Can any, qg or string theory reproduce dark matter ?
I can only say as regards what i am familiar with in non-string QG, and
AFAIK the answer there is NOT SO FAR. There is not any non-string QG so far, that I know of, that reproduces dark matter.
There is quite a lot of development going on in QG these days. One might do that in future.
A footnote to that concerns various MOND theories like Bekenstein and also like that of Moffat. These are not quantum gravity theories but are modifications of the classical theory of gravity. I think of them as slight "corrections" to General Relativity.
These MOND theories avoid the need for Dark Matter and they are TESTABLE within the solar system. (Bekenstein Magueijo paper on MOND habitats in the solar system).
It would help if some MOND theories could be tested and would either pass or fail. If some version of MOND gained credibility then one could try quantizing THAT instead of the plain vanilla Gen Rel. In that case the goal would be a quantum gravity that takes care of dark matter, simply by reproducing MOND at large scale.
I'm going to attend this seminar:
Canonical gravity, York map and non-inertial frames: is dark matter a relativistic inertial effect?
Abstract: After a review of the simultaneity problem from Newton to special relativity, I describe the status of the Hamiltonian description of ADM metric and tetrad gravity emphasizing the role of non-inertial frames, the only one allowed by the equivalence principle, which replaces the relativity principle in general relativity (GR). After having shown the dynamical nature of the chrnogeometrical structure of spacetime in GR, I show that the natural Hamiltonian for the spacetimes allowing the incorporation of particle physics is the weak ADM energy (the energy problem in GR is connected with the dependence upon the inertial potentials of the ADM energy density, whose role in the dark energy problem is unknown). Having built the York map, there is a clear separation between the physical tidal effects and the gauge variables inside the gravitational field. Which types of relativistic inertial effects are described by the gauge variables is explicitly shown. One of them (the trace of the extrinsic curvature) describes the freedom in the choice of the convention for the synchronization of distant clocks, namely in the definition of the instantaneous 3-space. This freedom is absent in Newton theory, where the Euclidean 3-space is absolute. This gauge variable, appearing as a relativistic inertial force in Hamilton equations, may change from attractive to repulsive in different regions of the simultaneity surface. It could be the origin of dark matter in the rotation curves of galaxies in a framework more general of the non-relativistic MOND model and less naive of the Cooperstock-Tieu proposal.
Marcus, MOND is a modified Newtonian mechanics. It's Newtonian gravity with an extremely strange modification in the low accelaration regime. It's not even specially relativistic. It's a fascinating phenomenological tool but it's certainly not something that makes sense to quantize IMO (plus it would be difficult to do so)
You might be interested in having a look at this
A Primer to Relativistic MOND Theory
Jacob D. Bekenstein (Jerusalem), Robert H. Sanders (Groningen)
6 pages, 1 figure, to appear in proceedings of IAP05 in Paris: Mass Profiles and Shapes of Cosmological Structures, G. Mamon, F. Combes, C. Deffayet and B. Fort (eds), (EDP-Sciences 2005)
"We first review the nonrelativistic lagrangian theory as a framework for the MOND equation. Obstructions to a relativistic version of it are discussed leading up to TeVeS, a relativistic tensor-vector-scalar field theory which displays both MOND and Newtonian limits. The whys for its particular structure are discussed and its achievements so far are summarized."
Wikipedia (not as authoritative as Bekenstein but indicative of common language usage) classifies TeVeS as a type of relativistic MOND.
Wiki says: "Tensor-Vector-Scalar gravity (TeVeS) is a proposed relativistic theory of Modified Newtonian dynamics (MOND),..."
MOND (like "Kleenex") has become a generic term that includes relativistic theories very different from the original MOND of Moti Milgrom in 1981. There is no other term for these theories in wide use, so for the present people are pretty much forced to say MOND.
Maybe you or someone will eventually get the terminology straightened out and make up a better word and get the experts to accept it. Language reform is difficult
I am worried about Lusanna because he sounds out of touch with current MOND developments. He mentions only "non-relativistic MOND" and does not mention relativistic MOND in his abstract!
There have been some interesting talks and papers at Perimeter Institute about this recently. The authors to check, if you do a search, are John Moffat, Jacob Bekenstein, Joao Magueijo.
Bekenstein is famous because of the Bekenstein-Hawking BH entropy formula (his Princeton thesis introduced the ideas of BH thermodynamics). He has developed a relativistic MOND he calls TeVeS (tensor-vector-scalar).
