Steven Weinberg offers a way to explain inflation

[marcus]

Mtd2 spotted this paper by Steven Weinberg that just went on arxiv.
http://arxiv.org/abs/0911.3165
Asymptotically Safe Inflation
Steven Weinberg
13 pages
(Submitted on 16 Nov 2009)
"Inflation is studied in the context of asymptotically safe theories of gravitation. It is found to be possible under several circumstances to have a long period of nearly exponential expansion that eventually comes to an end."

It could be an important paper, and in any case it's kind of elegant because the inflation episode occurs naturally, by the running of constants, without having to dream up some exotic matter field.

Reuter and Bonanno already proposed something along these lines. The essential arithmetic is very simple: there is evidence of the existence of a UV fixed point for gravity where the dimensionless forms of G(k) the running Newton and Lambda(k) the running dark energy constant both converge to finite values as the length scale k -> 0

But one can see by simple dimensional reasoning that their dimensionless forms are
G(k)/k² and Lambda(k)k².

So for them to go to finite limits as k->0 we must have G(k) getting very small and Lambda(k) growing enormous.

That's just the thing to cause rapid expansion. The Newton constant is almost nothing, so nothing to hold the geometry together, and the cosmological constant---the dark energy that accelerates expansion---totally huge.

But as inflation proceeds the scale k increases, which increases G and reduces Lambda. So the process eventually (actually quite quickly) shuts itself off.

 

[marcus]

Two things about this idea seem extremely appealing.
One is the "graceful exit" from inflation. People like Andrei Linde who dream up "inflaton" inflation scenarios have a terrible problem arranging for inflation to stop.
First they have to fantasize some exotic matter field never before seen in the real world just to get inflation to begin in the first place, and then they have to go into contortions about special "slow roll" down a potential slope so that inflation will stop. It is all very ad hoc.
Weinberg (and also Reuter and Bonanno) seem to have an inflation mechanism that is the opposite of ad hoc. Everything happens naturally, has to happen, because of the running of the main constants. And you even get a "graceful exit" to inflation.

The other thing that seems so appealing is that it doesn't use any machinery that we don't have already. It is very OCCAM. Occam says not to increase the number of entities in your model (if you can avoid it.) And we already have these two entities Newton constant and Lambda. They are the two main constants that occur in Einstein's basic GR equation. Just those two and the speed of light c (if you want to count that instead of setting it to equal one.)

Weinberg spoke about this in his 6 July CERN talk, which is on video. He said he had a renewed research interest in Asymptotic Safe QG, and particularly its application to cosmology. So we have been waiting for exactly this paper to appear. And now a little over four months later, here it is.

That 6 July talk was really enlightening. Especially the last 12 minutes, which you can get to by dragging the time button to minute 58. I should get the link. Here's the video:
http://cdsweb.cern.ch/record/1188567/
and here's a link to get slides PDF if desired:
http://indico.cern.ch/conferenceDisplay.py?confId=57283

 

[Sauron]

It is curious how few attention has got a seemingly challenging paper made by such an eminent physicist.

 

[Bob_for_short]

It is curious how few attention has got a seemingly challenging paper made by such an eminent physicist.

It was made public three days ago. What do you want?

 

[hamster143]

It is curious how few attention has got a seemingly challenging paper made by such an eminent physicist.

The whole idea of an asymptotically safe QG is a big stretch. (Although, whether it's a bigger stretch than the 100+ parameter SUSY, I cannot say.)

 

[marcus]

It is curious how few attention ...

Let me review. Weinberg lectured about asym.safeQG in 1976, published about it in 1979, the year he was awarded Nobel. Then early this year he posted a paper showing renewed interest in it and (as I recall) mentioning relevance to cosmo. That was in MARCH, http://arxiv.org/abs/0903.0568
(he described "his personal view" at that point.)
THEN PERIMETER decided to have a conference on on AsymSafe QG and discussed it with
Weinberg and Weinberg said he would attend.
THEN AT CERN ON 6 July he gave a talk opening a conference, with a lot of string theorists among others, which he
1. explained his renewed interest in AS, why he thinks it is worth investigating
2. said his own research was on AS and described the application to cosmo, explaining inflation
3. said string might not be needed for unification, and might not be how the world is.
4. sketched the history of "good old quantum field theory" and suggested that periodically it plateaus and people look at alternatives and then they abandon the alternatives and QFT advances to another plateau. He sketched a rough picture of the "stock market" for QFT over time and it looked like a flight of steps, ready to take another rise.
5. mentioned the Perimeter conference on AS that he would be attending in November.

