Shaposhnikov Wetterich predicted 126 GeV Higgs in 2009

[marcus]

Let's try to see the S&W prediction in connection with Derek Wise's beautiful paper on Cartan gravity and symmetry breaking.

http://arxiv.org/abs/1112.2390
The geometric role of symmetry breaking in gravity
Derek K. Wise
(Submitted on 11 Dec 2011)
In gravity, breaking symmetry from a group G to a group H plays the role of describing geometry in relation to the geometry of the homogeneous space G/H. The deep reason for this is Cartan's "method of equivalence," giving, in particular, an exact correspondence between metrics and Cartan connections. I argue that broken symmetry is thus implicit in any gravity theory, for purely geometric reasons. As an application, I explain how this kind of thinking gives a new approach to Hamiltonian gravity in which an observer field spontaneously breaks Lorentz symmetry and gives a Cartan connection on space.
4 pages. Contribution written for proceedings of the conference "Loops 11" (Madrid, May 2011)

 

[marcus]

In 2009 Shaposhnikov and Wetterich predicted that Higgs would be observed at 126 GeV based on the assumption of asymptotic safe gravity and that standard model couplings were asymptotically free. Their prediction of Higgs mass came in the same box with one that nature had no new physics between here and the Planck scale.

This is a startling conclusion. In other words, once electroweak symmetrybreaking is taken care of, the good old standard model behaves like a fundamental theory (not merely effective) and holds all the way to Planck. As a signature prediction they derive along with that the 126 GeV figure for Higgs mass.
http://arxiv.org/pdf/0912.0208
Asymptotic safety of gravity and the Higgs boson mass
Mikhail Shaposhnikov and Christof Wetterich

==quote Shaposhnikov and Wetterich conclusions paragraph==
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 scalar is predicted m_H = m_min ≃ 126 GeV with a few GeV uncertainty if all the couplings of the Standard Model, with the exception of the Higgs self-interaction λ , are asymptotically free, while λ is strongly attracted to an approximate fixed point λ = 0 (in the limit of vanishing Yukawa and gauge couplings) by the flow in the high energy regime. This can be achieved by a positive gravity induced anomalous dimension for the running of λ . A similar prediction remains valid for extensions of the SM as grand unified theories, provided the split between the unification and Planck-scales remains moderate and all relevant couplings are perturbatively small in the transition region. Detecting the Higgs scalar with mass around 126 GeV at the LHC could give a strong hint for the absence of new physics influencing the running of the SM couplings between the Fermi and Planck/unification scales.
==endquote==

Thanks to Mitchell for reminding us of this this. Hermann Nicolai gave a talk in 2009 where he talked about this same "big desert" idea and referred to work by Shaposhnikov. It's a striking idea to say the least.

 

[marcus]

Now what I'm wondering is if the Derek Wise paper can have any relevance. Does anyone see a possible connection? Off hand one would say not.

But the Wise paper is, in my view, beautiful, deep, and revolutionary. By and large physicists have always used FLAT tangent spaces. Or more generally a VECTOR BUNDLE, a fiber bundle where the fiber is basically Euclidean. Wise generalizes from that and says they ought to allow curved fibers---homogeneous spaces, as in Cartan geometry.

What happens when you try to do AsymSafe gravity in the context of Cartan geometry? And then what happens to Shapo&Wetterich's idea when you translate that into the context of Cartan geometry?

I'll not try to answer these questions. I'll rely on the verdict of others. If there's nothing of interest here, so be it. If anyone thinks so, please let me know.

 

[dhillonv10]

A very interesting prediction, I do have a question though, marcus can you elaborate a bit on what you meant by: "Their prediction of Higgs mass came in the same box with one that nature had no new physics between here and the Planck scale. " Does that imply in some sense that as we go smaller in scales the laws remain the same? Thanks.

 

[marcus]

A very interesting prediction, I do have a question though, marcus can you elaborate a bit on what you meant by: "Their prediction of Higgs mass came in the same box with one that nature had no new physics between here and the Planck scale. " Does that imply in some sense that as we go smaller in scales the laws remain the same? Thanks.

Vikram I think you have read what they said correctly and understand it at least as well as I do. So I can only say "yes that is what it seems to mean."

The laws remain the same, the coupling constants continue to run, and (in the scheme they are proposing) no new physics enters to affect the running.

The figure of 126 GeV is a consequence of all that. So it can serve as a kind of test or experimental signature indicating that their scheme could be right. Or, if it turned out not to be 126, or close to that, then that would discredit/falsify their idea.
==========================

One way to formally write down the "running" of constants with scale is to use the wavenumber or momentum scale "k", also thought of as reciprocal length. And let k→∞.
that is like what you said: consider smaller and smaller length scale.
And the "running" is just the gradual change in some of the constants g(k) in the theory which are allowed to vary with scale (e.g. according to "renormalization group flow equations")

You may be familiar with all this but in case you are not:
"asymptotic free" means that g(k) → 0 as k goes to infinity. this is characteristic of the interaction of quarks. They don't feel attraction for each other when very very close. They are "free" of influence from each other, in the limit as they get close. ("asymptotic" means "in the limit as k→∞)

"asymptotic safe" means that g(k) → γ some finite number if you start from correct values of the coupling constants which can be determined at some scale by experimental measurement. You only have to determine a finite set of numbers by experiment, at accessible, and then the renormalization group equations will guide you home to the correct limiting values of the constants. That is what "safe" means.

You can probably google "asymptotic safety" and find out more. Steven Weinberg got the idea of it around 1976-1979.

Their scheme assumes that most SM couplings run but are "free", except (as they say) for the Higgs self-interaction λ. And they want gravity to be Einstein except that the basic constants in the Einstein equation G and Lambda should run, or more exactly their dimensionless versions should run, and be "safe". That is a version of gravity which has been extensively studied by Percacci (SISSA Trieste) and by Reuter (U. Mainz). You can google it. Weinberg has gotten interested in it again after some years of doing other stuff.

