Modified Gravity: answer to Dark Matter/Energy?

HongSheng ZhaoUniv. of St Andrews, UK

Late acceleration+3rd peak

Einstein’s Eq. needs fix

1. RHS ⇒ Dark energy + DMe.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

a0]2 ~

=0

3

Deflection by φDM ~ φTeVeS

• Galactic Potential = lum+φTeVeS = lum+ φDM

ds2 = (1+2) dt2 - (1-2) ( dx2 + dy2 + dz2 )

• DM + DE --> Baryon-tracking Scalar field

Bekenstein (2004), Angus, Famaey, Zhao (2006)

Need Modified Gravity ~ Dark Matter

Bruneton, Famaey, Gentile, Nipoti, Zhao (2006)

(gDM/glum ).gDM ~ a0~ 1/2

A Fake Hybrid Spiral Galaxy

Scarpa; http://xxx.lanl.gov/pdf/astro-ph/0601478

MOND fails to fit (Good !!) DM fits fine

Stars

GasGas

Stars (with smaller M/L)

++Q- -

- -

+ +

++

▼. [s ▼ φ] = 4Glum = ▼. ▼ Φlum

Matter-tracking Dielectric s ~ ▼φ /a0 , a0 ~ 1/2

Polarisation ~ Bound Charge ~ Dark Matter ~ Scalar field

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 PerfectZhao, Bacon, Taylor, Horne (2006,MNRAS)

Skordis et al. (2005),PRL

• Fit WMAP,SDSSif 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 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!

Update Scores LCDM

TeVeS-MOND• Solar System ?

?

• Tides/vertical force

• Rot. curves HSB/LSB • Lensing by Ellip/Clusters

• Hubble Expansion/CMB ????

Stay Tuned!

Cluster Masses from X-rays

MOND says from velocity dispersion MTotal / MGas. ~ 2Need 2 eV neutrinos in clusters of galaxies.

Sanders & McGaugh: http://cul.arxiv.org/pdf/astro-ph/0204521

Neutrino Mass Limits

Maybe MOND + the galactic cluster results are the first measurement that the typical neutrino mass is ~2 eV ! (G.Godfrey 2006)

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).

Fit Non-spherical Lens with Shear

Shan & Zhao (in prep.)

Disk Lens J2004-1349 H0 ~ (R2

2 -R12 ) (1-k)/ (t2-

t1) f(zs,zl) ~ 70

Toy Lens with 3-baryon centres

Kappa map

Density 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

WMAP/Boomerang