SLAC Summer Institute, August 2003 Rocky Kolb, Fermilab & The University of Chicago

Transcription

1 Dark Matter and Dark Energy SLAC Summer Institute, August 2003 Rocky Kolb, Fermilab & The University of Chicago Rocky I: Evidence for dark matter and dark energy Rocky II: Dark matter candidates Rocky III: Dark energy reloaded

2 Ω i ρi Ω = ρ TOTAL 1 CRITICAL Cosmic Pie Heavy Elements: Ω= ν ν ν Neutrinos (ν): Ω= Stars: Ω=0.005 ΛCDM Free H & He: Ω=0.04 Dark Energy (Λ): Ω=0.70 Cold Dark Matter: Ω=0.25

3 What We Know * The matter density is dominated by cold dark matter, which we know nothing about! The baryon asymmetry arises in the GUT or EWK era through B, CP, and equilibrium violation (Sakharov s ingredients), EWK doesn t seem to work.gut scenarios are not simple! The perturbations arise from inflationary dynamics, which depends on particle physics at high energies, which we know nothing about! The universe is dominated by a cosmological term (dark energy, funny energy, quintessence, polenta, cosmological constant, cosmo-illogical constant,.), which we know less than nothing about! * It ain t what you don t know, it s what you know that ain t so!

4 ΛCDM We re almost free, I just felt the first drops of rain

5 Do we have concordance- a standard cosmological model?* Radiation Neutrinos Dark matter Dark baryons Dark energy Inflation Baryo/leptogenesis Hypotheses? Saving the appearances? Epicycles? * Do we want one? The goal is not concordance, but correctness!

6 If I had been present at creation, I would have suggested a simpler scheme. - Alfonse the Wise

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9 Epicycle I Inflation Inflation, as a whole, can be divided into three parts 1. Beginning eternal inflation, wave function of the universe, did the universe have a beginning???? 2. Middle density perturbations, gravitational waves, (particle production in the expanding universe) 3. End defrosting, heating, preheating, reheating, baryogenesis, phase transitions, dark matter, (particle production in the expanding universe)

10 Epicycle II Dark matter What is dark matter? Font & Navarro Frenk, White,... In questions like this, truth is only to be had by laying together many variations of error. -- Virginia Wolf A Room of Ones Own

11 Epicycle III Dark Energy What is the nature of dark energy In questions like this, truth is only to be had by laying together many variations of error. -- Virginia Wolf A Room of Ones Own

12 The universe observed Cosmological parameters: H Hubble's constant q t 0 T 0 Ω 0 0 i deceleration parameter the cosmic food chain ( Ω ) TOTAL, ΩM, ΩB, ΩΛ, Ωγ, Ων,... age of the universe temperature of the universe Power spectra: Pk ( ), Cl Standard model : Dark Energy and Dark matter ΛCDM

13 Big-Bang Bang Theory Robertson-Walker metric a t = cosmic scale factor () k = 0, ± 1 dr ds dt a () t r d 1 kr G = + Ω 2 = 8π GT µν µν Perfect-fluid stress tensor ρ = energy density p = pressure T µ ν = diag( ρ, p, p, p)

14 2 Field equations a k 8π G a + =expansion rate 2 = ρ H a a 3 a a 4π G a 1 = ( ρ + 3 p) q 2 =deceleration paramet er a 3 ah ρ ρm ρr ρ Λ = whatever whatever: p = wρ w= p ρ ρ a w w w 3(1 + w) matter: p = 0 w= 0 ρ a M radiation: p = ρ 3 w= 1 3 ρ a R R R vacuum: p = ρ w= 1 ρ a Λ Λ Λ M 3 4 0

15 age of the universe Cosmological constant (dark energy) dark energy dominant distance expands forever ever slowing dark matter dominant collapses

16 Hubble s Discovery Paper s v = Hd 0 ( H0 = Hubble's constant) -1-1 H0 = 100 h km s Mpc h = 5

17 University of Chicago 1909 National Champions

18 h h = 0.72 ±.03 ±.07 Freedman et al. (Hubble Key Project) = 0.57 ±.02 Sandage, Tammann, et al. Riess et al astro-ph/ Hubble s data

19 Einstein s Biggest Blunder? 1917 Einstein proposes cosmological constant 1929 Hubble discovers Expansion of the universe 1934 Einstein calls it my biggest blunder 1998 Astronomers find evidence for it

