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# Spergel, D. N. "Observational evidence for self-interacting cold dark matter." Physical review letters 84.17 (2000):3760.

## The Paper

The .pdf file can be found here

An external link to the paper is here.

The DOI is 10.1103/PhysRevLett.84.3760.

## Discussion

This paper can be viewed as an attempt to provide an observational test of one aspect of string theory, namely, the existence of extra dimensions. Or, it could be viewed as further evidence that the only way to confirm string theory is by being wrong. Take your pick.

The logic, however, is as follows: dark matter models with no self-interaction don't seem to hold up against certain observed behaviors. However, upper limits on self-interaction cross sections are different for systems of different size, larger for big ones, smaller for small ones, but roughly following the form of equation (1) from the paper. (In that equation, $v$, the “velocity dispersion,” is something like the standard deviation of velocities in the system under consideration.) The authors thus propose that instead of introducing a new form of interaction between the dark matter particles, we investigate the possibility of gravitational interaction, modified at small distances due to the presence of extra dimensions.

Since scattering cross section for a central potential of form $\frac{1}{r^n}$ is known, and given by their equation (4), with quantum corrections giving only overall factors, they match the two expressions in such a way as to have velocity cancel out, so as to not have a velocity-dependent mass of the dark matter particles (remember, they are “cold,” meaning non-relativistic, with a well-defined effective mass). This is possible only for $n=3$, and using a relation (obtained elsewhere) between the number and size of the compact spatial dimensions, they give an estimate of that size, which does place them into a range not yet well-tested by experiments. However, they do come up with a mass of the dark matter particles which is comparable to, or even smaller than, the neutrino masses, while the prevailing theory is that they are quite massive…

So there we have it.

P.S. I will bring cookies, on account of our Mighty Leader forbidding me from bringing anything I make in my kitchen (for reasons that I will leave to his discretion to disclose or not), as well as for reasons of inaptness at baking, and copious grading to do.

Bring borscht! -Mike

##### Questions
1. End of 2nd paragraph: What is the Local Group? Does every dark matter halo have a galaxy at its center?
2. End of 5th paragraph: I didn't follow their statement regarding how we know dark matter is “cold”. Lyman $\alpha$ absorbers?

$a^\dagger a$

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