Steven Weinberg offers a way to explain inflation

[marcus]

I made this point earlier in the thread. As the cutoff momentum k increases to infinity, the Planck mass goes to infinity. The Planck mass runs as k, and the S&W paper shows that it is asymptotically proportional to k.

All that M_P means is the low energy Planck mass. In the asymsafe picture, M_P(k) is the physically relevant Planck mass at scale k and it is scale dependent. At high energies, the low energy Planck mass is not relevant to black hole/particle physics. The physical Planck energy goes to infinity, so what does "transplanckian" particle collision mean? (The word "transplanckian gets thrown around not always thoughtfully or with clear significance.)

Newton constant is even more strongly scale dependent. It goes to zero as 1/k². I mentioned that in a post quite a few days back.
This is why I regard some of the old (say 1995-2003) discussion of "transplanckian" particle collisions forming black holes as unconvincing.
And even more dubious was the talk about "asymptotic darkness", but happily one hears very little about that nowadays. People were theorizing way beyond their base of solid understanding.

I see no indication that the obsolete discussion took the running of Newton's constant into account. What we have nowadays is a growing suspicion that gravity has an RG fixed point, and IF IT DOES, as many numerical studies now indicate it does, then G(k) falls off as 1/k².

The Shaposhnikov paper can even tell you the proportionality. So how is a black hole supposed to form? According to the asymsafe assumption gravity is essentially turned off at very high energy density, or at very high momentum transfer (q in the S&W paper) if we are discussing particle collisions.

So there is no indication that what the earlier authors had to say fits into OUR discussion which takes seriously the possibility that gravity is asymptotically safe and that the Renormalization Group plays an important role.

 

[marcus]

We can take a cue from the S&W paper http://arxiv.org/abs/0912.0208 .

Here's from the abstract:
"There are indications that gravity is asymptotically safe. The Standard Model (SM) plus gravity could be valid up to arbitrarily high energies. Supposing that this is indeed the case and assuming that there are no intermediate energy scales between the Fermi and Planck scales we address the question of whether the mass of the Higgs boson m_H can be predicted..."

Steven Weinberg's paper is in the same spirit. There are indications that gravity is asymsafe and that changes the picture. So let us see what we can do, assuming that it is.

These people show us what we ought to be going and what directions we ought to be looking. Assuming asymsafety we get
*a nice simple explanation of inflation.
*predictions that can be tested at accessible collider energies and probably also by astronomical observation.
*minimalistic approaches to unification.

And of course the assumption might be wrong! Predictions like Shaposhnikov and Wetterich derived might be falsified by LHC!
The point is that asymsafe unification is a good place to look for results and smart experienced people are focusing on it.
A defensive dismissal, at this point, based mostly on 1995-2003 papers or whatever, does not seem astute.

Here's from page 10 of Shaposhnikov and Wetterich:

"In conclusion, we discussed the possibility that the SM, supplemented by the asymptotically safe gravity plays the role of a fundamental, rather than effective field theory. We found that this may be the case if the gravity contributions to the running
of the Yukawa and Higgs coupling have appropriate signs. The mass of the Higgs..."

 

[oldman]

We should try to get this thread back on track as per the original Weinberg paper...

While this thread is temporarily dormant, there may be time for a naive question:

One of the reasons why inflation was invented was to explain the uniformity of the observed universe over regions too large to be causally connected in the early universe of the standard model.

If indeed gravity is asymptotically safe and is

...essentially turned off at very high energy density, or at very high momentum transfer

would this raison d'etrefor inflation be affected? Or does Weinberg's scenario merely resolve a puzzle with inflation?

It seems to me that the running down or switching off of gravity is such a drastic change in the physics of an expanding or inflating universe, ruled by gravity throughout its postulated history, that this is worth asking.

 

[marcus]

...

...If indeed gravity is asymptotically safe and is would this raison d'etrefor inflation be affected? Or does Weinberg's scenario merely resolve a puzzle with inflation?

It seems to me that the running down or switching off of gravity is such a drastic change in the physics of an expanding or inflating universe, ruled by gravity throughout its postulated history, that this is worth asking.

