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Deur's modified gravity: a type of MOND inspired by QCD

  1. Apr 19, 2014 #1
    I found a few curious arxiv papers by Alexandre Deur (via Twitter).

    Deur works in QCD. He explains QCD strings (flux line between quark and antiquark) as due to attraction between gluon field lines, ultimately due to gluon-gluon interactions. Phenomenologically this adds a linear term to the inter-quark potential. He proposes that something similar could happen in quantum gravity, owing to graviton-graviton interactions, but argues that the extra term would be logarithmic rather than linear. (All this is in his 2003 paper.)

    Then he suggests that this can substitute for dark matter, as an explanation of galactic rotation curves. He has a take on the Bullet Cluster (page 9 here), and even has his own new empirical regularity to report, regarding elliptical galaxies.

    I would welcome comment on the empirical plausibility of his idea, but I would especially like to have some insight into the theory side. The emergent linear term seems to be standard QCD, but how does his logarithmic correction to gravity look, e.g. from the perspective of the holographic principle? And is there anything like this attraction between lines of gravitational flux, in conventional quantum gravity?

    Deur's work has been mentioned on PF a few times before.
  2. jcsd
  3. Apr 20, 2014 #2


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    Well, I asked about this before... But I never got a satisfactory answer. But, well, this always looked like the best answer so far... Well, there's the 3.7KeV. But it doesn't mean it's all dark matter there is. It could just be another type of particle that just needs explaining, and might be just a tiny bit of all dark matter, just like the neutrinos is only a small fraction of dark matter.
    Last edited: Apr 20, 2014
  4. Aug 5, 2014 #3
    The theoretical justification for Deur's work is that gravitons carry energy-momentum and since gravity couples to energy-momentum (including rest mass, although it is zero for gravitons), then a graviton can directly couple to another graviton. This has been known for a long time. In the early 60s, in his gravitation lectures, Feynman was drawing his diagrams with graviton coupling to graviton.

    I don't know of any insight from the holographic principle, but the group theory way to understand this graviton self-interaction may be to realize that the gravity "charge" is the energy-momentun tensor. Since it is a matrix, it leads to a non-commutative group structure of gravity (if gravity can be described as a gauge theory). So gravity should be a non-abelian theory with self-interacting force carriers. Likewise for QCD: there are several QCD "charges" (the colors), so the group elements are matrices, so QCD is non-abelian. Then imposing local gauge invariance with the non-abelian group implies self-interaction terms for gluons. Does this make sense?

    The emergence of the log potential does not seem to be fundamental. Deur explains it (2014 paper) by the fact that in a planar distribution of matter, gravitons are confined to propagate in 2 dimensions. Any graviton that would wander out of the plan would be pulled back by gravity. A force confined in 2 dimensions goes as 1/r so its potential goes as log(r).

    I found a nice summary of Deur's work at:

  5. Aug 14, 2014 #4


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    FWIW, Dispatches From Turtle Island is my blog (Turtle Island is a pre-Columbian Native American name for North America).

    If Deur's math is right, then all phenomena attributable to dark matter can be attributed to non-linear effects of a General Relativity reproducing graviton particle based self-interaction that only manifests in cases that are not spherically symmetric, which is an underexplored area of mathematical modeling.

    In his analysis, dark matter phenemona increase in importance with mass scale (which is why MOND works at galactic scale, but underestimates galactic cluster scale effect), but only manifest to the extent that a system is not spherically symmetric, which is why elliptical galaxies appear to have proportionately less dark matter than spiral galaxies and why nearly spherical elliptical galaxies appear to have proportionately less dark matter than more elongated elliptical galaxies according to a set function that he shows holds on an empirical basis. It also explains why in the low mass solar system vicinity there are no observed DM effects.

    His approach also purports to explain the bullet cluster because in parts of the interaction of the colliding galaxies that are spherically symmetric, apparent MOND effects disappear, while in non-spherically symmetric regions they are strong.

    Of course the real genius of it all, if it works is that it does so with a theoretically well motivated functional form for these non-linear GR effects, with no new parameters not already found in GR (the none the less produce effects of the right order of magnitude), and with no non-SM particles other than the massless spin-2 graviton that quantum gravity theories almost universally assume to exist.

    But, the lack of replication or follow up on this very promising analysis by other investigators leaves one with pause over whether there is a flaw in this mathematical analysis.

    The most encouraging point on the front of replication is that there are a number of papers that explore fifth forth modifications of gravity with a Yukawa potential form of the type that Deur derives from first principles in the non-spherically symmetric GR case that similarly give rise to dark matter replicating results in systems to which he applies his analysis.

    Also it is somewhat encouraging to know that Deur's "day job" is in QCD physics, so while he might be mistaken, he is not likely to be mistaken in the way that a crackpot would be and it is entirely plausible that his familiarity with QCD mathematics of non-abelian gauge bosons might give him tools that lots of GR investigators would lack familiarity and comfort with using.

    Also encouraging is research arguing that the textbook maximum that one cannot generate a true tensor to describe the self-interaction of gravity on its own mass-energy and can only have a pseudo-tensor instead, is wrong because one can be generated if one permits oneself to consider second derivative terms and that this generates some version of f(R) gravity because the self-interaction term is proportionate to the Ricci tensor. http://arxiv.org/abs/1407.8028 This approach suggests that it may be possible to replicate Deur's work in the context of classical geometrical based formulations of GR simply by correctly deriving the self-interaction equation in GR which has been arguably inaccurately replaced with a flawed pseudo-tensor approach.

    Finally, it is worth noting the work of Juan Ramón González Álvarez who argues in http://juanrga.com/en/pdfs/General-relativity-as-geometrical-approximation-to-a-field-theory-of-gravity.pdf [Broken] that while he agrees with LQG investigators that it is fundamentally impossible to reproduce GR in a Minkowski space QFT, and that this can only be done in a truly background independent formulation such as LQG, that this doesn't mean that GR rather than a massless spin-2 graviton QFT in Minkowski space, rather than a quantum version of a truly background independent GR is the right choice. He argues that the differences are two subtle for current experimental tests of GR to distinguish and that where there are differences, the geometric approach of GR produces results that a problematic relative to a QFT of a graviton.

    His approach would suggest that a very simple massless spin-2 graviton extension of the SM, without any additional modifications, could fully achieve a quantum gravity theory that while not exactly equivalent to GR is identical in all ways that have been experimentally verified and is better than GR in particulars. The extreme flatness of space-time as measured experimentally argues that a Minkowski space approximations, even if not the truth, shouldn't be too much of a problem at least in weak fields.

    Taken together, these investigations open the door to a possible extension of the SM to include gravity including all phenomena attributed to DM, without new particles (other than the graviton) and without introducing any phenomena not already predicted by GR that simply have not been properly teased out of those equations with the right simplifying assumptions.
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