Now I would say that the whole thing went very smoothly. Most of the "news" got around quietly between March and July, and whatever shift and adjustment happened without provoking any reaction. Now we are in a different situation, different mental climate. There has been a large recent increase in attention to AsymSafe QG. Attention in the form of people doing research and attending the conference, and visibility.

The whole idea of an asymptotically safe QG is a big stretch. (Although, whether it's a bigger stretch than the 100+ parameter SUSY, I cannot say.)

Hamster, I'm curious why you see it subjectively as a "big stretch". What about it seems to you difficult to accommodate mentally?

Essentially no new concepts or mathematical entities are required, it uses the machinery already in place as of, say, 1980.
The basic issue is whether or not the renormalization flow has a UV fixed point, on a finite dimensional critical surface.
Since Reuter's 1998 paper, evidence that it has such a fixed point gradually built up until, this year, the situation reached a tipping point.

Conceptually it seems pretty simple, so I don't understand why you see it as a big mental stretch. Please explain.

 

[hamster143]

The basic issue is whether or not the renormalization flow has a UV fixed point

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.

Secondly, it's skirting the big issue: even if QFT is valid beyond Planck scale, why is it set up the way it is (SU(3)xSU(2)x1, three generations, etc.).

Fortunately, the theory is, in principle, falsifiable, if we measure enough couplings and prove that the point we get is not on the trajectory that leads to the fixed point. Unfortunately, we only know one coupling with any degree of certainty (1 in 10^5) and most of them are suppressed by powers of Plank mass, and precise measurements of those couplings are not in the cards in the foreseeable future.

 

[marcus]

It's the question whether we live in a universe that lies on the critical surface.

Sounds like you are imagining things in terms of a multiverse. AsymSafe doesn't connect with multiversy thoughts. The universe is not supposed to "lie on the critical surface".

The story here is basic 1970s Ken Wilson stuff, the renormalization group flow belonging to our one universe. There are no alternative universes or probabilities such as you seem to be imagining.

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.

This doesn't connect with the discussion in this thread, so it does not call for a response.

 

[hamster143]

This has nothing to do with a multiverse. The question is, what happens if we take the set of coupling values in our universe and use renormalization group to take the UV limit? A priori, there's no reason to expect that we get into the fixed point, because the subspace of initial values that lead to the fixed point is measure zero in the space of all possible initial values. Contrast with QCD, where you can start with any value of coupling constant and you'll inevitably end up in the UV fixed point.

Weinberg is basically saying "look, gravity COULD be a renormalizable theory..." because, if the initial conditions are on the invariant surface, renormalization flow does not blow up near Planck mass. But it's hard to justify why it SHOULD be renormalizable, precisely because Wilson & such have disposed with the requirement.

 

[Finbar]

Hamster makes an interesting point. But the reason we know QCD flows to the fixed point is because we know the bare action and hence the underlying degrees of freedom. In the RG approach to asymptotic safety we only have average effective action and not the bare action.

If we had the bare action and then said "this is my theory of gravity and look its asymptotically safe" then we would be in the same situation as QCD.

 

[Haelfix]

Even more problematic, the critical surface could be spurious. You have to show universality, existence and stability across every type of approximation (1/epsilon expansions, truncation schemes etc) and inclusion of almost infinitely different matter terms. That is, the space of couplings most likely changes as you progressively refine your theory. No one knows how to even approach proving these things in general, so the state of the art is simply numerical investigations on various different types of simple toy models.

Even if you can show all of those things, and that's the way the world works, the problem for model builders remains the same. Eg you still lack general predictivity without actually doing the experiments that fixes the actual couplings perse (and determining whether you are or are not on the critical surface). And we are back to the problem of having to build galaxy size accelerators to pin down the dynamics of quantum gravity.

