Hamber-Tomiuri vs Shaposhnikov-Wetterich?
|Feb6-13, 10:00 PM||#1|
Hamber-Tomiuri vs Shaposhnikov-Wetterich?
Marcus has suggested that "Inconsistencies from a Running Cosmological Constant" (Hamber & Tomiuri; PF thread) may cause problems for "Asymptotic safety of gravity and the Higgs boson mass" (Shaposhnikov & Wetterich; PF thread), because the latter relies on asymptotic safety, and asymptotic safety (apparently) assumes a running cosmological constant.
From my perspective, SW's idea is of broader interest than asymptotic safety (i.e. it might be derivable from some other assumption), and also I don't know much about asymptotic safety. And Hamber-Tomiuri don't mention asymptotic safety, and Shaposhnikov-Wetterich don't mention the cosmological constant. So we are dealing with ideas that have a life apart from each other.
But they do have an overlap, and it would be educational to see that there really is a contradiction, or even just to see what Hamber-Toriumi's argument looks like, applied specifically to Shaposhnikov-Wetterich's scenario.
So I propose that (at least to begin with) this thread should focus specifically on the theory defined by the Neutrino Minimal Standard Model with asymptotically safe quantum gravity. We should try to understand whether and why the cosmological constant runs in that theory, and we should try to understand Hamber-Toriumi's argument as it would be applied in the context of that theory. (Or theories, if there is more than one way to define asymptotically safe quantum gravity.)
|Feb6-13, 10:28 PM||#2|
The solution of the resulting renormalization group equation for the two couplings G(k) and λ(k) is then truncated to
￼￼￼￼￼￼￼[equation 107 inserted here]
the Einstein and cosmological terms, a procedure which is more or less equivalent to the derivative expansion discussed previously. A nontrivial fixed point in both couplings (G∗,λ∗) is then found in four dimensions, generally with complex relevant eigenvalues ν−1, with some dependence on the gauge parameters .
There seem to be two problems with the above approach...
Some Asymptotic Safety QG papers cited by Hamber Tomiuri.
 M. Reuter, Phys. Rev. D 57, 971 (1998);
M. Reuter and H. Weyer, Gen. Relativ. Gravit. 41, 983 (2009);
E. Manrique, M. Reuter and F. Saueressig, Annals Phys. 326, 463 (2011), and references therein.
 O. Lauscher and M. Reuter, Class. Quant. Grav. 19 483 (2002).
 D. F. Litim, Phys. Rev. Lett. 92 201301 (2004); P. Fischer and D. F. Litim, Phys. Lett. B 638, 497 (2006).
|Feb6-13, 10:56 PM||#3|
The first of those references - "Nonperturbative Evolution Equation for Quantum Gravity" by Reuter - also appears in Shaposhnikov-Wetterich as reference 5 (their A.S. references are items 1 to 10 in their bibliography). So clearly this paper by Reuter is the "ur-text" where we can seek some common ground.
As you say, the reference to Reuter in Hamber-Tomiuri is oblique. So the way to proceed is as follows: use Reuter to place the SW argument in its full AS context, then look at that through the eyes of HT.
The big picture is that we have some theory - nuMSM + Einstein gravity - which can be formally defined by a lagrangian. But then to get anything out of it we have to make assumptions, approximations, employ ansatze. The SW argument examines the running of various quantities under a particular ansatz. We should want to see how the c.c. behaves under that ansatz too, and then try out the HT critique.
|Feb7-13, 12:48 AM||#4|
Hamber-Tomiuri vs Shaposhnikov-Wetterich?
Looking over more recent papers, Shaposhnikov seems to be the main standard-bearer (rather than Wetterich). Of the two he seems more involved with developing vMSM ideas. Just my subjective impression. After that 2009 SW paper the followup has been been by Shaposhnikov collaborating with others, or so it seems.
Two recent Shapo vMSM papers we might focus on and assess their dependence on AS gravity, cc running in particular:
http://arxiv.org/abs/1301.5516 (this has no dependence on Asymptotic Safety, I think)
http://arxiv.org/abs/1205.2893 (this seems to involve AS, with cc running, but Hamber might be wrong)
|Feb7-13, 01:14 AM||#5|
I have a slightly better grasp on this now. Percacci's asymptotic safety FAQ was useful. A quick summary (not 100% reliable, but this is what I've gleaned from the papers):
Ordinary perturbative quantum gravity contains infinitely many undetermined couplings, the coefficients of terms of arbitrarily high order. Asymptotic safety posits that, because of a fixed point in the RG flow, only finitely many of these parameters need to be specified, rendering the theory predictive. These quantities will include Newton's constant, the cosmological constant, and presumably some assortment of higher-order couplings.
Shaposhnikov and Wetterich posit that the standard model plus gravity is asymptotically safe, but the only gravitational parameter they employ is Newton's constant, which controls the magnitude of the gravitational contributions to the beta functions (RG behavior) of the gauge couplings, top quark yukawa coupling, and Higgs self-coupling. The Higgs mass prediction comes from a few extra assumptions about the sign and high-energy behavior of these quantities.
Hamber and Tomiuri examine quantum gravity through a variety of formalisms, and in each case conclude that the cosmological constant doesn't run. They do not explicitly use Wetterich's exact renormalization group equation (ERGE), which is used in asymptotic safety, but make a few comments on the A.S. program.
So there is considerable "logical distance" between the arguments of HT and the arguments of SW. Also, we need to remember that different theories, formalisms, and ansatze may give different results. Pure gravity in one dimension, and gravity+SM in another dimension, might have different RG properties, for specific mathematical reasons. A particular "result" may be an artefact of an approximation, going away when more detail is included. It's even possible that both sides (in the QG debate here) are wrong, that real gravity is not asymptotically safe and that the c.c. runs! As we try to resolve the "contradiction", we should bear in mind such possibilities.
|Feb7-13, 01:24 AM||#6|
A bit off-topic: Shaposhnikov (as you might expect) was one of the more than 100 co-authors of a white paper about righthand neutrinos.
Light Sterile Neutrinos: A White Paper
I imagine that he and a lot of other people are excited by the recently revised WMAP9 report
Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
G. Hinshaw, D. Larson, E. Komatsu, D. N. Spergel, C. L. Bennett, J. Dunkley, M. R. Nolta, M. Halpern, R. S. Hill, N. Odegard, L. Page, K. M. Smith, J. L. Weiland, B. Gold, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, G. S. Tucker, E. Wollack, E. L. Wright
(Submitted on 20 Dec 2012 (v1), last revised 30 Jan 2013 (this version, v2))...
31 pages, 12 figures
Jester at Resonaances has a comment "How many neutrinos are in the sky?" that was picked up by Peter Woit. http://resonaances.blogspot.com/
It is suggested that the answer is 4, not 3.
|Feb7-13, 12:20 PM||#7|
Hamber Toriumi does cast doubt on AS, but it might be wrong, or it might not apply for some technical reason.
So that side of the nuMSM idea might still be OK, the business with AS gravity and the Higgs prediction. But still more exciting right now is the prospect of explaining Dark Matter, which has become more substantial with HINSHAW ET AL. WMAP9 finding that their socalled "Neff" ≈ 4 rather than around 3.
Neff is measured from the microwave background and is the effective number of non-interacting neutrino-like species.
Some conflicting news. A "Pre-Planck cosmological parameters" paper appeared today featuring Neff = 3.24 ± .39 instead of the Neff = 3.84 ± .40 (from combined data sets) that one sees in the Hinshaw et al. "WMAP9" report I mentioned earlier.
See Erminia Calabrese et al. Cosmological Parameters from Pre-Planck CMB Measurements
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