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Steven Weinberg offers a way to explain inflation

by marcus
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Haelfix
#127
Nov28-09, 12:26 AM
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Ok good, we are on the same page then. The regimes are paremetrized by the magnitude of the impact parameter relative to the Schwarschild radius (well technically some sort of radius between two shockwaves, which is order magnitude the same as the schwarschild radius) and only for the case where b << R do you need to worry about strong coupling effects.. No one knows what goes on there exactly (although you can make the point that you need to smoothly match between regimes)

But the point is a generic field theory of gravity at transplanckian center of mass energies must be able to accomodate blackhole states in their spectrum. It doesn't matter that those states are formed in regimes that are effectively classical or semiclassical (at large impact parameters). You still require that the entropy scales as the area, and there you run into a problem b/c at those ultra high energy scales the putative, apparently universal field theory under question has to be conformal and at no point can it have any states that satisfy this type of scaling.

If AS was an effective theory, there would be no problem, b/c you could just argue that you picked the wrong epsilon parameter to perturb around and you don't capture the correct physical regimes, but here this is supposedly *the* theory of all quantum gravity valid at all energy scales with arbitrary matter couplings. It has to be able to have a spectrum that contains high energy blackhole states, since we know its low energy behavior is normal GR and will thus also have Eikonal and Coulomb regimes in high energy scattering experiments.
Finbar
#128
Nov28-09, 08:26 AM
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Quote Quote by Haelfix View Post
Ok good, we are on the same page then. The regimes are paremetrized by the magnitude of the impact parameter relative to the Schwarschild radius (well technically some sort of radius between two shockwaves, which is order magnitude the same as the schwarschild radius) and only for the case where b << R do you need to worry about strong coupling effects.. No one knows what goes on there exactly (although you can make the point that you need to smoothly match between regimes)

But the point is a generic field theory of gravity at transplanckian center of mass energies must be able to accomodate blackhole states in their spectrum. It doesn't matter that those states are formed in regimes that are effectively classical or semiclassical (at large impact parameters). You still require that the entropy scales as the area, and there you run into a problem b/c at those ultra high energy scales the putative, apparently universal field theory under question has to be conformal and at no point can it have any states that satisfy this type of scaling.

If AS was an effective theory, there would be no problem, b/c you could just argue that you picked the wrong epsilon parameter to perturb around and you don't capture the correct physical regimes, but here this is supposedly *the* theory of all quantum gravity valid at all energy scales with arbitrary matter couplings. It has to be able to have a spectrum that contains high energy blackhole states, since we know its low energy behavior is normal GR and will thus also have Eikonal and Coulomb regimes in high energy scattering experiments.
Ok I think we agree on the black hole scattering points now. But we still need to address the entropy scaling. What you said wasn't entirely correct.

A generic fundamental QFT has only to be conformal at the UV fixed point; by definition. So its only at this point that scaling arguments apply. So the question is when and where is physics at the UV fixed point. In gravity it is when the curvature becomes Plackian such that classical physics breaks down and we require UV completion. This happens only at very short distances r<lpl where the Weyl curvature C>Mpl^2. This is the case for the singularity of a generic black hole. But we can only say that all the physics of the black hole is at the UV fixed point when the curvature all the way the way up to the horizon is Plackian. This only happens when the radius of the BH is r~lp.
marcus
#129
Nov28-09, 10:41 AM
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Quote Quote by Finbar View Post
Ok I think we agree on the black hole scattering points now...
Then maybe you would explain something. Can you describe a scattering experiment which, if it were performed and came out as you imagine, would invalidate the AS approach?
Finbar
#130
Nov28-09, 11:45 AM
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Quote Quote by marcus View Post
Then maybe you would explain something. Can you describe a scattering experiment which, if it were performed and came out as you imagine, would invalidate the AS approach?

There are researchers currently looking into this and I would expect papers to be published sometime in the near future.

This paper may be of some interest http://arxiv.org/pdf/0707.3983
atyy
#131
Nov28-09, 12:07 PM
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Quote Quote by Finbar View Post
Quote Quote by Finbar View Post
A generic fundamental QFT has only to be conformal at the UV fixed point; by definition. So its only at this point that scaling arguments apply. So the question is when and where is physics at the UV fixed point. In gravity it is when the curvature becomes Plackian such that classical physics breaks down and we require UV completion. This happens only at very short distances r<lpl where the Weyl curvature C>Mpl^2. This is the case for the singularity of a generic black hole. But we can only say that all the physics of the black hole is at the UV fixed point when the curvature all the way the way up to the horizon is Plackian. This only happens when the radius of the BH is r~lp.
In fig 1 if I fix impact parameter and move to higher and higher energies, I'll move into the the strong gravity or classical black hole region. Won't I need the UV completion at this point - the classical theory won't work because we expect Hawking radiation from thermodynamics, and semi-classical theory won't work because of information loss?
atyy
#132
Nov28-09, 10:42 PM
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I've asked this before, but still don't understand the answer, so here it is again. The UV fixed point should be scale invariant - under what assumptions is that equivalent to conformal invariance?
Finbar
#133
Nov29-09, 02:13 PM
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Quote Quote by atyy View Post
In fig 1 if I fix impact parameter and move to higher and higher energies, I'll move into the the strong gravity or classical black hole region. Won't I need the UV completion at this point - the classical theory won't work because we expect Hawking radiation from thermodynamics, and semi-classical theory won't work because of information loss?
Ok so if we're in the semi-classical regime the black hole is radiating so the horizon shrinks. But as it shrinks and the horizon approaches the Planck length and the temperature approaches the Planck mass we then need a UV completion.

