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!!

Dark Energy

70%

Cold Dark Matter25%

Baryonic Matter

5%

Cosmic Budget

Do We Really Need Dark Energy

CMB /SNe /LSS Constraints on Physical State of Dark Energy

SNAPsatellite

SabaruLSSTJDEMEUCLID

Equation of Statew = 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

Quadrupoleanisotropy

e

Linearly polarized

Thomsonscattering

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

FOREGROUNDREMOVAL

CMBSKY 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

l = 180 degrees/

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/2

CMB Anisotropy CTl 2013

CMB Polarization Power Spectra 2013

Best-fit 6-parameter ΛCDM model 2013

Tensor/Scalar Ratio and Spectral Index 2013ns=0.9675 and r < 0.11 (95% CL)

r=Tensor/Scalar =Ph(k)/PR(k) at k0=0.05 Mpc-1

Beyond ΛCDM model

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>

RedshiftLast scattering surface

DE Coupling to Electromagnetism

This leads to photon dispersion relation

± left/right handed η conformal time

then, a rotational speed of polarization plane

Carroll, Field,Jackiw 90

DE induced vacuum birefringence – Faraday rotation of CMB polarization

Liu,Lee,Ng PRL 06

electric-type magnetic-type

TE spectrum

φγ

β

CMB photon

Parity violating EB,TB cross power spectra

Radiative transfer equationμ=n·k, η: conformal timea: scale factorne: e densityσT: Thomson cross section

Source term forpolarization

Rotation angle

Faraday rotation

g(η): radiative transfer functionST: source term for anisotropySP=SP

(0) r=η0 -η

Powerspectra

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

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 PerturbationDark energyperturbation

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