20 Λ Field equation: R g R g GT 1 µν 2 µν Λ µν = 8π µν Perfect fluid stress tensor: T µ ν = diag ρ, p, p, p ( ) I found it very ugly indeed that the field law of gravitation should be composed of two logically independent terms connected by addition. About the justification of such feelings concerning logical simplicity it is difficult to argue. I cannot help to feel it strongly and I am unable to believe that such an ugly thing should be realized in nature. Einstein in a letter to Lemaitre, Sept. 26, 1947 Modern view: It belongs on the right-hand side, and has many contributions. T µ ν = diag ρ, ρ, ρ, ρ ρ =Λ 8 π G ( ) Λ Λ Λ Λ Λ ( ) R g R= G T + T 1 µν 2 µν 8π µν µν

21 L F= defines luminosity distance - "know" L, measure F 2 4π d L π L = area of centered on source at time of detection, d S t dr ds dt a t r d a t r 1 kr = () + Ω Area 4 π ( 2 = 0) Conservation of energy: flux redshifted: F= Distance-redshift relation light from comoving coordinate r at time t reaches us now redshifted by an amount (1 + z) = a( t ) at ( ) ( ) ( t ) z = a t0 a 1 (1 ) redshift of energy redshift of time interval : (1+ z) L 4 π a ( t ) r (1 + z) d = a( t ) r(1 + z) L 0 2

22 Distance-redshift relation d = a( t ) r(1 + z) L 0 light travels on geodesics 2 ds = 0 dr ds dt a () t r d 1 kr = + Ω 2 dr dt da = = 2 1 kr at () H( aa ) H = H 0 (1 Ω TOTAL)(1 + z) +Ω M (1 + z) +... Ω = i ρ TOTAL i ( 3H 2 ) 0 8πG Ω = Ω +Ω +Ω +Ω +... (1 Ω ) M Λ R w TOTAL k r 1 1 dr z a ( t0) H0 dz = 1 kr (1 Ω )(1 + z ) +Ω (1 + z ) +Ω (1 + z ) (1 + w) 0 M w

23 Distance-redshift relation d = a( t ) r(1 + z) L 0 at ( ) rfrom 0 r dr z a t H dz = 1 kr (1 Ω )(1 + z ) +Ω (1 + z ) ( 0) TOTAL M Example: matter + lambda Ω TOTAL =Ω M +ΩΛ Program: 2 measure (via d = L/4π F) and d L L Ωi at0 input and calculate ( ) r z Hd z Oz Ω 2 0 L = + ( ) i

24 Evolution of H(z) ) is a key quantity In a flat universe, many measures based on the comoving distance ( ) r z z = 0 dz H z ( ) Luminosity distance L ( ) = ( )( 1+ ) d z r z z Angular diameter distance d A ( z) = r( z) ( 1+ z) Comoving volume element 2 dv z r z ( ) ( ) ( ) = dzdω z H z ( ) Age of the universe ( ) t z = z 0 dz 1 ( 1+ z) H( z)

25 Type Ia supernova Luminosity / Solar Luminosity Supernova Cosmology Project Type Ia Supernovae (not calibrated) days

26 Type Ia supernova Luminosity / Solar Luminosity Supernova Cosmology Project Type Ia Supernovae (calibrated) days

27 apparent magnitude [log(distance)] Type Ia supernova

28 residuals (magnitudes) Type Ia supernova

29 High-z SNeIa are fainter than expected in an Einstein-deSitter model Ω VACUUM maximum theoretical bliss Ω MATTER cosmological constant, or some changing non-zero vacuum energy, or or some unknown systematic effect(s) The case for Λ: 1) Hubble diagram 2) subtraction Ω TOTAL = 1 Ω Μ = = 0.7 3) age of the universe 4) structure formation

30 Theorist s view of the universe (isotropic)

31 Temperature of the universe 100σ error bars Ω h = γ 2 5

32 Observer s view of the universe (fluctuations)

33 Angular power spectrum δt ( θ, φ ) 1 1 δt ( θ, φ ) 2 2 δ θφ θφ T(, ) = a Y (, ) lm lm C l a lm 2

34 Acoustic peaks At recombination, baryon photon fluid undergoes acoustic oscillations Acos kt+ Bsin kt Compressions and rarefactions change T γ Peaks in T γ correspond to extrema of compressions and rarefactions Multipole number corresponds to a physical length scale Hu

