Joseph Silk of the University of Oxford, England, and his co-workers say that these extra spatial dimensions can be inferred from the perplexing behaviour of dark matter. This mysterious stuff cannot be seen, but its presence in galaxies is betrayed by the gravitational tug that it exerts on visible stars. Silk and his colleagues looked at how dark matter behaves differently in small galaxies and large clusters of galaxies. In the smaller ones, dark matter seems to be attracted to itself quite strongly. But in the large galactic clusters, this doesn’t seem to be the case. Strongly interacting dark matter should produce cores of dark material bigger than those that are actually there, as deduced from the way the cluster spins.So writes Philip Ball in Nature and the New York Times.
Silk's basic idea is very simple. The existence of some form of dark matter has for over 30 years been inferred from various independent observational facts -- for instance the way that stars orbit around the center of a galaxy and the ways that galaxies move in large clusters of galaxies. In order to account for these motions there must be a considerable amount of gravitating matter in the universe that is not directly visible to us in any way, such as in the form of luminous stars. Furthermore, the amount of matter that must exist to account for the motions is far more than could exist in the form of "ordinary" matter composed of protons and neutrons (so-called "baryonic matter"). Indeed, for other reasons, this ordinary matter, both that which can actually seen and that which can't (because it doesn't glow as in a star), must be less than 15% of the total of all matter.
More detailed studies of the motions of galaxies in clusters reveal another problem -- there is a slight difference between the expected motions of galaxies, due to all the dark matter, in large clusters as compared to smaller ones. And one way to account for this difference would be the existence of "extra dimensions", which would cause some of the gravitational force due to the dark matter to "leak away". It turns out that three extra spatial dimensions would be needed to account for the discrepancy, if indeed this "leaking" effect is real.
In the Newtonian theory of gravity (as well as in Einstein's general relativity), gravitational force decreases as the square of distance. Silk and his collaborators calculate that if there were three additional spatial dimensions and if each were about a nanometer in extent (as opposed to billions of light years as for the three ordinary dimensions), then within that small distance gravity would decrease as the fifth power of distance. And this effect would be sufficient to explain the anomalous motion of galaxies in clusters. It was, in addition, even possible to compute the approximate mass of hypothetical elementary particles that could make up the dark matter -- about 3×10-16 times the mass of a proton. This is within the range considered possible for a hypothetical particle known as an axion, frequently suggested as the main constituent of dark matter.
Early reactions to Silk's idea involve a great deal of interest, but much skepticism too. However, if the idea turns out to be correct, it would provide indirect evidence for superstring theory, which requires six or seven extra "small" dimensions. The additional three or four additional dimensions needed by superstring theory might be even much smaller than those that Silk postulates, so that they would not affect the calculations.
A preprint of Silk's paper: Observational Evidence for Extra Dimensions from Dark Matter
Overview of dark matter with many other references: here
Overview of superstring theory with many other references: here
Blog entry: Dark Matter and Extra-Dimensional Modifications of Gravity
Blog entry: Dark matter and 3 extra dimensions
Older Arxiv preprint by Spergel and Steihnardt: Observational evidence for self-interacting cold dark matter
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