It looks as though regular Einstein gravity might actually be asymptotic safe. But no one is completely sure about that. Still, IF it is and if what they say is right about the SM couplings, then on that basis they make TWO consequences:
1. 126 GeV Higgs
2. SM and Einstein gravity shall act like fundamental theories and work all the way to Planck scale (i.e. no new physics enters the picture to affect how the couplings run).

I am just restating what I quoted in post #2, from

signature prediction they derive along with that the 126 GeV figure for Higgs mass.
http://arxiv.org/pdf/0912.0208
Asymptotic safety of gravity and the Higgs boson mass
Mikhail Shaposhnikov and Christof Wetterich

Their predictions are very bold and testable. They can be falsified if they are wrong. This, at least, is a virtue. Theory guys should try to only make theories that can be readily falsified if they are wrong. And Shaposhnikov Wetterich at least do this. (Many other theorists fail to obey this rule.)

 

[dhillonv10]

You remember my name, sweet! In any case, I remember reading something related. A paper showed that the idea of quantum foam having a widely different physics was actually wrong and in that paper the authors showed that the laws remain the same through plank scales. The 126 GeV prediction is still quite amazing to me. Also thanks for the explanation.

 

[friend]

Still, IF it is and if what they say is right about the SM couplings, then on that basis they make TWO consequences:
1. 126 GeV Higgs
2. SM and Einstein gravity shall act like fundamental theories and work all the way to Planck scale (i.e. no new physics enters the picture to affect how the couplings run).

How could there not be new physics? We still have to explain dark matter and dark energy.

 

[marcus]

How could there not be new physics? We still have to explain dark matter and dark energy.

Shaposhnikov Wetterich do not say there will be no new discoveries in physics They are talking about an intervening scale between electroweak and Planck that influences the running.
Here is the quote again so we can read it carefully:

A similar prediction remains valid for extensions of the SM [such] as grand unified theories, provided the split between the unification and Planck-scales remains moderate and all relevant couplings are perturbatively small in the transition region. Detecting the Higgs scalar with mass around 126 GeV at the LHC could give a strong hint for the absence of new physics influencing the running of the SM couplings between the Fermi and Planck/unification scales.​

Regarding "dark matter" Shapo-Wetter's scheme seems robust and flexible enough for some sort of dark matter particle to show up and join the SM party. You'd have to ask them about it.

As for "dark energy", more and more that looks simply like the cosmological constant and this constant runs (along with Newton G) in AsymSafe GR in a controlled way to finite values. I think there is no "dark energy" problem in Shapo-Wetter context, since they incorporate AsymSafe GR.

 

[mitchell porter]

Shaposhnikov is an advocate of the nuMSM, which features keV-scale right-handed neutrinos as the dark matter. See e.g. http://arxiv.org/abs/astro-ph/0703673.

 

[marcus]

Shaposhnikov is an advocate of the nuMSM, which features keV-scale right-handed neutrinos as the dark matter. See e.g. http://arxiv.org/abs/astro-ph/0703673.

Yes, thanks for pointing that out! In fact the νMSM (nu-minimal SM) is covered in a concise way in the 2009 paper by him and Wetterich. I should have mentioned that:

==quote Shaposhnikov Wetterich http://arxiv.org/abs/0912.0204 ==
Within this setting a very economical description of all interactions in Nature may be possible. One can assume that there is no new physics associated with any intermediate energy scale (such as Grand Unified scale or low energy supersymmetry) between the weak scale and k_tr. All confirmed observational signals in favor of physics beyond the Standard Model [such] as neutrino masses and oscillations, dark matter and dark energy, baryon asymmetry of the Universe and inflation can be associated with new physics below the electroweak scale, for reviews see [20, 21] and references therein. The minimal model – νMSM, contains, in addition to the SM particles, 3 relatively light singlet Majorana fermions and the dilaton. These fermions could be responsible for neutrino masses, dark matter and baryon asymmetry of the Universe. The dilaton may lead to dynamical dark energy [22, 23] and realizes spontaneously broken scale invariance which either emerges from the cosmological approach to a fixed point [22, 24] or is an exact quantum symmetry [25, 26]. Inflation can take place either due to the SM Higgs [27] or due to the asymptotically safe character of gravity [28]. Yet another part of new physics, related, for example, to the strong CP problem or to the flavor problem, may be associated with the Planck energy. In this Letter we show that this scenario leads to a prediction of the Higgs mass, which can be tested at the LHC...
==endquote==

 

[Thomas Larsson]

How could there not be new physics? We still have to explain dark matter and dark energy.

They say no new physics between the weak and Planck scales. There could still be new physics below the weak scale that went undetected because it interacts weakly.

I am terribly rusty with this kind of calculation and I never learned it properly anyway, so am not competent to judge its validity. It is a striking result though.

There seems to be the consensus that 126 GeV is the border where the SM becomes inconsistent. I wonder if calcuation that leads to this result is isomorphic to the SW calcuation, with a different interpretation. After all, they use the same in-data (e.g. top mass)

 

[atyy]

Motl links to http://www.ift.uam-csic.es/workshops/Xmas11/?q=node/2's talk at the IFT Inaugural conference, in which he discusses Shaposhnikov and Wetterich's prediction after 8 minutes from the start.

 

[MTd2]

Besides a Higgs at 126+-2 GeV being an indirect evidence of QG, THE FIRST ONE, what other thing we should see to have more confidence that we are seeing AS?

 

[ohwilleke]

There is a nice annotated bibliography on the asymptotic safety of gravity at http://www.percacci.it/roberto/physics/as/biblio.html. Experimental tests are suggested in the area of cosmological inflation.

The discussion of fractal dimensions in the emergent dimensionality of loop quantum gravity is suggestive of the possibility that some slight fractional deviation from four dimensionality in an experiment sensitive to fractal dimensionality of space-time might be observable.