Personally I like the question a lot. My standards of naive may be different from yours, in any case I don't think of it as naive. I think this idea of doing barebones unification and barebones early-U cosmology based on renormalization group flow is a new initiative and just getting under way.

In Reuter's treatment not only does G(k) -> 0, but also cosmological constant Lambda(k) -> infinity. Because their dimensionless versions Gk² and Lambda/k² go to finite values.
With a huge cosmo constant you get tremendous inflation, just as nowadays with a small cosmo constant we get very gentle acceleration.

Earlier I mentioned only the running of G(k) because it was relevant to the sidetrack distraction topic of blackoles.
If you are curious about the distinction between the dimensionless and dimensionful versions of the two basic quantities, ask. I'll attempt more explanation or someone else will jump in.
===================

Maybe I shouldn't have used the expression "switched off".
It is simply that at very high collision energies, or very short distances, or very high densities, the repulsive term Lambda is very large and the attractive term G is very small.

But the laws do not change, nothing goes away or gets turned off for any appreciable duration. It is simply that the effective physical magnitudes of forces are different for an extremely brief inflationary episode.

I don't know how you picture the start of expansion. I imagine it as a bounce or a rebound from prior contraction. I don't ASSUME that since so far it hasn't been proven. It is just a possible conjecture. One of several options for visualizing.
====================

We live with running constants all the time. Quarks attract each other when comparatively widely separate. Nearby quarks have little interest in each other. I shouldn't say "switched off". The law is still there and operative, but its force varies with proximity.

=====================

NOW THE MEAT OF YOUR QUESTION is whether running constants might explain other things that inflation was earlier postulated to explain! Or which it later turned out to explain so well. Two main things come to mind, I think.
*Flatness
*The angular power spectrum of the CMB (scale invariance of temperature fluctuations).

That's an interesting idea. At first sight I don't see how to avoid inflation. My mind may be so locked into the inflation picture that I can't easily get out. It seems to me that as a geometrical event a bounce with extremely rapid initial expansion would be just the thing to achieve flatness and the observed main overall features of the CMB.

It would make predictions though. I imagine one would not see as much gravity wave imprint on the CMB---just a wild guess.

And the asymptotic safety vision of the early-U would probably have something to say about entropy. A brief episode with negligible Newton G would, I imagine, reset the apparent entropy clock of "curdling" (your word for condensed structure formation). Black holes and other blemishes in the prior contracting phase would be erased by a kind of renormalization group "botox". How could wrinkles persist in a high density phase with G(k) negligible? A deplorably wild guess.

It's a good line of questioning. I'll think about it some.

I think right now, at first sight, that the answer is that with the asymsafe early-U picture
*you can't avoid inflation
*and inflation is still useful in explaining flatness and scale invariance
*and asymsafe early-U will be shown to predict observable effects and be falsifiable.

Any reactions?

 

[oldman]

...(the) idea of doing barebones unification and barebones early-U cosmology based on renormalization group flow is a new initiative and just getting under way ...We live with running constants all the time...the answer is that with the asymsafe early-U picture
*you can't avoid inflation
*and inflation is still useful in explaining flatness and scale invariance
*and asymsafe early-U will be shown to predict observable effects and be falsifiable.

Your perspective is illuminating, especially when taken together with your thread on "QMG" and Reuter's no-frills QG, which clarified what is meant by asymptotic safety for me. The kinds of questions that seem to be floating around these days are fascinating. One that interests me is:

Are there any fundamental all-embracing theories in physics?

Or are there only "effective" theories, like electromagnetism (which is important far from an electron, where the charge doesn't "run') or superconductivity (which is important when electrons and phonons co-exist only in cold solids). The importance of gravity as we know it seems to stretch over the lifetime of the observed universe, but if it didn't always rule in its present form, with a small cosmological constant, could it be classed as an "effective" theory that has running constants?

Incidentally, has anyone yet devised a dimensionless version of c that could run?

 

[marcus]

Interesting questions!

...
Are there any fundamental all-embracing theories in physics?

Or are there only "effective" theories, like electromagnetism (which is important far from an electron, where the charge doesn't "run') or superconductivity (which is important when electrons and phonons co-exist only in cold solids). The importance of gravity as we know it seems to stretch over the lifetime of the observed universe, but if it didn't always rule in its present form, with a small cosmological constant, could it be classed as an "effective" theory that has running constants?