35 Acoustic peaks Sound travel distance known Observed l peak ~ geometry Hyperbolic (open) Flat (Euclidean) Ω TOTAL = 1± 0.1 Spherical (closed)

36 WMAP David T. Wilkinson WMAP model WMAP science team

37 WMAP Angular Power Spectrum ΩTOTAL = 1.02 ± 0.02

38 Baryons Ω B h Ly α QSO WMAP: Ω Bh = ± Burles et al. Tytler

39 Matter Ω M 0.3 dynamics lensing Ω TOTAL = 1, Ω Μ = = 0.7 x-ray gas power spectrum

40 v (km/s) M33 rotation curve observed expected from luminous disk 5 10 R (kpc) galaxy & cluster dynamics gravitational lensing structure formation CMB observations

41 CO central regions Optical disks HI outer disk & halo Rotation curves Sofue & Rubin

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43 Observer s view of the universe NGC 6070 lumpy (inhomogeneous and anisotropic) full of stars, galaxies, clusters,.

44 Theorist s view of the universe Actual image of dark matter smooth (homogeneous and isotropic) full of dark matter (and dark energy)

45 Power spectrum Assume there is an average density Expand density contrast δ ( x ) in Fourier modes ρ( x) ρ δ x = δ exp ik x d k ( ) ρ k ( ) 3 Autocorrelation function defines power spectrum δρ( x) ρ ρ dk k = δ( x) δ( x) = 2 k 2π 0 k δ 2π k 2 ( k) P( k) δ 2 k k δ

46 Harrison-Zel dovich Spectrum Tegmark

47 Shape factor Γ Ω h 0.25 ± M Ω M h Ω M h Power spectrum 2dF data

48 High-z SNeIa are fainter than expected in an Einstein-deSitter model Ω VACUUM maximum theoretical bliss Ω MATTER cosmological constant, or some changing non-zero vacuum energy, or or some unknown systematic effect(s) The case for Λ: 1) Hubble diagram 2) subtraction Ω TOTAL = 1 Ω Μ = = 0.7 3) age of the universe 4) structure formation

49 t 0 : age of the universe Example: matter + lambda Ω TOTAL =Ω M +ΩΛ Integrate Friedmann equation: Ht 0 = 1 TOTAL 1 Ω + Ω 0 TOTAL Ω =Ω +Ω M Λ dx w 1 3w wx

50 t 0 : age of the universe white dwarf cooling nucleocosmochronology globular cluster evolution 12.6 ± 3 Gyr 13.5 ± 2 Gyr Chaboyer (2001) Cayrel (2001) H 0 =70 Flat Open Open Flat Flat Ω M Ω Λ t (Gyr) First measurement 12 of stellar uranium

51 Everything in the universe: Clusters Galaxies Stars Planets Poodles Pigeons Pond Scum Donald. Rumsfeld.. From inflationary perturbations

52 Silk damping of baryon pert ns ΛCDM (2dF)

53 Cosmo-illogical constant Mass density of space: ρ g cm 13 4 (10 GeV) 4 4 (10 ev) 4 4 (10 cm) Who ordered that?

54 Ω i ρi Ω = ρ TOTAL 1 CRITICAL Cosmic Pie Heavy Elements: Ω= ν ν ν Neutrinos (ν): Ω= Stars: Ω=0.005 ΛCDM Free H & He: Ω=0.04 Dark Energy (Λ): Ω=0.70 Cold Dark Matter: Ω=0.25

55 The cosmic food chain (Ω i ) Massless neutrinos (2) : 0.002% Photons: 0.005% Metals: 0.023% Massive Neutrino (1) m= 0.2 ev: 0.47 % Stars: 0.50 % Dark neutrons & protons: 4. % Dark matter: 25. % Dark energy: 70. %

56 Cosmological standard model ΛCDM Cosmological parameters h Ω = 1 TOTAL i i i i i Ω Ω Ω Ω Ω Λ CDM B ν γ 2 / 3 1/ Initial perturbations Harrison-Zel dovich (adiabatic curvature perturbations with an initial n=1 spectrum)

57 Dark Matter and Dark Energy SLAC Summer Institute, August 2003 Rocky Kolb, Fermilab & The University of Chicago Rocky I: Evidence for dark matter and dark energy Rocky II: Dark matter candidates Rocky III: Dark energy reloaded