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

** Late acceleration+3rd peakEinstein’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

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

**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

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

**A Fake Hybrid Spiral Galaxy** MOND fails to fit(Good !!) DM fits fine Stars Gas Gas Stars (with smaller M/L) Scarpa; http://xxx.lanl.gov/pdf/astro-ph/0601478

**Polarisation ~ Bound Charge ~ Dark Matter ~ Scalar field ** + + + - - +Q - - + + ▼. [s▼φ] = 4Glum = ▼. ▼Φlum Matter-tracking Dielectric s ~ ▼φ /a0, a0 ~ 1/2

** 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

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

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

**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

**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).

** Lensing as usual, but in strong regime**

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

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

**Not Perfect** Zhao, Bacon, Taylor, Horne (2006,MNRAS)

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

**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?

**Why gravity = a0 somewhere inevery 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!

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

**Cluster Masses from X-rays** MOND says from velocity dispersion MTotal / MGas. ~ 2 Need 2 eV neutrinos in clusters of galaxies. Sanders & McGaugh: http://cul.arxiv.org/pdf/astro-ph/0204521

**Neutrino Mass Limits** Mνe< 2.2 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< 18 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)

**Fit Non-spherical Lens with Shear ** Disk Lens J2004-1349 H0 ~ (R22 -R12 ) (1-k)/ (t2-t1) f(zs,zl) ~ 70 Shan & Zhao (in prep.)

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

**Duality of Gravity: DM-MOND** • Acceleration V2/R = -▼Φ = E • Polarisation▼φ = P = D – E = -▼Φlum + ▼Φ Tracking ▼. [s ▼φ]= 4Glum = ▼. ▼Φlum Dielectric s ~ ▼φ /a0, a0 ~ 1/2 Baryon = Free Charge DM = Polarisation

**Predict Cosmology …without further tuning**

**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

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