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The Dark Energy Problem

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

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The Dark Energy Problem

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  1. The Dark Energy Problem Kin-Wang Ng Institute of Physics & Institute of Astronomy and Astrophysics, Academia Sinica, Taiwan NTHU Nov 2006

  2. 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 L term, vacuum energy, quintessence, phantom, … or modified Einstein gravity, modified Newtonian dynamics (MOND),… • How we test DE theories? ongoing and next-generation observations

  3. The Standard Model of Elementary Particles Sources • matter • radiativity • cosmic rays • accelerators • reactors

  4. The Hot Big Bang Model What is CDM? Weakly interacting but can gravitationally clump into halos What is DE??Inert, smooth, anti-gravity!!

  5. expansion rate total energy G Newton’s constant R scale factor or radius H≡R/R Hubble parameter ρ energy density p pressure k=1, 0, -1 closed, flat, open curvature . H2 = 8pG (ρM+ρDE) / 3 – k / R2 1 = M + DE – k/(R2H2) ≡8pGρ/ 3H2 H0=100 h km s-1 Mpc-1 acceleration total pressure .. R/R = −4pG (ρM+ρDE+3pM+3pDE) / 3 2q = M (1+3wM) + DE(1+3wDE) de-acceleration parameter q≡−RR/R2 equation of state w≡ p /ρ .. . M≈CDM=0.25, wCDM≈0 ; DE≈=0.7, w≈ -1 q<0Universe is accelerating!! 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…

  6. Standard Candles!!

  7. Supernova Ia and Dark Energy deaccelerating accelerating Wang etal 03 Tonry etal 03 Riess etal 04

  8. SNAP satellite Supernova Ia and Dark Energy

  9. 大霹靂模型 最後散射面 宇宙誕生 Cosmic Microwave Background • Relic photons of hot big bang • First observed in 1965 • Black body radiation of temperature about 3K • Mostly isotropic and unpolarized • 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)

  10. 2006 John Mather George Smoot 1978 Arno Penzias Robert Wilson CMB Milestones AT&T Bell NASA NASA Plus many other observations

  11. CMB Spectrum T=2.725 ± 0.002 1992

  12. Quadrupole anisotropy Thomson scattering e Linearly polarized 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

  13. SKY MEASUREMENT RAW DATE MAPMAKING MULTI-FREQUENCY MAPS FOREGROUND REMOVAL CMB SKY MAP CMB Measurements • 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

  14. CMB Foreground and Removal WMAP 02 COBE 92

  15. q l = 180 degrees/ q CMB Anisotropy and Polarization Angular Power Spectra Decompose the CMB sky into a sum of spherical harmonics: T(θ,φ) =Σlm alm Ylm (θ,φ) (Q − iU) (θ,φ) =Σlm a2,lm 2Ylm (θ,φ) (Q + iU) (θ,φ) =Σlm a-2,lm -2Ylm (θ,φ) 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 CBl=Σm (a*2,lm a2,lm− a*2,lm a-2,lm) B-polarization power spectrum CTEl= −Σm (a*lm a2,lm) TE correlation power spectrum magnetic-type electric-type (Q,U)

  16. Theoretical Predictions for CMB Power Spectra Boxes are predicted errors in future Planck mission • 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 TE E B l(1+1) Cl / 2p

  17. Data Pipeline and Extraction of Cosmological Parameters CMB sky map Pixelization T(xi), Q(xi),U(xi) Xi : ith pixel Maximum likelihood analysis Anisotropy & Polarization Power Spectra CTl, CEl, CBl, CTEl χ2 fitting Cosmological Parameters

  18. Experimental Detections and Limits CEl CTl CTEl

  19. 2002 NASA WMAP Data and Cosmological Parameters CTl CTEl

  20. WMAP 3-year TT, TE, EE, CMB power spectra

  21. Cosmological Parameters from WMAP + SDSS Galaxy Clustering

  22. WMAP Data and Dark Energy NASA WMAP 2002 SNIa CMB

  23. Timbie 02 Mauna Loa Chile South Pole Tenerife Princeton South Pole New Mexico South Pole South Pole AMiBA CBI DASI VSA CAPMAP Boomerang Maxipol BICEP QUAD Interferometer Radiometer Balloon-borne bolometer Bolometer Ongoing CMB Experiments NASA WMAP launched in 6/2001 3rd year data 3/2006 0.2o l<1000 AMiBA at Mauna Loa Taiwan, Australia, USA

  24. SPOrt aboard the International Space Station 7o l<20 Large-format radiometer arrays Large-format bolometer arrays: South Pole Telescope Atacama Cosmology Telescope Polarbear ESA Planck 2007 0.2o l<1000 NASA Inflation Probe (Beyond Einstein Program) Future CMB Space Missions and Experiments

  25. Gravitational Lensing Effects Caused by Dark Matter Halos Hubble Space Telescope

  26. Weak Lensing by Large-Scale Structure Jain et al. 1997 1x1 deg Cosmic Shear γ Shear Variance in circular cells with size θ σ2γ(θ) = ‹γ2› background galaxies CDM halos Ellis et al. 02

  27. 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=−1.05 +0.15/-0.20 • Almost no constraints on dynamical DE with a time-varying w

  28. Do We Really Need Dark Energy

  29. Naïve expectation for the vacuum (zero-pt.) energy ≈ MP4, but ρ≈ 10-120 MP4!! Planck scale MP ~ 1018GeV E=ħω/2 SU(2) gauge field with coupling constant g: S= ∫d4x FμνFμν Quantum tunneling Θ vacuum: n-1 n n+1 Degenerate vacua S0=8π2/g2 Instanton action for tunneling Cosmological Constant and Vacuum Energy (w= −1) But K is infinite☻

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

  31. SU(2) gauge field on extra dimensions of radius R0 - without any ad hoc Higgs field (Cho, Ho, Ng 05) M~1/(4gR0)

  32. potential energy kinetic energy K 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 < 1quintessence • any f(φ)→ negative K→ w < -1phantom . V(φ) DE as a Scalar Field (Bose Condensate)

  33. Affect the locations of CMB acoustic peaks Increase <w> Time-averaged <w>= -0.78 Time-varying w(z) and Early Quintessence(Lee, Lee, Ng 03) =0.7 =0.3 SNIa Redshift Last scattering surface

  34. Generation of primordial B fields 10-23G Induction of the time variation of the fine structure constant 10Mpc Time varying α Lee,Lee,Ng 01, 03 DE Coupling to Electromagnetism SDE-photon= ∫d4x [c φ(E2+B2) + ĉ φE·B]

  35. Liu,Lee,Ng 06 DE Coupling to Electromagnetism BETA= ĉ < 10-3

  36. Weak Interaction → Standard Model SU(3)xSU(2)xU(1) → ……. → Unification of all Four Forces 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? Baryons and Leptons Only 5%!!

  37. Cold Dark Matter is 25% - crucial for the formation of galaxies. Desperately seeking for WIMPssuch 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!

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