Transcript Document 7285461

Modified Gravity: answer to
Dark Matter/Energy?
HongSheng Zhao
Univ. of St Andrews, UK
rd
acceleration+3
Late
peak
Einstein’s Eq. needs fix
1. 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]
= 4Glum
= ▼. ▼ 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 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. ~ 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<
τ - → 2 π - + π+ + ντ
18 MeV
(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
Shan & Zhao (in prep.)
H0 ~ (R22 -R12 ) (1-k)/ (t2-t1) f(zs,zl) ~ 70
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]= 4Glum
= ▼. ▼ 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