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. CMB /SNe /LSS Constraints on Physical State of Dark Energy
SNAP
satellite
Equation of State
w = pDE / ρDE
Sabaru
LSST
JDEM
EUCLID

5. 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

6. 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

7. 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

8. 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

9. CMB Anisotropy CTl

10. CMB Polarization Power Spectra 2013

11. Best-fit 6-parameter
ΛCDM model

12. Beyond ΛCDM model Tensor/Scalar Ratio and Spectral Index 2013
ns= 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=− /−0.3 (Planck 13+WMAP)
Combined all: DE=0.69, constant w=− /−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. 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 → < w < 1 quintessence
any f(φ)→ negative K→ w < phantom
kinetic energy K
potential energy .
V(φ)

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. 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

19. 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

20. 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

21. Parity violating EB,TB cross power spectra

22. 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

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

24. 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

25. 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

26. 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