Not really too the point but interesting and potentially practically relevant is this paper suggesting that some of the mathematical and calculation intractability of full fledged Einstein gravity may be due to our failure to discern that lots of problematic to calculate terms cancel out:

Z. Bern, J.J. Carrasco, D. Forde, H. Ita, H. Johansson (2007)
Unexpected Cancellations in Gravity Theories.
Phys. Rev. D77, 025010
arXiv:0707.1035 [hep-th]
Presents evidence that pure Einstein theory may have unexpected cancellations.

A paper by B.F.L. Ward addresses another topic that is one of the less discused but most fundamental theoretical inconsistencies between the Standard Model and GR:

B.F.L. Ward (2004)
Massive elementary particles and black holes.
JCAP 0402, 011.
arXiv:hep-ph/0312188
Performs a resummation of perturbative series using the Yennie-Frautschi-Suura method and shows that point particles are not black holes as a consequence of quantum effects.

And, for people who are worried about how to make dark energy work there are a series of papers along the lines of:

F. Bauer and L. Schrempp (2008)
Relaxing neutrino mass bounds by a running cosmological constant.
JCAP 0804, 006
arXiv:0711.0744 [astro-ph]

The most recent exposition of the basic idea of the 2009 paper is found at:

J.C.C. Felipe, L.C.T. Brito, M. Sampaio and M.C. Nemes (2011)
Quantum gravitational contributions to the beta function of quantum electrodynamics.
Phys. Lett. B700, 86-89 (2011)
arXiv:1103.5824 [hep-th]
A perturbative evaluation of the quadratic divergences due to gravity, emphasizing the source of ambiguities.

Since the AS Gravity effects manifest via the beta functions of the Standard Model, it follows that sufficiently precise precision tests of those beta functions at sufficiently high energies ought to be able to discern divergences between the non-quantum gravity corrected versions and those that are quantum gravity corrected long before they have any macroscopic impact. I personally have always been concerned about the strong importance SUSY gives to making the coupling constants converge at a triple point at high energies when there might be something inaccurate about the beta functions at high energies and AS Gravity supplies just such a potential correction.

Finally, for the fan club, PFs BSM favorite, had a paper on the subject shortly after it was proposed by Weinberg and a couple of his peers before going his own way with early LQG:

Lee Smolin (1982)
A fixed point for quantum gravity.
Nucl. Phys. B 208, 439-466
It was shown in this paper that a fixed point must exist in 4-d gravity in the leading order of a 1/N approximation.

 

[marcus]

Ohwilleke, thanks for the links.

Anyone following this might want to note some papers that came out today 7 Feb. For instance:
https://cdsweb.cern.ch/record/1421964/files/hcomb.pdf
"An excess of events is observed around mH∼126 GeV with a local significance of 3.5 standard deviations (σ)"

Taking account of look-elsewhere effect reduces the significance considerably
https://cdsweb.cern.ch/record/1421948/files/hgg.pdf
"..., the largest excess with respect to the background-only hypothesis in the mass range 110-150 GeV is observed at 126.5 GeV with a local significance of 2.9 standard deviations. The uncertainty on the mass position (±0.7 GeV) due to the imperfect knowledge of the photon energy scale has a small effect on the significance. When this uncertainty is taken into account using pseudo experiments, the significance is 2.8 standard deviations; this becomes 1.5 standard deviations when the look elsewhere effect [42] for the mass range 110-150 GeV is included."

So it's interesting but still too early to draw conclusions.

 

[marcus]

As you might expect, Cai Easson cite Shaposhnikov Wetterich in their new paper proposing a Higgs curvaton mechanism that would have generated the observed CMB fluctuations in the AsymSafe QG context.

Higgs Boson in RG running Inflationary Cosmology
Yi-Fu Cai, Damien A. Easson
(Submitted on 6 Feb 2012)
An intriguing hypothesis is that gravity may be non-perturbatively renormalizable via the notion of asymptotic safety. We show that the Higgs sector of the SM minimally coupled to asymptotically safe gravity can generate the observed near scale-invariant spectrum of the Cosmic Microwave Background through the curvaton mechanism. The resulting primordial power spectrum places an upper bound on the Higgs mass, which for canonical values of the curvaton parameters, is compatible with the recently released Large Hadron Collider data.
5 pages

Cai Easson's reference:
[14] M. Shaposhnikov and C. Wetterich, Phys. Lett. B 683, 196 (2010) [arXiv:0912.0208 [hep-th]]

==Cai Easson page 1==
...In this paper, we propose that the Higgs boson may play an important role in the early inflationary universe if the gravitational theory is asymptotically safe. In the frame of AS gravity, the gravitational constant G and cos- mological constant Λ are running along with the energy scale, and thus vary throughout the cosmological evolu- tion. It has been argued that if there are no intermediate energy scales between the SM and AS scales, the mass of the Higgs boson is predicted to be mH = 126 GeV with only several GeV uncertainty [14]. We find a suitable inflationary solution can be obtained in a cosmological system which contains a Higgs boson and AS gravity, along the lines of [15]. In this model, there are effectively two scalar degrees of freedom, one being the adiabatic mode and the other being an iso-curvature mode. We find the corresponding perturbation theory leads to both the primordial power spectrum for the curvature perturbation and the entropy perturbation. When the cutoff scale runs lower than a critical value, inflation abruptly ends and the Higgs field can give rise to a reheating phase. During this phase, the fluctuations seeded by the Higgs field can be converted into the curvature perturbation through the curvaton mechanism [16, 17]. We derive a relation between the spectral index of the primordial power spectrum and the Higgs mass. We confront this relation with the latest cosmological observations and collider experiment data, and find they are consistent under a group of canonical values of curvaton parameters.
==endquote==

[15] Y. -F. Cai and D. A. Easson, Phys. Rev. D 84, 103502 (2011) [arXiv:1107.5815 [hep-th]].
That might be interesting:
http://arxiv.org/pdf/1107.5815.pdf
Jordan-Brans-Dicke variant of GR.

