Dynamical Dark Energy and Its Coupling to Matter

1. 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

2. The Hot Big Bang Model What is CDM? Weakly interacting but can gravitationally clump into halos What is DE??Inert, smooth, anti-gravity!!

3. Do We Really Need Dark Energy

4. SNAP satellite CMB /SNe /LSS Constraints on Physical State of Dark Energy

5. 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

6. 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?

7. potential energy kinetic energy K 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 < 1quintessence • any f(φ)→ negative K→ w < -1phantom . V(φ) DE as a Scalar Field

8. 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

9. Affect the locations of CMB acoustic peaks Increase <w> Time-averaged <w>= -0.78 Time-varying Equation of State w(z)(e.g. Lee, Ng 03) =0.7 =0.3 SNIa Redshift Last scattering surface

10. 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 SDE-photon=(1/Mp)∫d4x [κφ(E2+B2) + βφE·B]

11. 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 Lee,Lee,Ng 01,03 DE Coupling to Electromagnetism SDE-photon=(1/Mp)∫d4x [κφ(E2+B2) + βφE·B]

12. Quadrupole anisotropy Thomson scattering e Linearly polarized 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

13. SKY MEASUREMENT RAW DATE MAPMAKING MULTI-FREQUENCY MAPS FOREGROUND REMOVAL CMB SKY MAP 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

14. 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 (Q + iU) (θ,φ) =Σlm a-2,lm -2Ylm (θ,φ) l = 180 degrees/ q 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 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) CMB Anisotropy and Polarization Angular Power Spectra

15. Theoretical Predictions for CMB Power Spectra Boxes are predicted errors in future Planck mission • 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 TE E B [l(1+1) Cl/2p]1/2

16. 3-year WMAP CMB TT, TE, EE power spectra Mar 2006 Reionization bump

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

18. Parity violating EB,TB cross power spectra

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

20. Power spectra g(η): radiative transfer function ST: source term for anisotropy SP=SP(0) r=η0 -η

21. <TB> c.l. M reduced Planck mass Constraining β by CMB polarization data 2003 Flight of BOOMERANG Likelihood analysis assuming reasonable quintessence models

22. Gravitational-wave B mode mimicked by late-time quintessence evoution (z<10) Future search for B mode Lensing B mode mimicked by early quintessence evolution CAUTION!Must check with TB and EB cross spectra

23. Lee,Liu,Ng 06 DE Coupling to Cold Dark Matter n: coupling strength to cold dark matter

24. 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