So far AS "solves" the information paradox by saying that the information is stored in a Planck size remnant. But I don't think this is a satisfactory solution.
atyy
#134
Nov29-09, 02:37 PM
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Quote Quote by Finbar View Post
Ok so if we're in the semi-classical regime the black hole is radiating so the horizon shrinks. But as it shrinks and the horizon approaches the Planck length and the temperature approaches the Planck mass we then need a UV completion.

So far AS "solves" the information paradox by saying that the information is stored in a Planck size remnant. But I don't think this is a satisfactory solution.
Hmmm, let me think about that. I was hoping that AS would prevent high energy scattering experiments by allowing only asymptotically dS spaces by enforcing a positive cosmological constant through the renormalization flow. (No, I don't really know what I'm talking about.)

What's wrong with the remnant solution?
Finbar
#135
Nov29-09, 02:37 PM
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Quote Quote by atyy View Post
I've asked this before, but still don't understand the answer, so here it is again. The UV fixed point should be scale invariant - under what assumptions is that equivalent to conformal invariance?
I think that scale invariance is a sub group of conformal in variance. But I'm not sure. So if a theory is conformal in the UV it has to be scale invariant and hence at a fixed point.
atyy
#136
Nov29-09, 02:42 PM
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Quote Quote by Finbar View Post
I think that scale invariance is a sub group of conformal in variance. But I'm not sure. So if a theory is conformal in the UV it has to be scale invariant and hence at a fixed point.
Yes, I think that's true. What I don't understand is why the UV fixed point must be conformal, though I understand it has to be scale invariant. I think that under some additional assumptions like unitarity, Poincare invariance or something, then scale invariant theories are conformal - but I don't know what the exact conditions are.

Eg. http://arxiv.org/abs/hep-th/0504197 or footnote 3 of http://arxiv.org/abs/0909.0518
Finbar
#137
Nov29-09, 02:43 PM
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Quote Quote by atyy View Post
Hmmm, let me think about that. I was hoping that AS would prevent high energy scattering experiments by allowing only asymptotically dS spaces by enforcing a positive cosmological constant through the renormalization flow. (No, I don't really know what I'm talking about.)

What's wrong with the remnant solution?
http://arxiv.org/pdf/hep-th/9508151

The Black Hole Information Paradox
Steven B. Giddings†
Department of Physics University of California Santa Barbara, CA 93106-9530
Abstract
A concise survey of the black hole information paradox and its current status is given. A summary is also given of recent arguments against remnants. The assumptions underly- ing remnants, namely unitarity and causality, would imply that Reissner Nordstrom black holes have infinite internal states. These can be argued to lead to an unacceptable infinite production rate of such black holes in background fields.
(To appear in the proceedings of the PASCOS symposium/Johns Hopkins Workshop, Baltimore, MD, March 22-25, 1995).


Theres also a another paper by Giddings but I can't find it right now
marcus
#138
Nov30-09, 06:17 PM
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The paper by Weinberg which is our topic is
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."
================

The basic idea is to explain a self-terminating inflation episode, without making up some exotic "inflaton" matter field, as a natural consequence of the running of couplings such as Newton's G. The couplings can be assumed to be at or near their UV limit at the start of expansion. And this by itself, Weinberg shows, is sufficient to cause exponential expansion.

We can think of the scale as related to density. As the universe expands, the density falls off, and the couplings depart from their values at the UV-limit. After some 60 e-foldings of expansion the density is low enough that inflation ends.

Some readers may wish to question this statement of Weinberg:

"We will work with a completely general generally covariant theory of gravitation. (For simplicity matter will be ignored here, but its inclusion would make no important difference.)"

More about matter in the context of Asymptotic Safety is here:
http://physicsforums.com/showthread.php?t=349513
in the "Grav. + GUT" thread.
uniquo87
#139
Dec1-09, 12:21 AM
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I would like to know the derivation of the field equations of quantum electrodynamics.
marcus
#140
Dec9-09, 09:00 PM
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We should try to get this thread back on track as per the original Weinberg paper.

There is no physical reason to assume black holes are especially relevant or significant in this context, and the Weinberg paper is not about black holes. It is about inflation. Asymsafe QG provides a neat and economical way to explain inflation.

Since I started the thread a great paper by Shaposhnikov and Wetterich has come out. http://arxiv.org/abs/0912.0208 I'll quote some excerpts. Here's from page 2.

From the studies of the functional renormalization group for Γk one infers a characteristic scale dependence of the gravitational constant or Planck mass,
MP2 (k) = MP2 + 2ξ0k2
where MP = (8πGN )−1/2 = 2.4 × 1018 GeV is the low energy Planck mass, and ξ0 is a pure number, the exact value of which is not essential for our considerations.

From investigations of simple truncations of pure gravity one finds ξ0 ≈ 0.024 from a numerical solution of FRGE [5, 11, 12]. For scattering with large momentum transfer q the effective infrared cutoff k2 is replaced by q2 . Thus for q2 ≫ MP2 the effective gravitational constant GN(q2 ) scales as 1/(16πξ0q2) , ensuring the regular behavior of high energy scattering amplitudes.
marcus
#141
Dec9-09, 09:32 PM
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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 MP means is the low energy planck mass. In the asymsafe picture, MP(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 in to OUR discussion which takes seriously the possibility that gravity is asymptotically safe and that the Renormalization Group plays an important role.
marcus
#142
Dec9-09, 09:45 PM
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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 mH 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
#143
Dec13-09, 01:44 AM
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Quote Quote by marcus View Post
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
#144
Dec13-09, 12:52 PM
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Quote Quote by oldman View Post
...

...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 cant 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.


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