 

[tom.stoer]

assume asymptotic safety + standard model is consistent and physically correct; then all the enormous work on LQG and other QG theories would be based on the fundamentally wrong assumption that GR cannot be quantized using standard QFT methods - and would be pointless.

 

[marcus]

Hi Tom!
As you can imagine, I have heard that said many times, since I've been reporting AsymSafe research here since, I guess, 2004 or 2005.
I'm not sure it has any meaning, except emotional, however.

It may be that LQG is wrong whether or not AS is right. We just have to see.
I suppose it could also be that LQG will eventually explain why gravity is asymptotically safe.
Both could provide good approximations to nature in the appropriate circumstances.

So far (to my knowledge) AS is not background indep, in any straightforward way at least, because if there is no scale then how can things run with scale? Reuter has tried to work around this problem at least since 2006, often referring to it and to possible solutions.

I'm an agnostic. I don't "pick winners" and as long as it's mathematically OK and not ruled out by observation I don't declare in advance that such and such is wrong. You claim to be certain that AS and LQG are incompatible? I don't claim to know that. Maybe they are, maybe not.

What matters to me is that right now both research programs have energy, are going places, getting new ideas, involving people i respect.

Reuter as I recall was one of the invited plenary speakers at the Loops 2005 conference. I remember being very impressed by his talk. Since then AS has not progressed as fast or drawn in as many researchers as I thought it would, but that's OK. On the other hand Loop has generally exceeded my expectations since then. Both programs remain very interesting. Perhaps you agree?

 

[tom.stoer]

I think it's amazing that such an enormous work and resulting profound insights can perhaps (!) be traced back to a wrong assumption ;-) That does not necessarily mean that the reults are wrong, of course

It would be interesting to find a close relationship between AS and LQG.

I saw some recent results on AS applied to Holst action with different results as for Einstein-Hilbert. This is striking.

The cosmological constant is treated differently in both approaches; in LQG one tries to incorporate it already when defining the algebraic foundations as a q-deformation of SU(2); in AS it behaves as a standard running coupling 'constant'; these two ideas seem to be incompatible at a very fundamental level.

 

[marcus]

...
The cosmological constant is treated differently in both approaches; in LQG one tries to incorporate it already when defining the algebraic foundations as a q-deformation of SU(2); in AS it behaves as a standard running coupling 'constant'; these two ideas seem to be incompatible at a very fundamental level.

It's 12 midnight here and I'm falling asleep. Have to sign off soon. In one paper I read the physical meaning of q has to do with the scale of angular resolution. I'm not sure that the fuzziness of angle measurement can't run. But you're probably right. I'll think about it in the morning. Have to get to bed.

==================
Next morning. Feeling more waked up. I assume that there are several ways to incorporate Lambda in LQG. A few papers have been written exploring the way using q-deformation. I'll keep an eye out for alternatives. Ashtekar recently posted a paper about positive Lambda in LQC (no mention of q-deformation, I haven't read enough of it to paraphrase or comment.)

I think LQG is a side issue in this thread, but to address your point:

assume asymptotic safety + standard model is consistent and physically correct; then all the enormous work on LQG and other QG theories would be based on the fundamentally wrong assumption that GR cannot be quantized using standard QFT methods - and would be pointless.

I think the fundamental assumption is to take the backgroundless ("no prior geometry" JA Wheeler) character of GR seriously: to ask if and how you can build a quantum field theory without any prior geometry. And make it conservative/minimalist in a sense: just 4D, no boundary, no extra jazz.
I think it's a worthy quest, exciting so far, generating many new ideas.

There might be some way to make AsymSafe QG backgroundless---they may have already done this and I simply missed it. Or the universe might really have a preferred geometry so that GR is basically wrong. So then one should not even try for a quantum field theory with no prior geometry.

 

[Haelfix]

I would say it the opposite way actually. LQG requires the asymptotic safety program as a necessary condition in order for it to have any hope of being theoretically consistent. That is, unless there are new hitherto unknown objects in the theory that could unitarize the physics in some novel way.

Anyway, there has been really interesting exact work and solutions in 2+1 pure gravity recently by Maloney et al.
http://arxiv.org/abs/arXiv:1111.1987

The belief is that there might be a mathematically rigorous proof in principle of the AdS/CFT relation in 3 dimensions just around the corner.

What is really interesting imo (if I was a quantum gravity guy and/or interested in LQG), is that they have found a partition function (strictly speaking the Ising model) and a pure quantum theory that has no semiclassical limit!

Doesn't that ring a bell!

 

[marcus]

I don't want to lose the main thread here which is the possible relevance of the Shapo-Wetter scenario related to their 126 GeV Higgs prediction. Since we've turned a page, here's a reminder (post #16) that Cai Easson cite Shaposhnikov Wetterich in their new paper proposing a Higgs curvaton mechanism that would have generated the observed CMB fluctuations in the AsymSafe QG context.

http://arxiv.org/abs/1202.1285
Higgs Boson in RG running Inflationary Cosmology
Yi-Fu Cai, Damien A. Easson
(Submitted on 6 Feb 2012)
An intriguing hypothesis is that gravity may be non-perturbatively renormalizable via the notion of asymptotic safety. We show that the Higgs sector of the SM minimally coupled to asymptotically safe gravity can generate the observed near scale-invariant spectrum of the Cosmic Microwave Background through the curvaton mechanism. The resulting primordial power spectrum places an upper bound on the Higgs mass, which for canonical values of the curvaton parameters, is compatible with the recently released Large Hadron Collider data.
5 pages

Cai Easson's reference:
[14] M. Shaposhnikov and C. Wetterich, Phys. Lett. B 683, 196 (2010) [arXiv:0912.0208 [hep-th]]

