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!