Probing Dark Energy Birefringence by CMB polarization

1. Probing Dark Energy Birefringence by CMB polarization Kin-Wang Ng (吳建宏) Institute of Physics & Institute of Astronomy and Astrophysics, Academia Sinica, Taiwan IOP Mar 27, 2013 Collaborators: Guo-Chin Liu (TKU) Seokcheon Lee (KIAS) Da-Shin Lee (NDHU) Wolung Lee (NTNU)

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 Equation of State w = pDE / ρDE Sabaru LSST JDEM EUCLID

5. 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

6. 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

7. 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

8. 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

9. CMB Anisotropy CTl 2013

10. CMB Polarization Power Spectra 2013

11. Best-fit 6-parameter ΛCDM model 2013

12. Beyond ΛCDM model Tensor/Scalar Ratio and Spectral Index 2013 ns=0.9675 and r < 0.11 (95% CL) r=Tensor/Scalar =Ph(k)/PR(k) at k0=0.05 Mpc-1

13. Constant w w=w0+wa z/(1+z)

14. 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=0.70, constant w=−1.7+0.5/−0.3 (Planck 13+WMAP) • Combined all: DE=0.69, constant w=−1.13+0.13/−0.14 (Planck 13+WMAP+SNe) • A cosmological constant? Not Yet! Very weak constraint on dynamical DE with a time-varying w

15. What is Dark Energy • DE physical state is measured indirectly through its gravitational effects on cosmological evolution, but what is the nature of DE? • It is hard to imagine a realistic laboratory search for DE • Is DE coupled to matter (cold dark matter or ordinary matter)? If so, then what would be the consequences?

16. V(φ) 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) • f(φ)=1 → K=φ2/2→ -1 < w < 1quintessence • any f(φ)→ negative K→ w < -1phantom .

17. 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 ~

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

19. DE Coupling to Electromagnetism Carroll, Field, Jackiw 90 This leads to photon dispersion relation ± left/right handed η conformal time then, a rotational speed of polarization plane

20. magnetic-type electric-type β γ φ CMB photon TE spectrum Liu,Lee,Ng PRL 06 DE induced vacuum birefringence – Faraday rotation of CMB polarization

21. Parity violating EB,TB cross power spectra

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

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

24. 2003 Flight of BOOMERANG Likelihood analysis assuming reasonable quintessence models <TB> c.l. M reduced Planck mass Constraining β by CMB polarization data More stringent limits from WMAP team and QUaD team ‘09

25. 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

26. Dark energy perturbation Including Dark Energy Perturbation time and space dependent rotation • Perturbation induced polarization power spectra in previous • quintessence models are small • Interestingly, in nearly ΛCDM models (no time evolution of • the mean field), birefringence generates <BB> while <TB>=<EB>=0

27. Dark energy perturbation with w=-1 Lee,Liu,Ng 13 Birefringence generates <BB> while <TB>=<EB>=0 B mode B mode

28. 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, BAO • 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 - Mean field time evolution → <BB>, <TB>, <EB> - Include DE perturbation→ <BB>, <TB>=<EB>=0 - This may confuse the searching for genuine B modes induced by gravitational lensing or primordial gravitational waves, so de-rotation is needed to remove vacuum birefringence effects Kamionkowski 09, Ng 10