What is the Planck Scale for AS gravity?

[MTd2]

The coupling constant runs so the Planck scale changes. What is it at the AS point?

 

[marcus]

The coupling constant runs so the Planck scale changes. What is it at the AS point?

Newton's G --> 0 at the AS point.

This could be seen as a weakness of the AS approach. The Planck scale fails to exist at the fixed point.

Weinberg alluded to this in his AS talk at Strings 2010. He has been trying to model the early universe using AS---and to get a grip on inflation, for example. He has had difficulty.

That is one reason why I suspect AS might not succeed in producing a model of the early universe.
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You may recall that what converges at the fixed point is the dimensionless version of G, namely if k --> infinity is the momentum/wavenumber scale then the dimensionless coupling number is Gk². Therefore G must go to zero as 1/k².

The Planck length is sqrt(hG) so unless Planck's constant h also runs and goes to infinity we must face the prospect that as G goes to zero the Planck length also goes to zero.

In other words, the AS theory may be predictive in the sense that once a finite number of constants are determined (like as few as 3 parameters) you get predictions out to arbitrarily high energy. But still the AS predictions may be wrong. This is just my guess, nothing special to back it up.

I very much admire Weinberg's effort to understand early universe cosmology using AS. This effort must be made, and it still could succeed!
I wish more people would help him get the job done. And I am a Weinberg fan. Cosmology is the testing ground for QG. But Weinberg's effort to get a good cosmology from AS may very well fail and that would mean AS is ultimately no good. This kind of thing happens in theoretical physics. *shrug*

 

[MTd2]

What is the problem in not having a Planck scale?

 

[marcus]

What is the problem in not having a Planck scale?

The main point I was making is that there has been a substantial effort to understand the early universe using AS. I mentioned that Weinberg has been trying for a couple of years. Reuter has been trying for much longer and so far he has not convinced people that he's on the right track cosmologywise.

By itself you can forget about the Planck scale disappearing at high energy in AS. That is just one little peculiar detail about AS. What you have to look at is Weinberg's talk. And how did the Perimeter conference November 2009 go? Where are the papers using AS to model early universe that should have appeared in 2010?

Just my hunch, I don't want to argue about it. I'll be happy if we see some new AS papers this spring with definite signs of progress in cosmology.

 

[MTd2]

Cosmological constant goes to infinity, right?

 

[marcus]

Right

 

[MTd2]

So, if you have a vanishingly small constant gravitational tensor and a huge cosmological constant, it means that you have a de sitter space in the beginning of the universe, right?

So, the universe, as it is now, begins and ends on de sitter space, according to this, right?

 

[murray92]

I think it is interesting to see that Asymptotic safety is certainly the QG approach with the most momentum right now,... and certainly a good field to start working right now...
Will be interesting to see how it turn's out, (maybe a large chunk of the really big work is/was already done by Ward (after all he is the (?) first to compute the experimental value of the cosmological constant!
... And no thread on Physicsforums has appeard about it ( I made a post about it in the thread where the new stuff is advertised, forgot it's name, maybe time to start one, (But i's generally fascinating to seen the number of AsySaf threads that are oppened right now.)
Well I better learn find some time to learn more physics...

 

[MTd2]

Well, he calculate it from the Higgs value, which is not known anyway...

 

[Finbar]

There are no fixed mass scales at a fixed point by definition. The physics becomes scale independent at a fixed point. However since the gravitational fixed point is non-gaussian the physics is also strongly coupled at the fixed point. Hence the theory we are looking for is a strongly coupled scale invariant one.

However the meaning of "the Planck scale" is independent of whether there is a fixed point. Instead it is the scale k for which the dimensionless coupling k^2 G(k)= 1. If G(k) doesn't run much then it would be given by its perturbative definition Mpl = 1/Sqrt(G) but taking into the running it may be lower or higher than this depending on how G(k) runs. But if there is a fixed point the point is that this scale no longer effecting the physics at the fixed point.

