1. Observational Evidence for Extra Dimensions from Dark Matter Bo Qin National Astronomical Observatories, China Bo Qin, Ue-Li Pen & Joseph Silk, PRL, submitted (astro-ph/0508572)

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: 3 + n + m = 9 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 -33 cm 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/0402168 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 Solutions---Modify CCDM  Self-Interacting DM (Spergel & Steinhardt, 2000, PRL)  Warm Dark Matter (not favored by WMAP, early reionization)  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 Solutions---Modify CCDM  Self-Interacting DM (Spergel & Steinhardt, 2000, PRL)  Warm Dark Matter (not favored by WMAP, early reionization)

9. DM self-interaction cross section:  xx /m x  8  10 -(25-22) cm 2 /GeV (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/0006344 Starkman et al., 1990, PRD Qin & Wu, 2001, PRL

10. 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

11. Velocity of DM particles in different systems System Mass Typical velocity Glaxy clusters 10^15 M_sun 1000 km/s Milky Way 10^12 M_sun 200 km/s Dwarf Galaxies 10^9 M_sun a few tens km/s

12. Nature of SIDM  xx Maybe velocity dependant Firmani et al. (2000):  xx /m x  4  10 -25 (100kms -1 /v) cm 2 /GeV v DM self-interaction--- m 1 Long-range forces? m 2

13. 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

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

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

16. Speculative? What we have done? Observations---Self-interacting Dark Matter (although debated) + String scenarios (ADD)

17. A very strange and « weired » picture? Huge number density of CDM particles, 10^15 /cm^3 Extremely small spacial seperation between the CDM particles 10^-5 cm Large de Broglie wavelength of ~ km But a mean free path of CDM collision ~ kpc! Each DM particle have just ONE or several interactions with others, during the cosmic age. Extremely low probability of scattering.