==Cai Easson page 1==
...In this paper, we propose that the Higgs boson may play an important role in the early inflationary universe if the gravitational theory is asymptotically safe. In the frame of AS gravity, the gravitational constant G and cos- mological constant Λ are running along with the energy scale, and thus vary throughout the cosmological evolution. It has been argued that if there are no intermediate energy scales between the SM and AS scales, the mass of the Higgs boson is predicted to be m_H = 126 GeV with only several GeV uncertainty [14]. We find a suitable inflationary solution can be obtained in a cosmological system which contains a Higgs boson and AS gravity, along the lines of [15]. In this model, there are effectively two scalar degrees of freedom, one being the adiabatic mode and the other being an iso-curvature mode. We find the corresponding perturbation theory leads to both the primordial power spectrum for the curvature perturbation and the entropy perturbation. When the cutoff scale runs lower than a critical value, inflation abruptly ends and the Higgs field can give rise to a reheating phase. During this phase, the fluctuations seeded by the Higgs field can be converted into the curvature perturbation through the curvaton mechanism [16, 17]. We derive a relation between the spectral index of the primordial power spectrum and the Higgs mass. We confront this relation with the latest cosmological observations and collider experiment data, and find they are consistent under a group of canonical values of curvaton parameters.
==endquote==

[15] Y. -F. Cai and D. A. Easson, Phys. Rev. D 84, 103502 (2011) [arXiv:1107.5815 [hep-th]].
That might be interesting:
http://arxiv.org/pdf/1107.5815.pdf
Jordan-Brans-Dicke variant of GR.

[16]D. H. Lyth and D. Wands, Phys. Lett. B 524, 5 (2002)
http://arxiv.org/abs/hep-ph/0110002
Generating the curvature perturbation without an inflaton
David H. Lyth, David Wands
(Submitted on 28 Sep 2001)
We present a mechanism for the origin of the large-scale curvature perturbation in our Universe by the late decay of a massive scalar field, the curvaton. The curvaton is light during a period of cosmological inflation, when it acquires a perturbation with an almost scale-invariant spectrum. This corresponds initially to an isocurvature density perturbation, which generates the curvature perturbation after inflation when the curvaton density becomes a significant fraction of the total. The isocurvature density perturbation disappears if the curvaton completely decays into thermalised radiation...
8 pages.

 

[MTd2]

So, inflation, according to this view, is very closely related to the electroweak force. Maybe some neutrinos are transported by some sort of inflation, which makes it warp drive?

 

[marcus]

So, inflation, according to this view, is very closely related to the electroweak force. Maybe some neutrinos are transported by some sort of inflation, which makes it warp drive?

I'm not sure what your reasoning is but I'll try to comment. The Higgs field is not DRIVING inflation in the Cai Easson picture. I suspect what drives inflation is simply Lambda because in AS Lambda(k) increases without bound as the scale k increases.

So you could say that a uniform classical "dark energy" (which is simply the cosmo constant) is what motivates inflation.

What that leaves unanswered is what causes fluctuations which we observe in CMB and which we think were the seeds of structure. the CMB has temperature fluctuations of about 1/1000 of one percent.

So many people prefer to believe in an "inflaton" field instead of simply RG large Lambda.

But that "inflaton" idea leads to elaborate fairy tales of eternal proliferating bubble universes.

So Cai Easson just say look you do not need an "inflaton field" to explain the fluctuations, the fluctuations are already explained just right by the Higgs field!
So then one can go back to the large running Lambda (natural for AS) to drive inflation.

 

[tom.stoer]

I would say it the opposite way actually. LQG requires the asymptotic safety program as a necessary condition in order for it to have any hope of being theoretically consistent. That is, unless there are new hitherto unknown objects in the theory that could unitarize the physics in some novel way.

I still don't see why LQG should be inconsistent (due to missing degrees of freedom) b/c totally different approaches claim something like that.

 

[marcus]

Hi Tom, didn't see your post. This is clarification in case other people are reading the thread.
Just to be sure everybody understands in the basic AsymSafe picture that Shapo-Wetter are using, and also Cai Easson, the whole idea is that the dimensionless versions of G and Λ go to finite values as the skale k goes to infinity.
Think of k as momentum or wavenumber or as inverse length. Then k² is inverse area.
Now Λ is a constant curvature quantity, an inverse area. So the dimensionless number λ = Λ/k². This is what goes to a finite limit as k→∞ (say the AS people Reuter Percacci and friends). The only way this can happen is if the dimensionful cosmo constant Λ becomes huge as k increases.

So as you go back in time towards the start of expansion (whether it is a Loop cosmology bounce or whatever however caused it) the energy density gets very big and k increases and so Λ becomes huge, so it is responsible for inflation. No "inflaton".

Cai Easson are just working out details of where the matter came from and the fluctuations.
It is a natural extension of the AsymSafe story.

==========another topic===============
Tom, since you and Haelfix continue being interested in the relation of Loop to AS (even though it might not be exactly on topic) I should put in a pointer to Ashtekar about LQC with positive cosmo constant. It is NOT a q-deformation in this LQC treatment---it is just a constant which presumably could run as one desires in AsymSafe.
http://arxiv.org/abs/1112.0360
Positive cosmological constant in loop quantum cosmology
Tomasz Pawlowski, Abhay Ashtekar
(Submitted on 1 Dec 2011)
The k=0 Friedmann Lemaitre Robertson Walker model with a positive cosmological constant and a massless scalar field is analyzed in detail. If one uses the scalar field as relational time, new features arise already in the Hamiltonian framework of classical general relativity: In a finite interval of relational time, the universe expands out to infinite proper time and zero matter density. In the deparameterized quantum theory, the true Hamiltonian now fails to be essentially self-adjoint both in the Wheeler DeWitt (WDW) approach and in LQC. Irrespective of the choice of the self-adjoint extension, the big bang singularity persists in the WDW theory while it is resolved and replaced by a big bounce in loop quantum cosmology (LQC). Furthermore, the quantum evolution is...
36 pages

The two have certainly not been joined yet! And with Loop cosmo in present form seem to me temporarily at least a bad match. But perhaps not ultimately incompatible.

