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!!

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=− /-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 S= ∫d 4 x [f(φ) ∂ μ φ∂ μ φ/2 −V(φ)] EOS w= p/ρ= ( K-V)/(K+V) Assume a spatially homogeneous scalar field φ(t) f(φ)=1 → K=φ 2 /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 = SNIa Affect the locations of CMB acoustic peaks Increase Redshift Last scattering surface

DE Coupling to Electromagnetism S DE-photon =(1/M p )∫d 4 x [ κφ(E 2 +B 2 ) + 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 Electromagnetism S DE-photon =(1/M p )∫d 4 x [ κφ(E 2 +B 2 ) + β φE·B ] Lee,Lee,Ng 01,03 q= k/H 0 Cooling of horizontal branch stars => C<10 7 τ= η/H 0 c≡β Generation of primordial B fields G 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 Quadrupole anisotropy e Linearly polarized Thomson scattering

 Point the telescope to the sky  Measure CMB Stokes parameters: T = T CMB − T mean, Q = T EW – T NS, U = T SE-NW – T SW-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 RAW DATE MULTI-FREQUENCY MAPS MEASUREMENT MAPMAKING SKY FOREGROUND REMOVAL CMB SKY MAP CMB Measurements

CMB Anisotropy and Polarization Angular Power Spectra Decompose the CMB sky into a sum of spherical harmonics: (Q − iU) (θ,φ) =Σ lm a 2,lm 2 Y lm (θ,φ) T(θ,φ) =Σ lm a lm Y lm (θ,φ) (Q + iU) (θ,φ) =Σ lm a -2,lm -2 Y lm (θ,φ) C B l =Σ m (a* 2,lm a 2,lm − a* 2,lm a -2,lm ) B-polarization power spectrum C T l =Σ m (a* lm a lm ) anisotropy power spectrum C E l =Σ m (a* 2,lm a 2,lm + a* 2,lm a -2,lm ) E-polarization power spectrum C TE l = − Σ m (a* lm a 2,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 spectra Mar 2006 Reionization bump

DE induced vacuum birefringence – Faraday rotation of CMB polarization Lue et al. 99 Feng et al. 06 Liu,Lee,Ng 06 electric-type magnetic-type TE spectrum φ γ β CMB photon

Parity violating EB,TB cross power spectra

Radiative transfer equation μ=n·k, η: conformal time a: scale factor n e : e density σ T : Thomson cross section Source term for polarization Dark energy perturbation Rotation angle Faraday rotation

g(η): radiative transfer function S T : source term for anisotropy S P =S P (0) r=η 0 -η Power spectra

Constraining β by CMB polarization data 2003 Flight of BOOMERANG 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,Ng 06 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 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