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