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)

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

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

CMB Measurements Point the telescope to the sky RAW DATE MULTI-FREQUENCY MAPS MEASUREMENT MAPMAKING SKY 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

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 l = 180 degrees/ q (Q,U) electric-type magnetic-type

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. Boxes are predicted errors in future Planck mission T TE E B [l(1+1) Cl/2p]1/2

CMB Anisotropy CTl 2013

CMB Polarization Power Spectra 2013

Best-fit 6-parameter ΛCDM model 2013

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

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

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

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?

S= ∫d4x [f(φ) ∂μφ∂μφ/2 −V(φ)] EOS w= p/ρ= ( K-V)/(K+V) 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)

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 ~

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

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

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

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 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 <TB> Likelihood analysis assuming reasonable quintessence models c.l. M reduced Planck mass More stringent limits from WMAP team and QUaD team ‘09

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

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

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

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