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Modified Gravity: answer to Dark Matter/Energy?. HongSheng Zhao Univ. of St Andrews, UK. Late acceleration+3 rd peak Einstein’s Eq. needs fix. RHS ⇒ Dark energy + DM e.g., Vaccum energy, Chaplygin gas 2. LHS ⇒ Modified gravity

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Modified Gravity: answer to Dark Matter/Energy?


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

    2. 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

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

    4. 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

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

    6. 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

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

    8. 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

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

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

    11. 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

    12. 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).

    13. Lensing as usual, but in strong regime

    14. 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):

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

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

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

    18. 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?

    19. 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!

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

    21. 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

    22. 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)

    23. 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.)

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

    25. 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

    26. Predict Cosmology …without further tuning

    27. 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 

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