1. Observational Evidence for Extra Dimensions from Dark Matter
Bo Qin
National Astronomical Observatories, CAS
Bo Qin, Ue-Li Pen & Joseph Silk, PRL, submitted
(astro-ph/ )

2. Main results
Astronomical observations of systems of dark matter in recent years suggest that dark matter particles may have considerable self-interaction.
We find that the properties of this self-interaction are precisely the consequences of a gravity of the r-5 law at r<~1nm, corresponding to a world of 3 large extra dimensions of size R~1nm.

3. String Theory: Extra Dimensions: --- Have never been tested
How to test?
---From gravitational behavior at small distance scales
r<R
Size of extra dimensions: Planck scale ~10-33 cm
Large Extra Dimensions:
Arkani-Hamed, Dimopoulos & Dvali (ADD) 1998, Phys. Lett. B
Gravity: F ~ r-(2+n) at r<R,
R~10(30/n)-17 cm (for n=2, R~1mm)
Opens New Window:
Experimental test of string theory + Searches for extra dimensions,
by precise measurement of gravity at submm scales

4. Gravity has only been accurately measured
at ~1cm and beyond
But was extrapolated for 33 orders of
magnitude down to ~10-33cm
Does Newton’s Inverse Square Law still hold---
1. At very small distance scales?
2. In very weak regimes? a ~10-8 cm s-2
Modified Newtonian Dynamics (MOND?) Milgrom 1983

5. Experimental tests of Newton’s law at sub-mm scales & Searches for large extra dimensions
e.g.:
Long et al., Nature (2003)
Hoyle et al., PRL (2001); PRD (2004)
Chiaverini et al. PRL (2003)
( & e.g. hep-ph/ for a review )
No deviation from Newtonian has been found from ~1cm down to ~1μm

6. Potential challenge to CDM model
 Collisionless Cold Dark Matter (CCDM)
Very successful in explaining the origin and evolution of
cosmic structure on large scales,
but may have problems on galactic and sub-galactic scales
Theory vs. Observation  Conflict (Crisis?)
Cuspy core problem of DM \rho ~r^-1 (NFW)
~r^-0.5 (Obs.)
Solutions---Modify CCDM
Self-Interacting DM (Spergel & Steinhardt, 2000, PRL)
Warm Dark Matter (not favored by WMAP, early reionization)

7. xx/mx  810-(25-22) cm2/GeV DM self-interaction cross section:
(Spergel & Steinhardt 2000, PRL)
Nature of this self-interaction is unknown:
Introduce a new interaction beyond the Standard Model?
SIMPs? (Strongly Interacting Massive Particles)
Wandelt et al., astro-ph/
Starkman et al., 1990, PRD
Qin & Wu, 2001, PRL

8. Further studies of SIDM
In galaxy clusters:
( X-ray / strong lensing / weak lensing )
 xx is much smaller
In galaxies: still room to argue
xx may not be constant, but varies with mass of the system---
more massive systems (clusters) have smaller xx, while less massive systems (like dwarf galaxies) have larger xx

9. xx Maybe velocity dependant
Nature of SIDM
xx Maybe velocity dependant
Firmani et al. (2000):
xx/mx  410-25(100kms/v) cm2/GeV v
DM self-interaction m1
Long-range forces? m2

10. Why Extra Dimensions? DM self-interaction  some Variant of Gravity?
If n extra dimensions, gravity would be F~r-(2+n),
greatly enhanced at r<R.
May naturally provide the DM self-interaction.
Advantages: (of attributing DM self-interaction to extra dimensions)
1. Using the existing framework
2. Without introducing any new or fine-tuned interaction
3. Link string scenarios with observable/astronomical
phenomena

11. At small scales gravity takes the general form:
where =Rn , from the boundary condition that at r=R,
The gravitational scattering cross section
(1)
And the DM self-interaction cross section from observations:
(2)

12. The results  The only solution is n=3 R~1nm mx~3×10-16GeV (axions?)
Combining Eq (1) and (2):
 The only solution is n=3
R~1nm
mx~3×10-16GeV
(axions?)
Speculative?