The original motivation for dropping field theory in the first place, was this generic futility argument. It didn't really matter if you found a plausible candidate theory of quantum gravity and figured out all the general principles. B/c unless you had some extra local symmetry group acting on your theory (say lots of SuSY or perhaps a conformal symmetry) you couldn't in general pin everything down uniquely. That was why string theory became so dominant, b/c there everything is fixed by consistency constraints and if you could figure out the solution, you had a unique theory across all energy scales.

Then there is the more theoretical issues (such as the wrong scaling behaviour of field theories in black holes) and so forth.

 

[hamster143]

But the reason we know QCD flows to the fixed point is because we know the bare action and hence the underlying degrees of freedom.

We don't know even that for sure. We know that a "toy QCD" with no dimension 5+ operators flows to the fixed point. There could be (there probably are) dimension 5+ operators suppressed by powers of some energy scale, and, once we reach that energy scale, QCD can do anything it wants. Below that scale the flow is in fact in the direction of a trivial UV fixed point. We tend to ignore higher-dimension operators because there's a lot of interesting dynamics even without them.

In GR, dimension 5+ operators are essential.

 

[Finbar]

unique theory? string theory? eh?

I don't follow you Haelfix?

And that black hole argument is rather silly...

 

[Haelfix]

Eh? String theory is completely unique. There are no independant adjustable free parameters. You can't 'tweak' the theory by adding new couplings or new matter content.

The black hole scaling argument is not 'silly' either! You have a major problem when general thermodynamic arguments implies degrees of freedom that scale as the area, whereas your general prediction for any *local* field theory are volume degrees of freedom.

 

[Finbar]

We don't know even that for sure. We know that a "toy QCD" with no dimension 5+ operators flows to the fixed point. There could be dimension 5+ operators suppressed by powers of some energy scale, and, once we reach that energy scale, QCD can do anything it wants. But, up to that scale, the flow is in fact in the direction of a trivial UV fixed point.

Indeed, QCD should be viewed as an effective theory and so should asymptotically safe gravity(if it exists) otherwise we won't get unification. The point with asymptotic safety is that we don't need to go beyond QFT or the symmetries we are aware of in nature to quantise gravity. Its just a call to Occam's razor.

 

[Finbar]

Eh? String theory is completely unique. There are no independant adjustable free parameters. You can't 'tweak' the theory by adding new couplings or new matter content.

The black hole scaling argument is not 'silly' either! You have a major problem when general thermodynamic arguments implies degrees of freedom that scale as the area, whereas your general prediction for any field theory are volume degrees of freedom.

So your telling me there is only one string theory, one vacuum? I'm not so sure.


It is a silly argument. The argument is that all QFT should be conformal at there UV fixed point. But an event horizon is not at the fixed point. Clearly an event horizon is an IR property as I can have an arbitrarily large black hole. If I could have a black hole with a radius of well under the Planck length then it would be a problem. But asymptotic safety predicts that black holes cannot have a mass of less than the Planck mass. So at the UV fixed point there is no horizon and hence no contradiction.

 

[Haelfix]

I can't decipher your last post. A few remarks.

1) There are many QFTs, an infinite space of possible theories. Now, each particular QFT typically has a single vacuum (or possibly multiple meta stable vacuums). String theory is the opposite. There is one single theory, but it has a large, possibly infinite amount of classical solutions. This isn't just pedantic, its a big difference. So for instance you can never talk about the critical surface of coupling constants in string theory, b/c that surface is a universal point.

2) "An event horizon is not at the fixed point", "At the UV fixed point there is no horizon", "But asymptotic safety predicts that black holes cannot have a mass of less than the Planck mass"

Those sentences don't make much sense... Nor do they have anything to do with the scaling properties of field theories.

 

[Finbar]

I can't decipher your last post. A few remarks.

