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

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

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

6. 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, w CDM ≈0 ;  DE ≈   =0.7, w  ≈ -1 q<0 Universe is accelerating !! H 2 = 8  G (ρ M +ρ DE ) / 3 – k / R 2 1 =  M +  DE – k / (R 2 H 2 ) 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 expansion rate total energy curvature  ≡8  Gρ/ 3H 2. R / R = −4  G (ρ M +ρ DE +3p M +3p DE ) / 3 2q =  M (1+3w M ) +  DE (1+3w DE ) de-acceleration parameter q≡−RR / R 2 equation of state w≡ p /ρ accelerationtotal pressure... H 0 =100 h km s -1 Mpc -1

7. Standard Candles!!

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

9. Supernova Ia and Dark Energy SNAP satellite

10. 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) 大霹靂模型 最後散射面 宇宙誕生

11. 2006 John Mather George Smoot 1978 Arno Penzias Robert Wilson Plus many other observations AT&T Bell NASA CMB Milestones

12. CMB Spectrum T=2.725 ± 0.002 1992

13. 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 Quadrupole anisotropy e Linearly polarized Thomson scattering

14.  Point the telescope to the sky  Measure CMB Stokes parameters: T = T CMB − T mean, Q = T EW – T NS, U = T SE-NW – T SW-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

15. CMB Foreground and Removal WMAP 02 COBE 92

16. CMB Anisotropy and Polarization Angular Power Spectra  l = 180 degrees /  Decompose the CMB sky into a sum of spherical harmonics: (Q − iU) (θ,φ) =Σ lm a 2,lm 2 Y lm (θ,φ) T(θ,φ) =Σ lm a lm Y lm (θ,φ) (Q + iU) (θ,φ) =Σ lm a -2,lm -2 Y lm (θ,φ) C B l =Σ m (a* 2,lm a 2,lm − a* 2,lm a -2,lm ) B-polarization power spectrum C T l =Σ m (a* lm a lm ) anisotropy power spectrum C E l =Σ m (a* 2,lm a 2,lm + a* 2,lm a -2,lm ) E-polarization power spectrum C TE l = − Σ m (a* lm a 2,lm ) TE correlation power spectrum (Q,U) electric-type magnetic-type

17. 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 

18. Data Pipeline and Extraction of Cosmological Parameters CMB sky map T(x i ), Q(x i ),U(x i ) X i : ith pixel Anisotropy & Polarization Power Spectra C T l, C E l, C B l, C TE l Cosmological Parameters Maximum likelihood analysis χ 2 fitting Pixelization

19. Experimental Detections and Limits CTlCTl C TE l CElCEl

20. NASA WMAP Data and Cosmological Parameters CTlCTl C TE l 2002

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

22. Cosmological Parameters from WMAP + SDSS Galaxy Clustering

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

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

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

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

27. Weak Lensing by Large-Scale Structure Cosmic Shear γ background galaxies CDM halos Shear Variance in circular cells with size θ σ 2 γ (θ) = ‹γ 2 › Jain et al. 1997 1x1 deg Ellis et al. 02

28. 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

29. Do We Really Need Dark Energy

30. Cosmological Constant and Vacuum Energy (w= −1) SU(2) gauge field with coupling constant g: S= ∫d 4 x F μν F μν Θ vacuum: Degenerate vacua n-1 n n+1 Quantum tunneling But K is infinite ☻ Naïve expectation for the vacuum (zero-pt.) energy ≈ M P 4, but ρ  ≈ 10 -120 M P 4 !! Planck scale M P ~ 10 18 GeV E=ħω/2 S 0 =8π 2 /g 2 Instanton action for tunneling

31. SU(2) gauge field with a Higgs doublet ( Yokoyama 02 ) Higgs potential S= ∫d 4 x [ F μν F μν + D μ Φ D μ Φ −V(Φ)] where V(Φ)=λ(|Φ| 2 −M 2 /2) 2 /2 Finite ☺

32. SU(2) gauge field on extra dimensions of radius R 0 - without any ad hoc Higgs field ( Cho, Ho, Ng 05 ) M~1/(4gR 0 )

33. DE as a Scalar Field (Bose Condensate) S= ∫d 4 x [f(φ) ∂ μ φ∂ μ φ/2 −V(φ)] EOS w= p/ρ= ( K-V)/(K+V) Assume a spatially homogeneous scalar field φ(t) f(φ)=1 → K=φ 2 /2 → -1 < w < 1 quintessence any f(φ)→ negative K→ w < -1 phantom kinetic energy K potential energy. V(φ)

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

35. DE Coupling to Electromagnetism S DE-photon = ∫d 4 x [ c φ(E 2 +B 2 ) + ĉ φE·B ] Generation of primordial B fields 10 -23 G 10Mpc Induction of the time variation of the fine structure constant Time varying α Lee,Lee,Ng 01, 03

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

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

38. 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!