They are suggesting that the observed rotation curves of galaxies, which in the cold dark matter model is provided by a halo of dark matter throughout the galaxy, can be explained with a purely gravitational approach.
Firstly, the galactic rotation curves are just one of several different lines of evidence that point to the existence of dark matter. I would have to disagree with EdipisReks in that we don't know for sure whether dark matter exists since it's effects have only been observed indirectly.
I have a couple of concerns about this paper. Firstly, they are cagey about how much mass exactly is needed to produce this type of behaviour. They say
...our correlation of the flat velocity curve is acheived with disk mass of an order of magnitude smaller than the envisaged halo mass of exotic dark matter
Well, this would still mean that the galaxy would have something like 50% more matter than it is observed to. The don't say this explicitly and don't suggest how this could be the case.
Secondly, they say
It should be noted that the approximation scheme would break down in the region of the galactic core should the core harbor a black hole...
There is some pretty indelible evidence that our galaxy does indeed harbor a 3,000,000 solar mass black hole at it's core. It's a minor point regarding their paper, but they don't say how their theory might be altered as a whole by the presence of a black hole at the galactic core.
Since the rotation curve is a small part of the dark matter evidence, even if what these guys are saying in the paper is true, they still have to explain a host of other observations. eg. if there's no dark matter, how do they explain cluster dynamics? Why does the CMB imply a baryonic mass component significantly smaller than would be required for their theory? What about measurements of galaxy masses via gravitational lensing that show that the visible matter is a small component of the total matter in the galaxy?
I could go on, but I don't think this puts a dent into the dark matter model. It's interesting nonetheless, and I wish that the gravity folks could come up with a model that did close to what the cold dark matter model could do (since nonconcordance in the field tends to stimulate research).