1) There are many QFTs, an infinite space of possible theories. Now, each particular QFT typically has a single vacuum (or possibly multiple meta stable vacuums). String theory is the opposite. There is one single theory, but it has a large, possibly infinite amount of classical solutions. This isn't just pedantic, its a big difference. So for instance you can never talk about the critical surface of coupling constants in string theory, b/c that surface is a universal point.

2) "An event horizon is not at the fixed point", "At the UV fixed point there is no horizon", "But asymptotic safety predicts that black holes cannot have a mass of less than the Planck mass"

Those sentences don't make much sense... Nor do they have anything to do with the scaling properties of field theories.

1) There is at least 5 string theories which are conjectured to be all low energy approximations to M-theory.

2) Why doesn't it make sense? The UV fixed point is where the energy scale goes to infinity or the length scale goes to zero. Classical general relativity where one finds event horizons is the IR approximation to the theory.

Think of it this way if we ignore quantum effects we get black holes in classical relativity. Hence they are a feature of the theory at energies much lower than the Planck scale. The classical theory however will break down as the curvature diverges at the central singularity, but certainly not at the event horizon of a macroscopic black hole. The fact that the curvature diverges at the singularity implies that we need to use a quantum theory. So its here that we need to worry about the scaling of he theory not at the horizon.

To make sure, are you talking about the arguments in this paper?

http://arxiv.org/pdf/0709.3555

If not and you have some other argument can you show me another paper?

 

[atyy]

"... the asymptotic safety scenario. The recourse to uncontrolled truncations of the effective action, however, makes this program difficult to justify from a mathematical physics perspective." http://arxiv.org/abs/0906.5477

 

[MTd2]

1) There is at least 5 string theories which are conjectured to be all low energy approximations to M-theory.

All 5 superstring theories are the same, it`s just that they are different point of views of the same thing. As for M-Theory, I am not sure if there is just 1 coupling constant, given that thre are 3 fundamental entities, M2-branes, M5 branes and D0 branes.

Having said that, I really don`t like the fact that superstrings are both unique and have a huge number o classical low energy solutions. Sounds like what adjusting strings like epicycles until it fits a model.

 

[atyy]

All 5 superstring theories are the same, it`s just that they are different point of views of the same thing. As for M-Theory, I am not sure if there is just 1 coupling constant, given that thre are 3 fundamental entities, M2-branes, M5 branes and D0 branes.

Having said that, I really don`t like the fact that superstrings are both unique and have a huge number o classical low energy solutions. Sounds like what adjusting strings like epicycles until it fits a model.

Since there are only a finite number of possible low energy solutions, maybe none of them will fit this universe - so it isn't like epicycles.

 

[humanino]

Since there are only a finite number of possible low energy solutions, maybe none of them will fit this universe - so it isn't like epicycles.

Finite, like how many ? If there one solution per fermion in the visible universe ? Is there one per wavelength accomplished since the big bang by all photons in the visible universe ? Can you compare your number of solutions to anything "reasonably definable" ?

 

[atyy]

Finite, like how many ? If there one solution per fermion in the visible universe ? Is there one per wavelength accomplished since the big bang by all photons in the visible universe ? Can you compare your number of solutions to anything "reasonably definable" ?

10^500 or whatever the latest number is.

 

[humanino]

10^500 or whatever the latest number is.

I understand that this is a lower bound, and that the uncertainty is in the exponent, and it would not be a surprise if this exponent would grow by an order of magnitude. Besides, I asked you to name anything reasonable counting that many.

 

[atyy]

Besides, I asked you to name anything reasonable counting that many.

Oh, I don't know - why does that matter?

 

[humanino]

Oh, I don't know - why does that matter?

In principle, it does not, at least to me. But in practice, I do not think it is fair to say "there is a finite number of vacua, so the theory is falsifiable" because we need to somehow reduce the number of possible vacua, we could possibly not test all those predictions even in principle.

 

[atyy]

In principle, it does not, at least to me. But in practice, I do not think it is fair to say "there is a finite number of vacua, so the theory is falsifiable" because we need to somehow reduce the number of possible vacua, we could possibly not test all those predictions even in principle.

I agree - but won't it keep experimentalists happy for longer?

