broken]

(then the one selfAdjoint cited, and then)

Is Quantum Einstein Gravity Nonperturbatively Renormalizable? (18 pages)
http://arxiv.org/hep-th/0110021 [Broken]

Renormalization Group Flow of Quantum Gravity in the Einstein-Hilbert Truncation (58 pages)
http://arxiv.org/hep-th/0110054 [Broken]

Towards Nonperturbative Renormalizability of Quantum Einstein Gravity (10 pages)
http://arxiv.org/hep-th/0112089 [Broken]

=======

After that, there come 11 papers from Martin Reuter,
between 2002 and the present. They seem to be longer and more
technical, judging superficially, than some of the first 2001 bunch.

Again judging superficially, it would seem that he got a hot idea
sometime in 2001, and called it "Quantum Einstein Gravity", and
began a very active line of research on that.

I have bolded the first paper where "Quantum Einstein Gravity" appears in the title---maybe that should be considered the first paper of this line of development and the earlier ones just as preliminaries

Well, we may or may not be able to shed any light on this. selfAdjoint could probably explain what it's about. I notice that Abhay Ashtekar was citing Reuter along with other QG developments, in his most recent survey paper ("Gravity and the Quantum" bottom of page 28) so Reuter QEG fits somewhere in Ashtekar's scheme of things.

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14. Nov 8, 2004

### marcus

Skipping to the most recent Reuter paper, I see on page 1, in the introduction, he refers to Ambjorn Jurkiewicz Loll
Emergence of a 4D world from causal dynamical triangulations
and cites a bunch of Loll et al papers

this recent Reuter paper is
Proper Time Flow Equation for Gravity
8 pages
http://lanl.arxiv.org/abs/hep-th/0410191

references [22] and [23] are to the dynamical triangulations work
esp. the Monte Carlo computer simulations

selfAdjoint, you mentioned that the AJL paper was getting a lot of attention, including notice in the most recent issue of Physics Today
but i dont remember if you noted this tie-in by Reuter.

I still dont know what I think about Reuter's gambit----basically because i dont have a feel for the "asymptotically safe" concept.

15. Nov 8, 2004

Staff Emeritus
I think the first page and a half of http://arxiv.org/hep-th/0108040 [Broken] would be a good introduction to the idea of theories that are perturbatively nonrenormalizable but nonpertubatively renormalizable. There's a lot of math involved in "factoring out the non", but this is a high level description. The key here is that the exact renormalization flow equation is a new thing from the 90's, although apparently the idea goes back to the introduction of RG in the 1970s. The question of whether you can nonpertubatively renormalize a theory turns of the nature of the RG fixed points.

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16. Nov 8, 2004

### Haelfix

I must admit I am intrigued by this line of research, im surprised I haven't heard of it before (well I knew Weinbergs conjecture), but I didn't realize it had been solved for D = 4.

The 2002 paper is somewhat of a heroic attempt in calculation afaics, and rather amusing mathematically (lots of heat kernel equations).

Theres a few things that make me uneasy though, I'll get back on that.