3. Modified Gravity: answer to Dark Matter/Energy?
HongSheng Zhao
Univ. of St Andrews, UK

4. Late acceleration+3rd peak Einstein’s Eq. needs fix
RHS ⇒ Dark energy + DM
e.g., Vaccum energy, Chaplygin gas
2. LHS ⇒ Modified gravity
e.g., 1/R gravity (Carroll et al., 2003) dominates late

5. Bekenstein’s TeVeS for MOND=0
a0]2 ~ 3

6. Deflection by φDM ~ φTeVeS
Bekenstein (2004), Angus, Famaey, Zhao (2006)
Galactic Potential  = lum+φTeVeS = lum+ φDM
ds2 = (1+2) dt2 - (1-2) ( dx2 + dy2 + dz2 )
DM + DE --> Baryon-tracking Scalar field

7. Need Modified Gravity ~ Dark Matter
(gDM/glum ).gDM ~ a0~ 1/2
Bruneton, Famaey, Gentile, Nipoti, Zhao (2006)

8. A Fake Hybrid Spiral Galaxy
MOND fails to fit (Good !!) DM fits fine
Stars
Gas
Gas
Stars (with smaller M/L)
Scarpa;

9. Polarisation ~ Bound Charge ~ Dark Matter ~ Scalar field+ + + - - +Q - - + +
▼. [s ▼ φ] = 4Glum = ▼. ▼ Φlum
Matter-tracking Dielectric s ~ ▼φ /a0 , a0 ~ 1/2

10. Predict Cosmology without further tuning
Constraints:
z=1010 (BBN) tBBN = 1sec  initial cond.
z=1100 (CMB) Horizon 1 degree
z=0 (LRR) Gravity varies <4x10-13 yr-1

11. Match D(z) without Λ nor CDM!
Dielectric s ~ dφ/dt a0 , a0 ~ 1/2

12. Matching Horizon, Distance, H0, BBN, … (Zhao et al. 06)

13. Falsifiable Beyond d /d R
d  /d Z
Vertical oscillation of Sun-like stars
d2/d R2
Roche Lobes of star clusters & dwarf galaxies
d  /d t
Hubble expansion/CMB/structure formation

14. A baryonic TeVeS is incomplete
Fail in
Globular clusters (zero DM)
Galaxy clusters (lots of DM, e.g., 1 ev neutrino)
Some lenses elliptical galaxies (with DM core)
Falsifiable from vertical force near Sun (GAIA).

15. Lensing as usual, but in strong regime

16. Compare with CDM Smaller image separation Longer time delay
< 0.3 (GM/a0)1/2~ 3 kpc for M~1011
Longer time delay
(or need H0 closer to 70):

17. Lensing angle distribution in TeVeS
Chen & Zhao (2006, ApJ, Lett. submitted)

18. Not Perfect
Zhao, Bacon, Taylor, Horne (2006,MNRAS)

20. Skordis et al. (2005),PRL Fit WMAP,SDSS if neutrino is massive
(~0.17)
(← first peak location)

21. MOND as fortune-teller to DM/DE
Why/When it works?
Often (LSB/SNIa)
but not always (globular/galaxy clusters)!
E.g., Hydrogen Balmer Line = (1/22 - 1/n2) R leads to new physics: quantum/duality concepts of particle/wave
(gDM /gDM ).gDM ~ a0 ~  ½ clues to DM/DE, even better physics [duality of gravity?]
All structures in universe are characterized by the same internal energy density . Why?

22. Why gravity = a0 somewhere in every object?
GlobularCluster, MolecularCloud, dwarf, Ellip, X-Cluster
 ½ ~ a0 ~ Velocity2 /Length scale ~ cH0/6 ~ 100Msun/pc2
A good theory (DM/DE/MOND…) should explain this!
The location of an object above or below the a0 line tells of the internal dynamics and how far they are from Newtonian.
It is not claiming a velocity-dispersion size correlation.
It is not clear how Newtonian theory with dark matter might account for the fact that these different objects, with a large range in size and environments, all have comparable internal accelerations.

23. Update Scores LCDM TeVeS-MOND
Solar System ? ?
Tides/vertical force
Rot. curves HSB/LSB
Lensing by Ellip/Clusters
Hubble Expansion/CMB ????
Stay Tuned!

24. Cluster Masses from X-rays
MOND says from velocity dispersion MTotal / MGas. ~ 2
Need 2 eV neutrinos in clusters of galaxies.
Sanders & McGaugh:

25. Neutrino Mass Limits
Mνe< eV Tritium decay endpoint measurements (But much better
will come from KATRIN ~2007). A much lower mass limit would rule out neutrinos being a significant DM mass in galactic clusters.
Mνµ< 170 KeV π+ → µ+ + νµ
Mντ< MeV τ - → 2 π - + π+ + ντ
(Mνe + Mνµ + Mντ) < .68 eV WMAP (March 2006 results for 3 years of data),
but uses Einstein’s Field Eqn. for structure formation (ie: Newton, which is not the MOND force law).
Maybe MOND + the galactic cluster results are the first measurement that the typical neutrino mass is ~2 eV ! (G.Godfrey 2006)

27. Fit Non-spherical Lens with Shear
Disk Lens J
H0 ~ (R22 -R12 ) (1-k)/ (t2-t1) f(zs,zl) ~ 70
Shan & Zhao (in prep.)

28. Toy Lens with 3-baryon centres
Density map
Kappa map
Angus, Famaey, Zhao (2006, MNRAS)

29. Duality of Gravity: DM-MOND
Acceleration V2/R = -▼Φ = E
Polarisation ▼ φ = P = D – E
= -▼Φlum + ▼Φ
Tracking
▼. [s ▼ φ]= 4Glum
= ▼. ▼ Φlum
Dielectric s ~ ▼φ /a0 ,
a0 ~ 1/2
Baryon = Free Charge
DM = Polarisation

30. Predict Cosmology …without further tuning

31. CMB peaks: sensitive to baryon and dark matter
B h2  (shift of zero point of oscillation)
→ first peak height 
second peak height 
Mh2  (increases the depth of potential well
decreases radiation relative to matter(ISW))
→ first peak height  second peak →
third peak height 

32. trouble with higher (second and third) peaks of CMB(Slosar-Melchiorri-Silk,2005)
(←　Silk damping
for baryons)
WMAP/Boomerang
WMAP