Dark matter evidence for extra dimensions 물리 이야기

Joseph Silk from Oxford university and his two chinese colleagues recently wrote an highly speculative but also highly interesting paper on the property of dark matter and extra dimensions.

It has been long time to notice the requirement of introducting DM to explain unexpected velocity profile of galaxies. From the recent observations including the expansion rate of far supernovae and precise measurement of CMBR(cosmic microwave background radiation), now it is almost confirmed that the majority of the energy in the universe is composed of DM and unknown energy resources (Dark energy).

The physical property of DM can be bestly explained by the slow (non-relativistic) moving particle and usually we call it as a Cold DM or CDM. Collisionless CDM model (CCDM) essentially well explain the large scale structure of the universe and CMBR observations. And WIMP(weakly interacting massive particle) of supersymmetric particle has been thought as the best candidate. However various numerical simulations on the galactic halo with CCDM typically could not fit the actual data in the central part of Galaxies. In reality, the density profile of the galactic halo tends to be flat upto very long distance from the center but CCDM simulation shows very steep increasement near the center. Simply both cannot match each other.

A solution was suggested by Spergel and Steinhardt of Princeton university in their famous PRL paper published in 1999. The point is that we can understand the flatness if there is self-interaction between CDM(SCDM). If it is the case, we expect the mean free path of CDM can have the size which is precisely required to explain the flatness near the center. The required rate can be best described by [cross section]*[mean velocity]/[mass of DM] = 10^(-25) cm^2/GeV.

Joseph and his colleagues' new idea is that we can derive the formulae if there are 3 extra dimensions following the large extra dimension model by Arkani-Hamed, Dimopoulos and Dvali where the newton's law will be altered beneath the scale about 1 nm from 1/r^2 to 1/r^5 with three extra spatial directions. In that case, the gravity will be stronger in the small distance regime and the interaction cross section of SCDM can be written as [cross section]*[mean velocity] = [a G*M]^0.5 where a=volume of extra dimension then M= 3*10^-16 GeV wll match the formula. The mass range is roughly the axion mass.

Of course, it is far from confirmation of the existence of extra dimension and string theory but still this kind of observation deserves further study! You may want to visit Nature about this story.


\begin{eqnarray} \hbar c =197.3 \text{MeV fm}\\ (\hbar c)^2=0.389 \rm{GeV}^2 \rm{mb}\\ 1.0{\rm pb}=\frac{2.568\times 10^{-3}}{\rm TeV^2}\\ =10^{-40} {\rm m}^2 \end{eqnarray}

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