Magueijo (Perimeter and London Imperial) is also prominent. He recently co-authored this
MOND habitats within the solar system
Jacob Bekenstein, Joao Magueijo
Phys.Rev. D73 (2006) 103513
"MOdified Newtonian Dynamics (MOND) is an interesting alternative to dark matter in extragalactic systems. We here examine the possibility that mild or even strong MOND behavior may become evident well inside the solar system, in particular near saddle points of the total gravitational potential. Whereas in Newtonian theory tidal stresses are finite at saddle points, they are expected to diverge in MOND, and to remain distinctly large inside a sizeable oblate ellipsoid around the saddle point. We work out the MOND effects using the nonrelativistic limit of the TeVeS theory, both in the perturbative nearly Newtonian regime and in the deep MOND regime. While strong MOND behavior would be a spectacular 'backyard' vindication of the theory, pinpointing the MOND-bubbles in the setting of the realistic solar system may be difficult. Space missions, such as the LISA Pathfinder, equipped with sensitive accelerometers, may be able to explore the larger perturbative region."
Recently Magueijo gave an interesting talk about this paper at Perimeter, video is available online.
the point is that the general category MOND includes relativistic MOND, such as TeVeS, and a relativistic MOND has a NONRELATIVISTIC LIMIT which is similar to but not exactly the same as Newton gravity, and this nonrelativistic limit can be TESTED by spaceprobe observations within the solar system. In fact, according to him, by the LISA probe in the inner solar system.
John Moffat, also at Perimeter, has a couple of different Scalar-Tensor-Vector versions of MOND which he has been working out ways to test in the solar system (by some outer planet mission)
He manages to fit his MOND both to the Pioneer anomaly data and to galaxy rotation curve data
Time Delay Predictions in a Modified Gravity Theory
J. W. Moffat
"The time delay effect for planets and spacecraft is obtained from a fully relativistic modified gravity theory including a fifth force skew symmetric field by fitting to the Pioneer 10/11 anomalous acceleration data. A possible detection of the predicted time delay corrections to general relativity for the outer planets and future spacecraft missions is considered. The time delay correction to GR predicted by the modified gravity is consistent with the observational limit of the Doppler tracking measurement reported by the Cassini spacecraft on its way to Saturn, and the correction increases to a value that could be measured for a spacecraft approaching Neptune and Pluto."
I see that Moffat makes a helpful distinction! In effect, he says MOG instead of MOND. He calls his "Scalar-Tensor-Vector" theory a kind of "Modified Gravity". But I fear other people would refer to it as a kind of MOND because that is the usual term---as witness Bekenstein.
Scalar-Tensor-Vector Gravity Theory
J. W. Moffat
Comments: 20 pages. Section on cosmology added.
JCAP 0603 (2006) 004
"A covariant scalar-tensor-vector gravity theory is developed which allows the gravitational constant G, a vector field coupling $\omega$ and the vector field mass mu to vary with space and time. The equations of motion for a test particle lead to a modified gravitational acceleration law that can fit galaxy rotation curves and cluster data without non-baryonic dark matter. The theory is consistent with solar system observational tests. The linear evolutions of the metric, vector field and scalar field perturbations and their consequences for the observations of the cosmic microwave background are investigated."
If the other professionals in the field could be persuaded to say MOG instead of MOND when talking about relativistic versions of MOND, then the confusion would be straightened out.
Semi-related humorous remark:
Dark matter is really light. But so is dark energy. Its all there, but only when you look. No strings attached.
Yesterday I've attended the Lusanna's seminar...
In the past days I've taken a look to papers about MOND that you suggested.
I have no deep knowledge, only feelings... but I prefer Lusanna approch than Bekenstein one, because the former sounds more natural: it doesn't invoke nothing more than seriusly considering the relativistic non-inertial framework. By now he hasn't given results for the DE problem, only hints, but he is firmly persuaded that this is the right way...
Maybe I can share a convinction of this kind...
BTW he has suggested me a paper also with a philosophycal point of view
Explaining Leibniz-equivalence as difference of non-inertial appearances:
dis-solution of the Hole Argument and physical individuation of point-events
Authors: Luca Lusanna (INFN, Firenze), Massimo Pauri (Parma Univ.)
Is the einstein tensor unfinished? It addresses spacetime with matter in it. Did Einstein intentionally not address spacetime in the absence or near absence of matter? Assume you write the tensor while facing a black hole and then turn around and extrapolate the tensor into cosmologically empty spacetime. Do you get MOND? I would think you would at some point in the extrapolation and what do you get when the gravitational energy density nears the cosmic background gravitational potential?
Separate names with a comma.