1. A Review of Dark Energy Johns Hopkins University C. W. Kim Korea Institute for Advanced Study

2. Cosmology Birth, Evolution, and Fate of the Universe Introduction Discovery of Dark Energy Dark Energy Cosmological Constant Quintessence (K-essence) Extra Dimensions Others Summary

3. Three Major Miracles 1) Creation of the Universe ~ 14 billion years ago 2) Appearance of life on the Earth ~ 3.5 billion years ago 3) Anthropic Principle ? Why do we live now? Nancy Kerrigan: Why me, Why now ?

4.  Genesis: 4004 B.C., October 26 (King James Version) Even Newton believed it.  Hindu-Buddhism : Eternal existence  Modern Cosmology : Born 14 B ys ago  How? 11-dimensional space-time and Super strings were created from NOTHING. “Nothing” fluctuates, decays, and is unstable. (Uncertainty Principle)  Where ? Anywhere (our universe) Birth of Universe

5. 東洋의 十進法 일 一 10 0 십 十 10 1 열 십 백 百 10 2 온 백 천 千 10 3 즈 믄 천 만 萬 10 4 일만 만 억 億 10 8 억 억 조 兆 10 12 조 조 경 京 10 16 서울 경, 클 경, 경 경 해 垓 10 20 땅 가장자리 해 자 秭 10 24 만 억 억 양 壤 10 28 부드러운 흙 양 구 溝 10 32 도랑 구 간 澗 10 36 산골 물 간 정 正 10 40 바를 정 재 載 10 44 실을 재, 해 재 극 極 10 48 지극할 극 항하사 恒河沙 아승기 阿僧祇 나유타 那由他 불가사의 不可思議 무량수 無量數 갠지스 강의 무수한 모래라는 뜻 10 56 10 64 언덕 아, 중 승, 땅귀신 기, 헤아릴수 없는 수 10 72 어찌 나, 말미암을 유, 무량의 수 10 80 or 10 120 10 88 or 10 128 불가사의의 억배 일 一 10 0 분 分 10 -1 나눌 분 리 厘 10 -2 리 리 모 毛 10 -3 털 모 사 絲 10 -4 실 사 홀 忽 10 -5 문득 홀 미 微 10 -6 작을 미 섬 纖 10 -7 가늘 섬 사 沙 10 -8 모래 사 애 埃 10 -10 묘 渺 10 -11 막 漠 10 -12 사막 ( 아득할 ) 막 모호 摸湖 10 -13 법 모, 호수 호 준순 浚巡 10 -14 물러갈 준, 순행할 순 수유 須臾 10 -15 잠깐 수, 잠깐 유 순식 瞬息 10 -16 눈깜짝할 순, 숨쉴 식 탄지 彈指 10 -17 찰나 刹那 10 -18 육덕 六德 10 -19 六元德 = 知, 仁, 聖, 義, 忠, 和 허공 虛空 10 -20 빌 허, 빌 공 청정 淸淨 10 -21 맑을 청, 깨끗할 정 티끌 진. 10 -16 이란 해석도 있음 10 -9 진 塵 티끌 애. 진의 억분의 일, 즉 10 -24 이란 해석도 있음 아득할 묘, 10 -32 이란 해석도 있음 탄알 탄, 손가락 지, 손가락을 튀김 절 찰, 어찌 나, ksana 의 음역 불가사의

6. B ig Bang Cosmology  Experimental Evidence: Expansion,CMB, Element formation, ….  Einstein ’ s Gravity (1915)  Cosmological Principle Homogeneous and isotropic (No center)  Equation of State   ( current density) ( critical density ) o o c ~ 10 g/cm c -29    3 Modified by Inflation  (Flat Universe) = 1

7. SHBBM :  Horizon Problem  Flatness Problem, Age Problem  Problem,... Inflation : Expansion by more than 10 30 10 -35 sec 10 -32 sec all problems solved Predictions :   O = 1 : Flat Universe  created    Inflation

8. Fate of the Universe ○ t = 0 t 0 = 15 Bys t R k = -1,  0 < 1 k = 0,  0 = 1 k = 1,  0 > 1

9. Matter in The Universe ? 10 % Ordinary Matter ( proton, neutron, … ) < 1 % (Visible) Dark Matter  0 = 1 <

10. Matter and Dark Energy in The Universe ? 10 % Ordinary Matter : proton, neutron, neutrino… < 1 % (Visible) ?  = 0.73  = 0.27  0 = 1 ? X m <

11. Accelerating Universe R t t=0 t 0 =14b.y k = -1,  0 < 1 k = 0,  0 = 1 k = 1,  0 > 1

12. 0.5 0.27 0.0 1 1 0.73 LSS GL XX  matter SN Type I a BOOMERANG Maxima (CMB)

13. Rotation Curves Hot Gas Galaxy Halos Gravitational Lensing Large Scale structure  B = 0.044 ± 0.004  L = 0.005  < 0.015 (no degeneracy) M ~  m = 0.27 ± 0.04 m m  8G8G mm 3H 2 L ~

