Many Roads To Gravity.

Galactic rotation curves, lensing of light around galaxies, and the composition and lensing effects observed in galactic clusters, among other phenomena, all fail to behave the way Newtonian gravitational theories say that they should if most of the matter in the universe is in stars, which is overwhelmingly the case in the solar system and every other star system we have observed. Moreover, conventional wisdom is that Newton's theory of gravity is virtually equivalent to Einstein's Theory of General Relativity for these matters, except that in Einstein's theory, light is bent by gravitational fields. Even worse, almost all physicists who have studied the problem agree that no known kind of matter which is not visible can explain what we observe.

This is a problem.

Various attempts have been made to solve the problem.

Cooperstock and Tieu claim that the apparent problem comes because General Relativity is actually materially different from Newtonian gravity in these contexts and that scientists have simply been approximating the effects of General Relativity incorrectly. But, Korzynski, criticizing the paper say that Cooperstock and Tieu have made a hidden assumption that amounts to simply an unphysical form of dark matter to reach their result.

There have been about half a dozen serious efforts to argue that Einstein's Theory of General Relativity is not quite right and produce the phenomena we observe with considerable success. The first of these was Milgrom's Modified Newtonian Dynamics (MOND). Macrus at the Physics Forums has been focusing on another of these theories called Quantum Einstein Gravity. He examined the following papers on the topic, whose abstracts appear below:

Do we Observe Quantum Gravity Effects at Galactic Scales?
M. Reuter, H. Weyer
6 pages, 1 figure. Talk given by M.R. at the 21st IAP meeting "Mass Profiles and Shapes of Cosmological Structures", Paris, July 4-9, 2005; to appear in the proceedings

The nonperturbative renormalization group flow of Quantum Einstein Gravity (QEG) is reviewed. It is argued that there could be strong renormalization effects at large distances, in particular a scale dependent Newton constant, which mimic the presence of dark matter at galactic and cosmological scales.

Is Quantum Einstein Gravity Nonperturbatively Renormalizable?
O. Lauscher, M. Reuter
18 pages, 3 figures
Class.Quant.Grav. 19 (2002) 483-492

We find considerable evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity is 'asymptotically safe' in Weinberg's sense. This would mean that the theory is likely to be nonperturbatively renormalizable and thus could be considered a fundamental (rather than merely effective) theory which is mathematically consistent and predictive down to arbitrarily small length scales. For a truncated version of the exact flow equation of the effective average action we establish the existence of a non-Gaussian renormalization group fixed point which is suitable for the construction of a nonperturbative infinite cutoff-limit. The truncation ansatz includes the Einstein-Hilbert action and a higher derivative term.

Running Newton Constant, Improved Gravitational Actions, and Galaxy Rotation Curves
M. Reuter, H. Weyer
72 pages
PhysRevD.70.124028

A renormalization group (RG) improvement of the Einstein-Hilbert action is performed which promotes Newton's constant and the cosmological constant to scalar functions on spacetime. They arise from solutions of an exact RG equation by means of a 'cutoff identification' which associates RG scales to the points of spacetime. The resulting modified Einstein equations for spherically symmetric, static spacetimes are derived and analyzed in detail. The modifications of the Newtonian limit due to the RG evolution are obtained for the general case. As an application, the viability of a scenario is investigated where strong quantum effects in the infrared cause Newton's constant to grow at large (astrophysical) distances. For two specific RG trajectories exact vacuum spacetimes modifying the Schwarzschild metric are obtained by means of a solution-generating Weyl transformation. Their possible relevance to the problem of the observed approximately flat galaxy rotation curves is discussed. It is found that a power law running of Newton's constant with a small exponent of the order 10^{-6} would account for their non-Keplerian behavior without having to postulate the presence of any dark matter in the galactic halo.

Quantum Gravity at Astrophysical Distances?
M. Reuter, H. Weyer
46 pages, 4 figures, to appear in JCAP
JCAP 0412 (2004) 001

Assuming that Quantum Einstein Gravity (QEG) is the correct theory of gravity on all length scales we use analytical results from nonperturbative renormalization group (RG) equations as well as experimental input in order to characterize the special RG trajectory of QEG which is realized in Nature and to determine its parameters. On this trajectory, we identify a regime of scales where gravitational physics is well described by classical General Relativity. Strong renormalization effects occur at both larger and smaller momentum scales. The latter lead to a growth of Newton's constant at large distances. We argue that this effect becomes visible at the scale of galaxies and could provide a solution to the astrophysical missing mass problem which does not require any dark matter. We show that an extremely weak power law running of Newton's constant leads to flat galaxy rotation curves similar to those observed in Nature. Furthermore, a possible resolution of the cosmological constant problem is proposed by noting that all RG trajectories admitting a long classical regime automatically give rise to a small cosmological constant.

The conventional explaination of the phenomena we observe is called "Cold Dark Matter", a hypothetical new kind of stuff made up of "WIMPs" (weakly interacting massive particles), which are distributed in such a way as to make the equations work. But, this involves a great deal of fine tuning in the process of establishing distributions of this matter, which are poorly explained and requires the vast majority of the stuff in the universe to be made up of something which has never been directly observed. Moreover, while MOND correctly predicted many recent "missing mass" discoveries, dark matter theory has a far more spotting record of making accurate predictions.

QEG is the new kid on the block and has received a lot of attention in the last couple of years, but because it is new, it also hasn't yet faced the same level of rigorous scrutiny, thus far inconclusive in my opinion, that dark matter and MOND theory have received.