Imprint of Scalar Dark Energy on CMB polarization Kin-Wang Ng ( 吳建宏 ) Institute of Physics & Institute of Astronomy and Astrophysics, Academia Sinica, Taiwan Cosmology and Gravity Pre-workshop NTHU, Apr 11, 2014 Collaborators: Guo-Chin Liu (TKU) Seokcheon Lee (KIAS)
The Hot Big Bang Model Cosmic Budget Dark Energy 70% Baryonic Matter 5% Cold Dark Matter 25% 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 Sabaru LSST JDEM EUCLID SNAP satellite Equation of State w = p DE / ρ DE
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 Thomson scattering Linearly polarized
CMB Measurements 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 SKY MEASUREMENT MAPMAKING MULTI-FREQUENCY MAPS FOREGROUND REMOVAL CMB SKY MAP
CMB Anisotropy and Polarization Angular Power Spectra Decompose the CMB sky into a sum of spherical harmonics: 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) (Q + iu) (θ,φ) =Σ lm a -2,lm -2 Y lm (θ,φ) C T l =Σ m (a* lm a lm ) anisotropy power spectrum q l = 180 degrees/ q C E l =Σ m (a* 2,lm a 2,lm + a* 2,lm a -2,lm ) E-polarization power spectrum C B l =Σ m (a* 2,lm a 2,lm a* 2,lm a -2,lm ) B-polarization power spectrum C TE l = Σ m (a* lm a 2,lm ) TE correlation power spectrum (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. [l(1+1) C l /2p] 1/2 Boxes are predicted errors in future Planck mission T TE E B
CMB Anisotropy C T l 2013
CMB Polarization Power Spectra 2013 Planck B-polarization spectrum not yet released
Best-fit 6-parameter ΛCDM model 2013 Density perturbation (scalar)
ΛCDM model + Gravitational Waves (Tensor) Tensor/Scalar Ratio and Spectral Index 2013 n s =0.9675 and r < 0.11 (95% CL) r=tensor/scalar =P h (k)/p R (k) at k 0 =0.05 Mpc -1
POLARBEAR+BICEP2 B-mode Detection
ΛCDM model + Tensor +Running spectral index (n s )
Constant w w=w 0 +w a 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?
DE as a Scalar Field kinetic energy K potential energy 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 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 Last scattering surface Redshift
DE Coupling to Electromagnetism This leads to photon dispersion relation Carroll, Field, Jackiw 90 vacuum birefringence ± left/right handed η conformal time then, a rotational speed of polarization plane
DE induced vacuum birefringence Faraday rotation of CMB polarization electric-type magnetic-type Liu,Lee,Ng PRL 06 γ CMB photon β φ TE spectrum
Parity violating EB,TB cross power spectra cosmic parity violation
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 Faraday rotation Rotation angle
Power spectra g(η): radiative transfer function S T : source term for anisotropy S P =S P (0) r=η 0 -η
Constraining β by CMB polarization data 2003 Flight of BOOMERANG Likelihood analysis assuming reasonable quintessence models <TB> c.l. M reduced Planck mass More stringent limits from...ni et al.
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 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 14 Birefringence generates <BB> while <TB>=<EB>=0 B mode B mode
We Tried Many Scalar Dark Energy Models
Cosmic Birefringence Fluctuations Lee, Liu, Ng14 Nearly massless pseudo scalar
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