 

[Haelfix]

"I still don't see why LQG should be inconsistent (due to missing degrees of freedom) b/c totally different approaches claim something like that."

I didn't say that!

What we do know about unitarity in quantum gravity is a bit of a subtle story, and i'd be glad to explain (or rather point the way through the literature) a little some time in another thread. The problem is you really do need to sidetrack into toy models where we have exact or almost exact solutions (2+1gravity, AdS/CFT and string theory) to get some hold where people are coming from on this subject. In some sense, you can see where things go wrong by removing objects from the spectrum.

In particular, the physics of quantum black holes and what may or may not happen with high energy scattering essentially dictates that something very special seems necessary to rescue the tangible insights (like the area law) that we know from semiclassical gravity.

This is why the whole business about needing a UV completion or having some sort of special divergence structure (like AS) in the perturbation series is so paramount.

Of course this is subtle business to phrase exactly. Even in the QFT context, I'm sure you remember haggling about what one means exactly by tree level partial wave unitarity violation in field theories, and to what extent we can trust those types of results. Here, b/c of subtleties with horizons, the story is complicated tenfold.

Anyway some other time maybe!

 

[Harv]

What is really interesting imo (if I was a quantum gravity guy and/or interested in LQG), is that they have found a partition function (strictly speaking the Ising model) and a pure quantum theory that has no semiclassical limit!

Doesn't that ring a bell!

Ding Ding!

 

[marcus]

Ding Ding!

You Ding?

Lorentzian spinfoam propagator
Eugenio Bianchi, You Ding
(Submitted on 29 Sep 2011)
The two-point correlation function is calculated in the Lorentzian EPRL spinfoam model, and shown to match with the one in Regge calculus in a proper limit: large boundary spins, and small Barbero-Immirzi parameter, keeping the size of the quantum geometry finite and fixed. Compared to the Euclidean case, the definition of a Lorentzian boundary state involves a new feature: the notion of past- and future-pointing intertwiners. The semiclassical correlation function is obtained for a time-oriented semiclassical boundary state.
13 pages
http://arxiv.org/abs/1109.6538

 

[Finbar]

So far (to my knowledge) AS is not background indep, in any straightforward way at least, because if there is no scale then how can things run with scale? Reuter has tried to work around this problem at least since 2006, often referring to it and to possible solutions.

AS is background independent in a straightforward sense no specific background plays a prominent role. In LQG there is no background so it is background independent in a trivial sense. In AS there is a background but the running of the beta functions are independent of the background.


Now if a specific background is used, to make a calculation possible with current techniques, the result is that all the beta functions can not be distinguished. For example working on Einstein spaces one cannot tell between scalar curvature squared and Ricci squared.


So you see the only way to test AS properly such that we know the actual properties of the fixed point is to make no choice as of background.

 

[marcus]

Hi Finbar, I've heard Reuter make that argument on several occasions. The lack of straightforward freedom from any prior geometry seems to bug him.

His argument is that you need a prior geometry to set things up, but it doesn't matter WHICH prior geometry you pick. You need something to get started, to define the betafunctions, to set up the RG flow etc. But then, if you believe his argument, you always get the same fixed point.

In a sense that should be satisfactory, but the whole thing is still a little iffy and nebulous.

What if you are dealing with a situation where GR has a singularity and there IS no metric to use as your prior metric. What if you are trying to study the very Early, or black holes etc.

Personally I'd like to see Asymptotic Safety as the RESULT of some more fundamental theory like Loop. I think AS will turn out to be extremely useful as an effective layer based on some deeper understanding of geometry.

 

[marcus]

Finbar, I'd be really interested to know your reaction to the new paper by Damien Easson and Yifu Cai.

It looks like we can dispense with the "inflaton" idea and get inflation just from the run-up of Lambda at high density. AS seems to have a conspiracy of running constants to ensure a bounce---G goes to zero and Lambda gets infinitely large.

A more fundamental theory would probably not have Lambda actually go to infinity, but that is a detail.

BTW Arizona State seems to have gathered some notable talent in cosmology e.g. Lawrence Krauss as well as Easson. Cai is one of the ASU postdocs. I think the Cai Easson paper is a gamechanger and it helps to put ASU on the map for me.

You can get it by googling "Cai Easson higgs cosmology" or even just "cai easson higgs"
http://arxiv.org/abs/1202.1285.

What I'm looking for is for LQG to provide fundamental support for Asym Safety which works around classical singularities where a naive Reuter version of AS might fail, and which can use AS as an effective way to model inflation, bounce, primordial BH evaporation and other things of interest.

 

[Finbar]

Hi Finbar, I've heard Reuter make that argument on several occasions. The lack of straightforward freedom from any prior geometry seems to bug him.

His argument is that you need a prior geometry to set things up, but it doesn't matter WHICH prior geometry you pick. You need something to get started, to define the betafunctions, to set up the RG flow etc. But then, if you believe his argument, you always get the same fixed point.

In a sense that should be satisfactory, but the whole thing is still a little iffy and nebulous.

What if you are dealing with a situation where GR has a singularity and there IS no metric to use as your prior metric. What if you are trying to study the very Early, or black holes etc.

Personally I'd like to see Asymptotic Safety as the RESULT of some more fundamental theory like Loop. I think AS will turn out to be extremely useful as an effective layer based on some deeper understanding of geometry.

You seem to be implying that the background field method is dodgy? It is a well established tool in QFT and I don't see any reason to question it.

AS says that there are no unphysical divergencies so such singularities should not be in the Hilbert space. On the other hand I see no reason to not include metrics with curvature singularities which are sufficiently weak.