So its incorrect to say that the Planck scale runs it is a definite scale at which gravity becomes strongly coupled. Its the same with Lambda QCD the physics at the fixed point in QCD doesn't care about this scale its only when we go to lower energies that we see the effect of this mass scale enter the physics.

 

[murray92]

Oh thanks (didn't know that) (meant the fact about the higgs mass

 

[MTd2]

. The physics becomes scale independent at a fixed point.

Isn't de sitter space scale independent anyway?

 

[Finbar]

Isn't de sitter space scale independent anyway?

No, if i look at short enough scales compared to the cosmological horizon then it looks more and more like flat minkowski space. Further more de-sitter space is only ever a coarse grained description of the universe.


A scale independent "quantum" de sitter space would be one with which the cosmological horizon scales with the distance at which the space time is observed. For example if the cosmological horizon is set by Lambda at a fixed point...

 

[MTd2]

But I am talking about the solution of the einstein equation near the AS. Like in here:

https://www.physicsforums.com/showpost.php?p=3070380&postcount=7

 

[Finbar]

But I am talking about the solution of the einstein equation near the AS. Like in here:

https://www.physicsforums.com/showpost.php?p=3070380&postcount=7

The scale invariant de sitter space near a fixed point will be like a fractal space time not like a classical de sitter. If you like in the classical case there is a fixed scale set by the dimensionful cosmological constant.

 

[atyy]

@Finbar: what is the difference between scale invariant and conformal invariance? Is the fixed point scale and/or conformally invariant?

 

[MTd2]

The scale invariant de sitter space near a fixed point will be like a fractal space time not like a classical de sitter. If you like in the classical case there is a fixed scale set by the dimensionful cosmological constant.

Now that you say, I remember Dario Benedetti's expositions, but asymptotically, it is an integer value. Alright, It doesn't mean that it is not a fractal, but it is likely to be also a low dimensional surface. Perhaps a de sitter space in lower dimension? This does have the advantage of homogenizing all matter.

 

[MTd2]

Well, anyway:

http://arxiv.org/abs/hep-th/0508202

Fractal Spacetime Structure in Asymptotically Safe Gravity

O. Lauscher, M. Reuter
(Submitted on 26 Aug 2005)
Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-Planckian distances it predicts that spacetime is a fractal with an effective dimensionality of 2. The original argument leading to this result was based upon the anomalous dimension of Newton's constant. In the present paper we demonstrate that also the spectral dimension equals 2 microscopically, while it is equal to 4 on macroscopic scales. This result is an exact consequence of asymptotic safety and does not rely on any truncation. Contact is made with recent Monte Carlo simulations.

http://arxiv.org/abs/hep-th/0511021

A Minimal Length from the Cutoff Modes in Asymptotically Safe Quantum Gravity

Martin Reuter, Jan-Markus Schwindt
(Submitted on 2 Nov 2005)
Within asymptotically safe Quantum Einstein Gravity (QEG), the quantum 4-sphere is discussed as a specific example of a fractal spacetime manifold. The relation between the infrared cutoff built into the effective average action and the corresponding coarse graining scale is investigated. Analyzing the properties of the pertinent cutoff modes, the possibility that QEG generates a minimal length scale dynamically is explored. While there exists no minimal proper length, the QEG sphere appears to be "fuzzy" in the sense that there is a minimal angular separation below which two points cannot be resolved by the cutoff modes.

http://arxiv.org/abs/0811.1396

Fractal properties of quantum spacetime

Dario Benedetti
(Submitted on 10 Nov 2008 (v1), last revised 25 Mar 2009 (this version, v2))
We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to quantum gravity. In particular we analyze the cases of a quantum sphere and of $\k$-Minkowski, the latter being relevant in the context of quantum gravity.

 

[MTd2]

Alright, I got the answer. The real universe if of the TypeIIIa type flow. There is a minimum value but which flows to a slightly bigger one.

So, it should be expected that there are black holes with a stable minimum size. I guess there is a paper about this.