Incidentally, has anyone yet devised a dimensionless version of c that could run?

Some people might say it's all cut and dried---they might have a "correct" answer for each of your questions. On the contrary, I am not even sure that humans know what a "fundamental" theory is, or would recognize one if it stared them in the face.

About c: what occurs to me is that the scale parameter k is a momentum and there is no way you can combine c with a power of k to get something dimensionless.

So apparently, according to renormalization conventions, c cannot run. (Yet people construct frameworks in which they can talk about variable speed of light. I think there's a radical difference though.)

According to what I think is normal usage, we set c = hbar = 1 and then, since k is a momentum, Gk² is dimensionless. And Lambda is a reciprocal area, so it is the square of a momentum, and Lambda/k² is dimensionless.

In electromagnetism the operative running constant is alpha (approx. = 1/137) that relates charge to attraction and distance. Charge does not have to run, because alpha runs. As I recall it increases to more than 1/137 at very high energy and close proximity. Seem to recall alpha can get as big as 1/128
================

What I think is an intriguing question is what is meant by "fundamental".

It's not as simple an issue as some people may imagine. Percacci has a bit about this in his chapter in Oriti's book. And the new paper by Shaposhnikov and Wetterich has some bearing on the issue. For very high k, say with k being the momentum transfer in a collision, the Planck energy itself increases as k.
The Planck mass and the Planck energy go to infinity as k increases. So Shaposhnikov and Wetterich deal with this, and set out formulas for it, and build it into their equations.

Not everybody is so astute or careful. Others may for example assume that the Planck mass and energy are always equal to their low-energy values.

So the question arises what do you mean by saying a theory purports to be predictive out to arbitrarily high energy. Do we know enough about how nature behaves at Planck scale to distinguish between a "fundamental" theory and one which merely aspires to be applicable out to Planck scale?

And what is the appropriate "k" to use? People use various different handles on the scale, all supposed to give the same physical results. But why? what makes something a good handle? Energy density, collision energy, momentum transfer etc etc.
And why do coupling constants run? Can you always explain it by screening and antiscreening---by vacuum myths in other words---just so stories about the vacuum. And what is the vacuum. What is it when we throw out Minkowski space and declare that geometry is a dynamical something included in what we wish to explain? Why then do coupling constants run with scale? And what is scale? My basic feeling is that humans are wonderful animals but still rank beginners in this game.

So I can't answer your question about are there any really fundamental, not merely effective, physical theories. But glad you asked. Maybe someone else will put it into perspective for both of us.

 

[atyy]

A fundamental theory is one that does not predict its own breakdown. So QCD is a fundamental theory, as is Newtonian gravity, but both do breakdown.

 

[humanino]

A fundamental theory is one that does not predict its own breakdown. So QCD is a fundamental theory, as is Newtonian gravity, but both do breakdown.

It is an interesting point of view. Then I would say fundamental theories are in some sense inferior to effective theories, because we usually do not expect Nature to "breakdown", the prediction of new physics is the best we can get of any theory.

 

[DarMM]

It's not just that. It's the question whether we live in a universe that lies on the critical surface. Since the critical surface is most likely finite-dimensional and the space of all couplings is infinite-dimensional, the a priori probability that we actually live in such universe is zero. It would require either some not-as-of-yet-understood mechanism that puts the gravity in the UV fixed point, or the incredible amount of fine-tuning, to justify this scenario.

I don't fully understand this comment, maybe I'm missing something about the renormalization group.

I thought that the renormalized theory (i.e. one which has a continuum limit), is the renormalization group flow which emerges (roughly perpendicularly) from the critical surface at the fixed point. Provided the fixed point has only a finite number of rupulsive directions, then you have a theory. As long as the workers in this field can show that there is a critical point with a finite number of repulsive directions, then there will be finitely paramterised flows emerging from the fixed point. Which means a continuum theory with a finite number of parameters. I don't see why tuning would be necessary.

 

[DarMM]

Does AS really need a fixed point? Could it live with, say, a limit cycle?