 

[marcus]

How effective AS can be at modeling the "big bang" singularity or whatever replaces is is somewhat a matter of opinion. Here's what I mainly wanted to ask you about:
==quote post #32==
Finbar, I'd be really interested to know your reaction to the new paper by Damien Easson and Yifu Cai.

It looks like we can dispense with the "inflaton" idea and get inflation just from the run-up of Lambda at high density. AS seems to have a conspiracy of running constants to ensure a bounce---G goes to zero and Lambda gets infinitely large.

A more fundamental theory would probably not have Lambda actually go to infinity, but that is a detail.

BTW Arizona State seems to have gathered some notable talent in cosmology e.g. Lawrence Krauss as well as Easson. Cai is one of the ASU postdocs. I think the Cai Easson paper is a gamechanger and it helps to put ASU on the map for me.

You can get it by googling "Cai Easson higgs cosmology" or even just "cai easson higgs"
http://arxiv.org/abs/1202.1285.

What I'm looking for is for LQG to provide fundamental support for Asym Safety which works around classical singularities where a naive Reuter version of AS might fail, and which can use AS as an effective way to model inflation, bounce, primordial BH evaporation and other things of interest.
==endquote==

 

[marcus]

Safe gravity describes the Loop bounce (?)

Finbar, another point: you may have watched Steven Weinberg's invited talk at the Strings 2010 conference (in Texas that year) and recall that it was not about String but about Asym Safe gravity. He described his frustrations with trying to model the bang and inflation with AS.

It's a natural thing to try, given the growing recognition of early universe cosmology (euc) as an important arena for testing theories.

The very high energy density, high curvature, regime seems to be a Loop strong point, where it gets results. Being completely free of background geometry could be helping there.

So for any newcomers to the discussion I'll review the essential fact about Safe gravity:
the conjecture that the dimensionless forms of G and Λ run to finite numbers as the energy scale k → ∞.

But the dimensionless forms of the two couplings are g = k²G and λ = Λ/k².

That means as we go back to the alleged singularity, G as a physical quantity must go to zero and the physical Λ must grow without bound.

This is a clear recipe for a bounce.

Asymptotic Safe gravity is begging for a Loop basis.

 

[Finbar]

Personally I don't like the idea of the bounce. It may come out in some simple quantum cosmology setup but I think its due to there being to much simplicity in the model. The problem I see with the bounce is that it's a violation of the second law.


There is a long way to go in any theory of quantum gravity solving the problems of the early universe. A lot more research needs to be done before something like AS can get a grip on this.

 

[marcus]

... The problem I see with the bounce is that it's a violation of the second law. ...

I see you are focusing on (your) intuition about correctness, rather than on what the theories say.
What I wanted your reaction to is what I think is a significant overlap between Safe and Loop
(they could either turn out right or wrong descriptions of nature, that's secondary here).

I wonder if you have any thoughts on the observation that Safe seems to agree with Loop bounce---because going back in time you get G→0 and Λ→∞

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

As for your objection about entropy, for the law to apply the phase space must be continuously defined. I don't think you can even define the metric at the moment of the bounce, much less the gravitational entropy. So second law is moot.

 

[Finbar]

I see you are focusing on (your) intuition about correctness, rather than on what the theories say.
What I wanted your reaction to is what I think is a significant overlap between Safe and Loop
(they could either turn out right or wrong descriptions of nature, that's secondary here).

I wonder if you have any thoughts on the observation that Safe seems to agree with Loop bounce---because going back in time you get G→0 and Λ→∞

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

As for your objection about entropy, for the law to apply the phase space must be continuously defined. I don't think you can even define the metric at the moment of the bounce, much less the gravitational entropy. So second law is moot.

Actually I would say that the statement that you get G→0 and Λ→∞ is wrong. Its a meaningless statement to say G→n where n is a dimensionless number since G is dimensionful. Of coarse it is a subtle point when n=0 but I still think that it is a wrong statement and physically misleading.


Measured in meaningful units, i.e. the energy scale k which is being probed, both G and Λ are of order one close to the UV fixed point. So effects which are proportional to G cannot be neglected with respect to effects proportional to Λ at smaller distances.


So It is far from obvious whether there will be a bounce in AS. At least based on this reasoning.

 

[marcus]

I'll say the same thing but more carefully. I mean that the physical quantity Λ grows without bound, it becomes infinite *as a curvature* certainly not as a number (!) because it is not a number.
I did not mean what you thought I did, sorry. I just wrong Λ → ∞ as a shorthand to say that as a curvature term it gets infinitely large. You are quite correct to quibble about the language.

I'll repeat the simple explanation I gave earlier:

So for any newcomers to the discussion I'll review the essential fact about Safe gravity:
the conjecture that the dimensionless forms of G and Λ run to finite numbers as the energy scale k → ∞.

But the dimensionless forms of the two couplings are g = k²G and λ = Λ/k².

That means as we go back to the alleged singularity, G as a physical quantity must go to zero and the physical Λ must grow without bound.

This is a clear recipe for a bounce.

Asymptotic Safe gravity is begging for a Loop basis.

Finbar, the point I'm making is that in AS what goes to a finite number, like say 1.5 is the ratio of two physical quantities Λ /k² = λ → 1.5 (say )

For convenience we're using natural units where k can be interpreted as a wavenumber and k² as a curvature, so the ratio is dimensionless. So the limit in the UV with k growing without bound must have Λ grow without bound.

 

[marcus]

...So It is far from obvious whether there will be a bounce in AS. At least based on this reasoning.

It never occurred to me that there would be a bounce in AS. I certainly wouldn't say it is obvious! I don't think AS is sufficiently background independent so it is a partially lame theory which I don't suppose capable of resolving the cosmo singularity.

It may turn out that Loop can serve as a BASIS or vehicle to realize some AS insights. Because (by abuse of notation, of course they are not dimensionless numbers!) G→0 and Λ→∞.
That means what holds stuff together shrinks to nothing and what blows stuff apart gets huge. It is a recipe for a bounce. Loop can realize the bounce that AS suggests happens (but is too background dependent to be able to implement.)

