All of the information below is from Brian Koberlein’s article titled “Still in the Dark”
You may have a look at the article here.
The idea is following: one of the main astrophysical concepts after the emergence of Special and General Relativity and Quantum Mechanics is the idea of Dark Matter. It is the idea of a mysterious entity existing in the space and interacting with the normal baryonic matter only through the gravitational force. That makes it almost impossible to detect at least with our existing technologies. All we can do is to measure the velocities of stars and galaxies within the galaxies’ cores and clusters of galaxies. And the idea of Dark Matter fits perfectly on that scale. There is also evidence for dark matter in galactic collisions and gravitational lensing. (The above 2 links also lead to Brian Koberlein articles on the following topics).
So, the idea of dark matter seems to match up the observational data very well.. unless we use it for smaller scales (i.e. dwarf galaxies). The computer simulation suggests that the amount of such satellite dwarf-galaxies should be at least several hundred for our own Milky Way galaxy. Comparing this number to the real one (which is 11) will definitely puzzle you. There is also a contradiction in the orbiting direction of such dwarf-galaxies. Computer models suggest that such directions should be somewhat random, but they aren’t.
There is also another problem with the idea of Cold Dark Matter (CDM). The CDM model matches up with our observational data very well on the large scales. However, there is a problem with clumping of dark matter. If it is cold, it should clump towards the center of mass which means we expect to observe the large amount of CDM at the center of galaxies, but we don’t see this actually. The above problem is particularly relevant for the so-called Low Surface Brightness galaxies, or LSBs.
This makes us trying to search for other ways to describe the gravitational fields. There have been several ideas of so-called modified gravity models. The main idea of such models is that on large scales gravitational interactions should be described by different laws, not the General Relativity. The most popular of these models is so-called Modified Newtonian Dynamics or MoND. The predictions of MoND match up really well for LSB galaxies. However, where one of these models works really well, another one seems to fall. That what is happening with the MoND model for the clustering of galaxies. It is completely contradicted by such clustering.
So it seems like scientists should try to find the model which would work well for any scale somewhere in the intersection of CDM and MoND.