The Dark Energy Problem

Kin-Wang Ng

Institute of Physics &

Institute of Astronomy and Astrophysics,

Academia Sinica, Taiwan

NTHU Nov 2006

Outline• Dark Energy occupies 70% of the total

mass of the Universe supernova Ia, cosmic microwave background, large-scale

structure, gravitational lensing

• What is DE? cosmological constant or term, vacuum energy,

quintessence, phantom, … or modified Einstein gravity, modified Newtonian dynamics

(MOND),…

• How we test DE theories? ongoing and next-generation observations

The Standard Model of Elementary Particles

Sources• matter• radiativity• cosmic rays • accelerators• reactors

The Hot Big Bang Model

What is CDM?Weakly interacting but can gravitationally clump into halos

What is DE??Inert, smooth, anti-gravity!!

Cosmic Budget

BaryonicMatter

4%

Cold DarkMatter23%

DarkEnergy73%

Cosmic Expansion Equations and Cosmological Parameters

The goal of modern cosmology is to determine the cosmological parameters h, k, M, DE...where matter contains baryons, cold dark matter, neutrinos, photons…

M≈CDM=0.25 , wCDM≈0 ; DE≈=0.7, w≈ -1 q<0 Universe is accelerating !!

H2 = 8G (ρM+ρDE) / 3 – k / R2

1 = M + DE – k / (R2H2)

G Newton’s constantR scale factor or radiusH≡R/R Hubble parameterρ energy densityp pressurek=1, 0, -1 closed, flat, open

expansion rate

total energy curvature

≡8Gρ/ 3H2

.

R / R = −4G (ρM+ρDE+3pM+3pDE) / 3

2q = M (1+3wM) + DE(1+3wDE)

de-acceleration parameter q≡−RR / R2 equation of state w≡ p /ρ

acceleration total pressure..

.. .

H0=100 h km s-1 Mpc-1

Standard Candles!!

Supernova Ia and Dark Energy

Wang etal 03Tonry etal 03Riess etal 04

deaccelerating

accelerating

Supernova Ia and Dark Energy

SNAPsatellite

Cosmic Microwave Background

• Relic photons of hot big bang• First observed in 1965• Black body radiation of temp

erature about 3K• Mostly isotropic and unpolari

zed• Coming from last scatterings

with electrons at redshift of about 1100 or 400,000 yrs after the big bang (age of the Universe is about 14 Gyrs)

大霹靂模型

最後散射面

宇宙誕生

2006John MatherGeorge Smoot

1978Arno PenziasRobert Wilson

Plus many other observations

AT&T Bell

NASA

NASA

CMB Milestones

CMB Spectrum T=2.725 ± 0.002

1992

CMB Anisotropy and Polarization

• Acoustic oscillations in plasma on last scattering surface generate Doppler shifts

• Matter imhomogeneities generate gravitational red- or blue-shift

• 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, syst

em 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 Foreground and RemovalWMAP 02

COBE 92

CMB Anisotropy and Polarization Angular Power Spectra

l = 180 degrees/

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

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) C

l / 2

Data Pipeline and Extraction of Cosmological Parameters

CMB sky map

T(xi), Q(xi),U(xi) Xi : ith pixel

Anisotropy & PolarizationPower SpectraCT

l, CEl, CB

l, CTEl

CosmologicalParameters

Maximumlikelihoodanalysis

χ2 fitting

Pixelization

Experimental Detections and Limits

CTl

CTEl

CEl

NASA WMAP Data and Cosmological Parameters

CTl

CTEl

2002

WMAP3-yearTT,TE,EE, CMB power spectra

Cosmological Parameters from WMAP + SDSS Galaxy Clustering

WMAP Data and Dark Energy

NASA WMAP 2002

SNIa

CMB

Ongoing CMB Experiments

Balloon-borne bolometer

AMiBACBIDASIVSACAPMAPBoomerangMaxipolBICEPQUAD

Interferometer

Radiometer

Bolometer

Timbie 02

Mauna LoaChileSouth PoleTenerifePrincetonSouth PoleNew MexicoSouth PoleSouth Pole

NASA WMAP launched in 6/20013rd year data 3/20060.2o l<1000

AMiBA at Mauna LoaTaiwan, Australia, USA

Future CMB Space Missions and ExperimentsSPOrt aboard the International Space Station 7o l<20

ESA Planck 20070.2o l<1000

NASA Inflation Probe(Beyond Einstein Program)

Large-format radiometer arrays

Large-format bolometer arrays: South Pole Telescope Atacama Cosmology Telescope Polarbear

Hubble Space

Telescope

Gravitational Lensing Effects Caused by Dark Matter Halos

Weak Lensing by Large-Scale StructureCosmic Shear γ

background galaxies

CDM halos

Shear Variance in circular cells with size θ σ2

γ(θ) = ‹γ2›

Jain et al. 1997 1x1 deg

Ellis et al. 02

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=0.7, constant w <−0.78• Combined all: DE=0.7, constant w=−1.0

5 +0.15/-0.20• Almost no constraints on dynamical DE

with a time-varying w

Do We Really Need Dark Energy

Cosmological Constant and Vacuum Energy (w= −1)

SU(2) gauge field with coupling constant g:S= ∫d4x FμνFμν

Θ vacuum: Degenerate vacua

n-1 n n+1

Quantum tunneling

But K is infinite☻

Naïve expectation for the vacuum (zero-pt.) energy ≈ MP4,

but ρ≈ 10-120 MP4!! Planck scale MP ~ 1018GeV

E=ħω/2

S0=8π2/g2

Instanton action for tunneling

SU(2) gauge field with a Higgs doublet (Yokoyama 02) Higgs potentialS= ∫d4x [ FμνFμν+ DμΦ DμΦ −V(Φ)] where V(Φ)=λ(|Φ|2−M2/2)2/2

Finite ☺

SU(2) gauge field on extra dimensions of radius R0

- without any ad hoc Higgs field (Cho, Ho, Ng 05)

M~1/(4gR0)

DE as a Scalar Field (Bose Condensate)

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)

Time-varying w(z) and Early Quintessence (Lee, Lee, Ng 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 ElectromagnetismSDE-photon = ∫d4x [ c φ(E2+B2) + ĉ φE·B ]

Generation of primordial B fields 10-23G

10Mpc

Induction of the time variation of the fine structure constant

Time varying α

Lee,Lee,Ng01, 03

DE Coupling to Electromagnetism Liu,Lee,Ng06

BETA= ĉ < 10-3

Summary• By studying cosmic radiation, a seemingly unimportant particle was

discovered in 1936-- the muon (interacts the same way as the electron, but it is 200 times heavier). The theoretician Rabi is said to have exclaimed when the discovery was announced during a conference.

Who ordered muon?

Weak Interaction → Standard ModelSU(3)xSU(2)xU(1) → ……. →Unification of all Four Forces

Baryons and LeptonsOnly 5%!!

• Cold Dark Matter is 25% - crucial for the formation of galaxies. Desperately seeking for WIMPs such as SUSY neutralinos....

• Dark Energy is 70% - antigravity to accelerate the expanding Universe. Really do not know what DE is??

• We are in a golden age of precision cosmology – 10% accuracy now in measurements of cosmological parameters, a percent level in the near future

Thank you!