Yes, the Wilson-Kandoff renormalization group takes place on a block lattice with everything in units of the lattice spacing $$a = 1$$. In lattice units the regularized integrals of perturbation theory have no divergences as $$a \rightarrow 0$$, because $$a$$ has disappeared.

However the problem of renormalization has been replaced by the problem of taking a continuum limit, with no $$a$$ where is the continuum limit $$a \rightarrow 0$$. This problem is solved by the lattice correlation length, which roughly tells you how big correlations are in lattice units. If you fix the correlation length in physical units, then the lattice correlation length has to diverge as you approach the continuum, as lattice units are smaller and smaller compared to physical units.

So the continuum limit is associated with points with infinite lattice correlation length, which are fixed/critical points.

 

[oldman]

In electromagnetism the operative running constant is alpha (approx. = 1/137) that relates charge to attraction and distance. Charge does not have to run, because alpha runs.

Thanks for this correction.

What I think is an intriguing question is what is meant by "fundamental".

It's not as simple an issue as some people may imagine. ...
So I can't answer your question about are there any really fundamental, not merely effective, physical theories. But glad you asked. Maybe someone else will put it into perspective for both of us.

I hope so. But I suspect that it depends on "times that are a-changing", as Bob Dylan once sang, so that any answer may not be final. Perhaps Newton's gravity was once viewed as quite fundamental. It still is in atyy's sense:

A fundamental theory is one that does not predict its own breakdown

Maybe a lifetime ago General Relativity was formulated as a fundamental theory of gravity. There seem to be doubts nowadays.

 

[marcus]

... any answer may not be final. Perhaps Newton's gravity was once viewed as quite fundamental. It still is in atyy's sense:

A fundamental theory is one that does not predict its own breakdown

Maybe a lifetime ago General Relativity was formulated as a fundamental theory of gravity. There seem to be doubts nowadays.

It begins to seem as if accurately predicting its own limitations ("effective" in Atyy's sense) is a VIRTUE to be appreciated in a theory.

General Relativity has its Penrose et al singularity theorems. The particle Standard Model has (correct me if I am wrong) Landau poles---blow-up points---which can be shifted around but not entirely avoided. Both theories illuminate their own limitations.

 

[DarMM]

Sorry, in message #150 reply to atyy, I should clear up what I meant by "Yes" in the first line. I meant yes Asymptotic freedom needs a critical point and no it cannot do with a limit cycle.

 

[atyy]

Sorry, in message #150 reply to atyy, I should clear up what I meant by "Yes" in the first line. I meant yes Asymptotic freedom needs a critical point and no it cannot do with a limit cycle.

Do theories with a limit cycle have a physical interpretation?

 

[DarMM]

Do theories with a limit cycle have a physical interpretation?

No, one needs a critical point to have a continuum limit. So a renormalization group flow which exhibits a limit cycle is simply another theory without a continuum limit. No different from a theory without a limit cycle which doesn't approach the critical point.

 

[atyy]

http://arxiv.org/abs/nucl-th/0303038
An Infrared Renormalization Group Limit Cycle in QCD
Eric Braaten (Ohio State U.), H.-W. Hammer

http://arxiv.org/abs/0803.2911
The impact of bound states on similarity renormalization group transformations
Stanislaw D. Glazek, Robert J. Perry

 

[DarMM]

http://arxiv.org/abs/nucl-th/0303038
An Infrared Renormalization Group Limit Cycle in QCD
Eric Braaten (Ohio State U.), H.-W. Hammer

http://arxiv.org/abs/0803.2911
The impact of bound states on similarity renormalization group transformations
Stanislaw D. Glazek, Robert J. Perry

The second paper is not related to field theory, so I'll only talk about the first.
The paper is concerned with the infrared behaviour of the theory, in that specific case I'm not familiar with the meaning of limit cycles.
However asymptotic safety is related to the ultraviolet behaviour of a field theory and obtaining a continuum limit. For this you need a critical point, a limit cycle would not do, as it wouldn't provide a diverging lattice correlation. So for the ultraviolet the theory cannot make do with a limit cycle.

However maybe I haven't understood what you are asking, providing the links on their own without commentary doesn't indicate what you are trying to say.

 

[atyy]

But don't we just need all the couplings to be finite for arbitrary energies?