That is why I speculate that Asym Safe gravity is begging to be put on a Loop basis.
And that part is clearly just a speculative guess.

Yesterday Frank Saueressig gave a superb talk on Asym Safe gravity. The video is here:
http://pirsa.org/12020088/
It can serve both as a clear introduction for newcomers and a report on some of the interesting things that have come up in recent AS research. Recommend anybody interested in AS to watch it.

 

[Finbar]

Marcus,

When you say that AS in gravity is not background independent what is it you are referring to?
AS safety is a scenario for a field theory with an UV fixed point. It doesn't pick out any specific background as playing a role. Where backgrounds appear is in the construction of tools in QFT to test AS. This happens in the RG approach. However lattice gravity is another way to test for AS and this doesn't use any backgrounds.

So I would conclude that there is nothing in the AS conjecture that requires a background.
When you say " I don't think AS is sufficiently background independent" really you refer to some of the tools used to test for AS. Indeed for the RG approach being able to calculate on an a totally arbitrary background is the biggest challenge. But I do view this as a technical challenge and not a conceptual one.


I think your speculation about a loop basis is interesting. Ultimately one would like to know which are the relevant i.e. IR repulsive operators for the UV fixed point. Perhaps a loop basis would shed some light on this.

 

[marcus]

... But I do view this as a technical challenge and not a conceptual one...

Reuter gave several talks addressing the conceptual challenge. As I recall 2007 at Morelia and 2009 at Perimeter. I could be misremembering which talks, I know he was concerned about it at the time, maybe it's been resolved since.

The point is what defines scale so that couplings can run. You seem to need a prior metric to give you an idea of scale so you can get set up in the first place. So Reuter had been challenged about the background independence of the theory and when I heard him talk about it he was using a prior metric to define scale and then arguing that the end result did not depend on which prior metric you choose to start with.
It was not clear that this argument really goes thru and gets you background independence, at least to me.

 

[Finbar]

Reuter gave several talks addressing the conceptual challenge. As I recall 2007 at Morelia and 2009 at Perimeter. I could be misremembering which talks, I know he was concerned about it at the time, maybe it's been resolved since.

The point is what defines scale so that couplings can run. You seem to need a prior metric to give you an idea of scale so you can get set up in the first place. So Reuter had been challenged about the background independence of the theory and when I heard him talk about it he was using a prior metric to define scale and then arguing that the end result did not depend on which prior metric you choose to start with.
It was not clear that this argument really goes thru and gets you background independence, at least to me.

If the beta functions are independent of the background then then they are background independent. It seems pretty clean cut to me. Once beta functions are explicitly shown to be independent of the background then you would have to agree that this is background independent. Technically it is very hard to do this because one has to evaluate traces in the RG equation without specifying the background. But I do not think there is any conceptual barrier to doing these calculations.

 

[atyy]

Maybe AS is background independent, which would be nice. But if it isn't, does that matter? As long as the non-Gaussian fixed point exists it'll be ok, isn't it?

BTW, why not a limit cycle?

 

[Finbar]

Maybe AS is background independent, which would be nice. But if it isn't, does that matter? As long as the non-Gaussian fixed point exists it'll be ok, isn't it?

BTW, why not a limit cycle?

If a specific background is used to look for fixed point say a sphere or an Einstein space then one cannot actually calculate the individual beta functions say for scalar curvature squared and Ricci squared. Thus you can not show whether the fixed point exists unless you keep the background arbitrary.

So you see there really is no choice in order to show AS you have to have background independence.

 

[marcus]

Thus you can not show whether the fixed point exists unless you keep the background arbitrary. ...

That is right and that is the kind of thing I was talking about when I mentioned Reuter struggling with this problem in 2007-2009. He raised the issue and made a big deal of it.
You have to show that the fixed point you get does not depend on the prior metric you start out with.

Now this can be done, I believe (although not every step was clear to me) in a NONSINGULAR case.
Where it could break, I think, is precisely in situations where Loop resolving a singularity.

So far AS has not been successful in resolving bang or hole singularities.
I was just reading a Cai Easson paper where they apply AS to BH and they get some results about low temp and slow evaporation of small BH which are similar to Loop results (Modesto) but, in fact, they do not cure the singularity. So it is very good, and parallels Loop, but it does not go all the way.

As long as you cannot handle classical singularities you do not have complete background independence.

 

[Max™]

Not sure if it's bad to bump this, but it was suggested by the similar threads link, and well, the prediction seems worth new consideration given the recent 125~ GeV boson announcement at the LHC.

 

[MTd2]

Philip fits with 126GeV with the most recent data! WOW!

http://blog.vixra.org/2012/07/04/higgs-live-vixra-combinations/

 

[mfb]

Given the large number of predictions, I would not interpret too much in an agreement. The collection has 5 predictions in the range 124-126 (and a similar density for lower and higher masses), all with different models.

Edit: They had another prediction of 150 GeV at the same time.

 

[marcus]

Not sure if it's bad to bump this, but it was suggested by the similar threads link, and well, the prediction seems worth new consideration given the recent 125~ GeV boson announcement at the LHC.

Philip fits with 126GeV with the most recent data! WOW!

http://blog.vixra.org/2012/07/04/higgs-live-vixra-combinations/

Shapo-Wetterich prediction was based on a certain premise about the Standard Model and about the way some parameters run. The experimental result confirming their prediction makes their PREMISE (that it was based on) kind of interesting. Maybe we should take a closer look at the key assumption they used.

Max thanks for reminding us of this.

Their assumption would, I think, have consequences for Quantum Gravity. So it is relevant to BtSM forum.
At first sight it seems to favor the Asymptotic Safety QG approach of people like Percacci and Reuter. But that is just at first sight and I wouldn't necessarily take it for granted.