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
Cosmic Budget
Dark
Energy
73%
Baryonic
Matter
4%
Cold Dark
Matter
23%
What is CDM?
Weakly interacting but
can gravitationally clump
into halos
What is DE??
Inert, smooth, anti-gravity!!
Do We Really Need Dark Energy
CMB /SNe /LSS Constraints on Physical State of Dark Energy
SNAP
satellite
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
with 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
kinetic energy K
potential energy
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)
.
2
 f(φ)=1 → K=φ /2 → -1 < w < 1 quintessence
 any f(φ)→ negative K→ w < -1
phantom
V(φ)
A Coupling Dark Energy?
• 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
Remark: A coupling but non-dynamical
scalar (Λ) has no effect
Time-varying Equation of State w(z) (e.g. Lee, Ng 03)
Affect the locations of
CMB acoustic peaks
Increase <w>
=0.7
=0.3
SNIa
Time-averaged
<w>= -0.78
Last scattering surface
Redshift
DE Coupling to Electromagnetism
SDE-photon=(1/Mp)∫d4x [ κφ(E2+B2) + β φE·B ]
Induction of the time variation
of the fine structure constant
Fine structure constant α
Time varying
α
Lee,Lee,Ng
01,03
DE Coupling to Electromagnetism
Lee,Lee,Ng
01,03
SDE-photon=(1/Mp)∫d4x [ κφ(E2+B2) + β φE·B ]
Generation of primordial B fields 10-23G
τ= η/H0
c≡β
10Mpc
q= k/H0
C=100
Cooling of horizontal branch stars
=>
C<107
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
Quadrupole
anisotropy
Thomson
scattering
e
Linearly polarized
CMB Measurements
 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,
system noise, and foreground
contamination including polarized
galactic and extra-galactic
emissions
 Remove foreground contamination
by multi-frequency subtraction
scheme
 Obtain the CMB sky map
SKY
MEASUREMENT
RAW DATE
MAPMAKING
MULTI-FREQUENCY MAPS
FOREGROUND
REMOVAL
CMB
SKY MAP
CMB Anisotropy and Polarization Angular Power Spectra
Decompose the CMB sky into a sum of spherical harmonics:
T(θ,φ) =Σlm alm Ylm (θ,φ)
(Q − iU) (θ,φ) =Σlm a2,lm 2Ylm (θ,φ)
(Q + iU) (θ,φ) =Σlm a-2,lm
-2Ylm
(θ,φ)
q
CTl =Σm (a*lm alm) anisotropy power spectrum l = 180 degrees/ q
CEl =Σm (a*2,lm a2,lm+ a*2,lm a-2,lm ) E-polarization power spectrum
CBl =Σm (a*2,lm a2,lm − a*2,lm a-2,lm) B-polarization power spectrum
CTEl = − Σm (a*lm a2,lm) TE correlation power spectrum
magnetic-type
electric-type
(Q,U)
Theoretical Predictions for CMB Power Spectra
Boxes are predicted errors in future Planck mission
T
TE
E
[l(1+1) Cl/2p]1/2
• 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.
B
3-year WMAP CMB TT, TE, EE power spectra
Mar 2006
Reionization bump
DE induced vacuum birefringence –
Faraday rotation of CMB polarization
electric-type
γ
CMB photon
β
φ
TE spectrum
Lue et al. 99
Feng et al. 06
Liu,Lee,Ng 06
magnetic-type
Parity violating EB,TB cross power spectra
Radiative transfer equation
μ=n·k,
η: conformal time
a: scale factor
ne: e density
σT: Thomson cross section
Source term for
polarization
Dark energy
perturbation
Faraday
rotation
Rotation angle
Power
spectra
g(η): radiative transfer function
ST: source term for anisotropy
SP=SP(0)
r=η0 -η
Constraining β by CMB polarization data
2003 Flight of BOOMERANG
Likelihood analysis assuming
reasonable quintessence models
<TB>
c.l.
M reduced Planck mass
Future search for B mode
Gravitational-wave B mode
mimicked by late-time
quintessence evoution (z<10)
Lensing B mode mimicked by
early quintessence evolution
CAUTION! Must check with TB and EB cross spectra
DE Coupling to Cold Dark Matter
n: coupling strength to cold dark matter
Lee,Liu,Ng
06
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
matter power spectra
• DE coupled to photon => time variation of the fine
structure 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