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