Well, a bit more seriously, what do you think of these guys comments following "could we imagine showing that the data is fit by none of these theories, thus falsifying the theory?" on p37 of http://arxiv.org/abs/hep-th/0701050

 

[Haelfix]

"1) There is at least 5 string theories which are conjectured to be all low energy approximations to M-theory."

They are all dual to each other, and hence one theory with one hilbert space (called M theory -- not to be confused with the M theory that is a limit of 11 dimensional SUGRA)

"Classical general relativity where one finds event horizons is the IR approximation to the theory."

The ultra high energy behaviour of quantum gravity is and must be GR again. It becomes classical again at ultra high energy scales, where particle collisions and the (trans) Planckian energy densities simply creates larger and larger black holes (this is called asymptotic darkness). It is this limit that is problematic for a field theory description of gravity, not the IR limit.

So the argument is this: The high energy limit for any consistent field theory (eg not effective), must be asymptotically free or asymptotically safe, and hence scale invariant. The problem (as that paper you linked explains) is you cannot simultaneously be scale invariant, and still describe the classical theory of Einstein gravity (that would be Weyl gravity). So there is a clash.

 

[atyy]

So the argument is this: The high energy limit for any consistent field theory (eg not effective), must be asymptotically free or asymptotically safe, and hence scale invariant. The problem (as that paper you linked explains) is you cannot simultaneously be scale invariant, and still describe the classical theory of Einstein gravity (that would be Weyl gravity). So there is a clash.

How about this comment by Distler? "In any case, the existence of a “quantum” conformal symmetry in quantum gravity is compatible with there being a nontrivial dimensionful scale in the theory, so I don’t see a-priori why it’s incompatible with black holes." http://golem.ph.utexas.edu/~distler/blog/archives/001585.html

 

[humanino]

So the argument is this: The high energy limit for any consistent field theory (eg not effective), must be asymptotically free or asymptotically safe, and hence scale invariant. The problem (as that paper you linked explains) is you cannot simultaneously be scale invariant, and still describe the classical theory of Einstein gravity (that would be Weyl gravity). So there is a clash.

IIRC, in this approach the UV limit is ultralocal and 2D.

 

[Haelfix]

I don't know what he has in mind exactly there, but somehow the field theory has to lose a dimension (not 2 but 1) for the scaling to match. How that is realized, is something that people will need to explain. I'm not saying its impossible, but something peculiar needs to take place. (I am aware of the talk about losing dimensionality, but that's more at the level of the space of coupling constants)

He's very correct that all bets are off in DeSitter space. No one knows or even has an expectation of what the high energy behaviour is like there. There is no SMatrix!

 

[MTd2]

No one knows for sure how many low energy solutions there are in 10^500. Could be infinite , could be finite but very big, there are many ways to count, each one with different plausible consistency conditions. Heh, but isn`t this offtopic?

 

[atyy]

No one knows for sure how many low energy solutions there are in 10^500. Could be infinite , could be finite but very big, there are many ways to count, each one with different plausible consistency conditions. Heh, but isn`t this offtopic?

I guess the corresponding question in Asymptotic Safety is how many scenarios are there? Do predictions change depending on matter content? Or are there "universal" predictions, eg. spectral dimension (though that alone may not nail down AS, since it is consistent with Horava, if the scalar mode can be fixed). Also, can the spectral dimension be measured - in CDT one of these "dimension" measures was defined with a particle diffusing on a fixed background - isn't this at odds with background independence - so can it be measured with realistic matter content?

 

[MTd2]

There is really no similar situation in asymptotic safety. Asymptotic safety is phase state of certain theories in which all coupling constant are constrained to a finite value. This value is a vector that can span finite dimensional surface, formed by coupling constants which cannot be restrained while transitioning to a low energy scale, like the others are.

 

[atyy]

There is really no similar situation in asymptotic safety. Asymptotic safety is phase state of certain theories in which all coupling constant are constrained to a finite value. This value is a vector that can span finite dimensional surface, formed by coupling constants which cannot be restrained while transitioning to a low energy scale, like the others are.

But they'll need matter to make predictions. I do agree whether pure gravity is safe is an interesting question, but from there to incorporating matter what happens?