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Dynamical Dark Energy and Its Coupling to Matter . Kin-Wang Ng ( 吳建宏 ) ASIoP ( 中央研究院物理所 ) & ASIAA ( 中央研究院天文所 ), Taipei NTHU Oct 4, 2007. Thanks to D.-S. Lee( 李大興 ), W-L. Lee( 李沃龍 ) , S. Lee( 李碩天 ) , G.-C. Liu ( 劉國欽 ) for collaboration . The Hot Big Bang Model. What is CDM? - PowerPoint PPT Presentation
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Dynamical Dark Energy and Its Coupling to Matter
Kin-Wang Ng ( 吳建宏 )
ASIoP ( 中央研究院物理所 ) & ASIAA ( 中央研究院天文所 ), Taipei
NTHU Oct 4, 2007
Thanks to D.-S. Lee( 李大興 ), W-L. Lee( 李沃龍 ) , S. Lee( 李碩天 ) , G.-C. Liu ( 劉國欽 ) for collaboration
The Hot Big Bang Model
What is CDM?Weakly interacting but can gravitationally clump into halos
What is DE??Inert, smooth, anti-gravity!!
Cosmic Budget
BaryonicMatter
4%
Cold DarkMatter23%
DarkEnergy73%
Do We Really Need Dark Energy
CMB /SNe /LSS Constraints on Physical State of Dark Energy
SNAPsatellite
Observational Constraints on Dark Energy
• Smooth, anti-gravitating, only clustering on very large scales in some models
• SNIa (z≤2): consistent with a CDM model
• CMB (z≈1100): DE=0.7, constant w <−0.78• Combined all: DE=0.7, constant w=−1.05
+0.15/-0.20• Very weak constraint on dynamical DE wi
th a time-varying w
What is Dark Energy
• DE physical state has been measured via its gravitational influence, but what is it?
• It is hard to imagine a realistic laboratory search
• Is DE coupled to matter (cold dark matter or ordinary matter)? Then, what would be the consequences?
DE as a Scalar Field
S= ∫d4x [f(φ) ∂μφ∂μφ/2 −V(φ)] EOS w= p/ρ= ( K-V)/(K+V)Assume a spatially homogeneous scalar field φ(t) f(φ)=1 → K=φ2/2 → -1 < w < 1 quintessence any f(φ)→ negative K→ w < -1 phantom
kinetic energy K potential energy
.
V(φ)
• Weak equivalent principle (plus polarized body) =>Einstein gravity =>φFF (Ni 77)
• Spontaneous breaking of a U(1) symmetry, like axion (Frieman et al. 95, Carroll 98)
• DE coupled to cold dark matter to alleviate coincidence problem (Uzan 99, Amendola 00,..)
• etc
A Coupling Dark Energy?
~
Remark: A coupling but non-dynamical scalar (Λ) has no effect
Time-varying Equation of State w(z) (e.g. Lee, Ng 03)
=0.7
=0.3
Time-averaged <w>= -0.78
SNIa
Affect the locations of CMB acoustic peaks Increase <w>
RedshiftLast scattering surface
DE Coupling to ElectromagnetismSDE-photon=(1/Mp)∫d4x [ κφ(E2+B2) + β φE·B ]
Lee,Lee,Ng 01,03
Induction of the time variation of the fine structure constant
Time varying α
Fine structure constant α
DE Coupling to ElectromagnetismSDE-photon=(1/Mp)∫d4x [ κφ(E2+B2) + β φE·B ]
Lee,Lee,Ng01,03
q= k/H0
Cooling of horizontal branch stars=> C<107
τ= η/H0
c≡β
Generation of primordial B fields 10-23G
10Mpc
C=100
CMB Anisotropy and Polarization
• On large angular scales, matter imhomogeneities generate gravitational redshifts
• On small angular scales, acoustic oscillations in plasma on last scattering surface generate Doppler shifts
• Thomson scatterings with electrons generate polarization
Quadrupoleanisotropy
e
Linearly polarized
Thomsonscattering
Point the telescope to the sky Measure CMB Stokes parameters: T = TCMB− Tmean, Q = TEW – TNS, U = TSE-NW – TSW-NE
Scan the sky and make a sky map Sky map contains CMB signal, syst
em noise, and foreground contamination including polarized galactic and extra-galactic emissions
Remove foreground contamination by multi-frequency subtraction scheme
Obtain the CMB sky map
RAW DATE
MULTI-FREQUENCY MAPS
MEASUREMENT
MAPMAKING
SKY
FOREGROUNDREMOVAL
CMBSKY MAP
CMB Measurements
CMB Anisotropy and Polarization Angular Power Spectra
Decompose the CMB sky into a sum of spherical harmonics:
(Q − iU) (θ,φ) =Σlm a2,lm 2Ylm (θ,φ)
T(θ,φ) =Σlm alm Ylm (θ,φ)
(Q + iU) (θ,φ) =Σlm a-2,lm -2Ylm (θ,φ)
CBl =Σm (a*2,lm a2,lm − a*2,lm a-2,lm) B-polarization power spectrum
CTl =Σm (a*lm alm) anisotropy power spectrum
CEl =Σm (a*2,lm a2,lm+ a*2,lm a-2,lm ) E-polarization power spectrum
CTEl = − Σm (a*lm a2,lm) TE correlation power spectrum
(Q,U)
electric-type magnetic-type
l = 180 degrees/
Theoretical Predictions for CMB Power Spectra
• Solving the radiative transfer equation for photons with electron scatterings
• Tracing the photons from the early ionized Universe through the last scattering surface to the present time
• Anisotropy induced by metric perturbations
• Polarization generated by photon-electron scatterings
• Power spectra dependent on the cosmic evolution governed by cosmological parameters such as matter content, density fluctuations, gravitational waves, ionization history, Hubble constant, and etc.
T
E
B
TE
Boxes are predicted errors in future Planck mission
[l(1+
1) C
l/2
3-year WMAP CMB TT, TE, EE power spectraMar 2006
Reionization bump
DE induced vacuum birefringence – Faraday rotation of CMB polarization
Lue et al. 99Feng et al. 06Liu,Lee,Ng 06
electric-type magnetic-type
TE spectrum
φγ β
CMB photon
Parity violating EB,TB cross power spectra
Radiative transfer equationμ=n·k, η: conformal timea: scale factorne: e densityσT: Thomson cross section
Source term forpolarization
Dark energyperturbation
Rotation angle
Faraday rotation
g(η): radiative transfer functionST: source term for anisotropySP=SP
(0) r=η0 -η
Powerspectra
Constraining β by CMB polarization data
2003 Flight of BOOMERANG
<TB>
Likelihood analysis assuming reasonable quintessence models
c.l.
M reduced Planck mass
Gravitational-wave B mode mimicked by late-time quintessence evoution (z<10)
Lensing B mode mimicked by early quintessence evolution
Future search for B mode
CAUTION! Must check with TB and EB cross spectra
DE Coupling to Cold Dark Matter Lee,Liu,Ng06
n: coupling strength to cold dark matter
Summary • Future observations such as SNe, lensing, galaxy survey
CMB, etc. to measure w(z) at high-z or test Einstein gravity
• However, it is also important to probe the nature of DE • DE coupled to cold dark matter => effects on CMB and m
atter power spectra• DE coupled to photon => time variation of the fine structu
re constant and creation of large-scale magnetic fields at z ~ 6
• Using CMB B-mode polarization to search for DE induced vacuum birefringence, which may confuse the searching for B modes induced by gravitational lensing and primordial gravitational waves