Imprint of Scalar Dark Energy on CMB polarizationdark/pwgc/doc/nthu14.pdf · 2014. 4. 12. ·...
Transcript of Imprint of Scalar Dark Energy on CMB polarizationdark/pwgc/doc/nthu14.pdf · 2014. 4. 12. ·...
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
What is CDM?
Weakly interacting but
can gravitationally clump
into halos
What is DE??
Inert, smooth, anti-gravity!!
Dark
Energy70%
Cold Dark
Matter25%
Baryonic
Matter5%
Cosmic Budget
Do We Really Need Dark Energy
CMB /SNe /LSS Constraints on Physical State of Dark Energy
SNAP
satellite
Sabaru
LSST
JDEM
EUCLID
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
e
Linearly polarized
Thomson
scattering
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
RAW DATE
MULTI-FREQUENCY MAPS
MEASUREMENT
MAPMAKING
SKY
FOREGROUND
REMOVAL
CMB
SKY MAP
CMB Measurements
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,U) electric-type magnetic-type
q
l = 180 degrees/ q
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.
T
E
B
TE
Boxes are predicted errors in future Planck mission
[l(1
+1)
Cl/2p
]1/2
CMB Anisotropy CTl 2013
CMB Polarization Power Spectra 2013
Planck B-polarization spectrum not yet released
Best-fit 6-parameter
ΛCDM model 2013
Density perturbation (scalar)
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
ΛCDM model + Gravitational Waves (Tensor)
POLARBEAR+BICEP2 B-mode Detection
ΛCDM model + Tensor +Running spectral index (ns)
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
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)
• 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
A Coupling Dark Energy?
~
Time-varying Equation of State w(z) (Lee, Ng PRD 03)
=0.7
=0.3
Time-averaged
<w>= -0.78
SNIa
Affect the locations of
CMB acoustic peaks Increase <w>
Redshift Last scattering surface
DE Coupling to Electromagnetism
This leads to photon dispersion relation
± left/right handed η conformal time
Carroll, Field,
Jackiw 90
then, a rotational speed of polarization plane
vacuum birefringence
DE induced vacuum birefringence –
Faraday rotation of CMB polarization
Liu,Lee,Ng
PRL 06
electric-type magnetic-type
TE spectrum
φ γ
β
CMB photon
Parity violating EB,TB cross power spectra –
cosmic parity violation
Radiative transfer equation μ=n·k,
η: conformal time
a: scale factor
ne: e density
σT: Thomson cross section
Source term for
polarization
Rotation angle
Faraday
rotation
g(η): radiative transfer function
ST: source term for anisotropy
SP=SP(0) r=η0 -η
Power
spectra
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 ………..
….Ni et al.
Gravitational-wave B mode
mimicked by late-time
quintessence evoution (z<10)
Lensing B mode mimicked by
early quintessence evolution
Future search for B mode
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
Lee, Liu, Ng14 Cosmic Birefringence Fluctuations
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