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Transcript PPT - Academia Sinica
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
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 = pDE / ρDE
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
Thomson
scattering
e
Linearly polarized
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
SKY
MEASUREMENT
RAW DATE
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) =Σlm alm Ylm (θ,φ)
(Q − iU) (θ,φ) =Σlm a2,lm 2Ylm (θ,φ)
(Q + iU) (θ,φ) =Σlm a-2,lm
-2Ylm
(θ,φ)
q
CTl =Σm (a*lm alm) anisotropy power spectrum l = 180 degrees/ q
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)
Theoretical Predictions for CMB Power Spectra
Boxes are predicted errors in future Planck mission
T
TE
E
[l(1+1) Cl/2p]1/2
• 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.
B
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?
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 < 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)
Affect the locations of
CMB acoustic peaks
(Lee, Ng PRD 03)
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
± left/right handed η conformal time
then, a rotational speed of polarization plane
DE induced vacuum birefringence –
Faraday rotation of CMB polarization
electric-type
γ
CMB photon
β
φ
TE spectrum
Liu,Lee,Ng
PRL 06
magnetic-type
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
Likelihood analysis assuming
reasonable quintessence models
<TB>
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
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