15. 0.5 0.27 0.0 1 1 0.73 LSS GL   matter SN Type I a BOOMERANG Maxima (CMB)

16.                  Hydrogen Atom     : electron  : proton : photon  t ~ 380,000 ys : T ~ 3000 K  Universe then was 1000 1 ° inininin in size

17. First Light Expansion of the Universe (  10 3 ) Microwaves

19. WMAP

24. “Best” Cosmological parameters : Wilkinson Microwave Anisotropy Probe(WMAP) Observations : Preliminary Result -a From COBE (Mather, J. C. et al., 1999, ApJ 512, 511) -b Derived from COBE (Mather, J. C. et al., 1999, ApJ, 512, 511) Description Symbol Value + uncertainty -uncertainty Total density  tot 1.02 0.02 0.02 Age of universe (Gyr) t 0 13.7 0.2 0.2 Hubble constant h 0.71 0.04 0.03 Equation of state of quintessence  < -0.78 95%CL - Dark energy density   0.73 0.04 0.04 Matter density  m 0.27 0.04 0.04 Baryon density  b h 2 0.0224 0.0009 0.0009 Baryon density  b 0.044 0.004 0.004 Baryon density(m -3 ) n b 0.25 0.1 0.01 Matter density  m h 2 0.135 0.008 0.009 Light neutrino density  h 2 <0.0076 95% CL - CMB temperature (K) a T cmb 2.725 0.002 0.002 CMB photon density (cm -3 ) b n  410.4 0.9 0.9 Baryon-to-photon ratio  6.1  10 -10 0.3  10 -10 0.2  10 -10 Baryon-to-matter ratio  b  m -1 0.17 0.01 0.01 Age at decoupling (kyr) t dec 379 8 7 Decoupling time interval (kyr)  t dec 118 3 2 Redshift of matter-energy equality z eq 3233 194 210

25. Curvature of the Universe CMB   = 1, k = 0 ( flat ) 0   > 1, k = + 1 ( Closed ) 0   < 1, k = – 1 ( Open ) 0 (Observer)    1° Horizon size = 1 o

26. The Power Spectrum 30 degree 1 degree0.1 degree

27. 4/30/01 New York Times Relative amplitude 6 4 2 0 71 0.50.30.250.2................ Main tone harmonics Angular scale : degree (Latest BOOMERANG DATA)

28. K = + 1 K = 0 K = -1 Boomerang determines the curvature

29. 0.5 0.27 0.0 1 1 0.73 LSS GL   matter SN Type I a BOOMERANG Maxima (CMB)

32. Standard Candle (SN) d L = H0H0 1 [ Z + 2 1 (1 - q) Z 2 + ……. ] Hubble’s LawCorrections Deviation from Hubble’s Law can tell values of q (deceleration parameter). q  – RH 2 R ‥ > 0 : deceleration < 0 : acceleration Direct measurement

33. Z = 0.2 Z = 0.5 Z = 1.0 Z = 1.7 mm  mm   mm mm    0 SN Type Ia (Standard candle)

35. Chandra X-Ray Satellite

36. 1 b years ago 3.5 b years ago 6.7 b years ago Clusters seen by X-rays

37. Recent Independent Confirmation from CHANDRA X-ray Obsevatory About 6 Billion years ago the Universe began to accelerate. Emit X-ray  New Method to measure Dark Energy (How fast the Universe is expanding)  Observed 26 Clusters of galaxies at 1bly ~ 8bly Clusters : Hundreds of Galaxies + Dark Matter + Hot Gases d = f (z, q)  q (deceleration Parameter) “Consistent with SN Ia data” measured

38. Dark Energy Characteristic of space-time (?) Uniformly distributed (?) Acceleration of Expansion: Negative p E = mc 2  gravity No interference with formation of structures (?)  ~ 10 -29 g/ ㎤ ~ 0.73 x total density X Changes very slowly in time (?)

39. Standard Matter (Including Energy) Satisfy: 3 p +  > 0 Define : W   p (Equation of state func) 3 p +  > 0  - 3 1 w > Universe with Standard Matter and Energy with deceleration Usual expansion: ( Including dark matter) q ∝ - (3 p +  ) <0 Matter and energy p: total pressure  : total density

40.  X ~ R -3(1+W) Equation of State Func. W X = — pXXpXX Non-relativistic matter : W M = –— ~ 0  M ~ R -3 pMMpMM Relativistic matter : W = –— ~ — 1313 pp  R ~ R -4 Cosmological constant:W = - 1  ~ R 0 = constant  Behavior of  as a function of W

41. W of Dark Energy = + ≃ (matter dominated) Experiment : = 0.73 acceleration W < -0.46 Data shows : W < -0.78 (95% C.L.) Significant acceleration!

42. W T = – — N3N3 N = 1 for strings 2 for walls  Topological defects W Q = : –1 < W Q < 1 —  2 – V(  ) 1212 —  2 + V(  ) 1212 Some changes in time Clusters slightly on very large scale  Quintessence (Rolling, Dynamic Scalar Field)  Vacuum Energy (Cosmological Constant,  ) W  = –1 : Satisfies all requirements   = constant Strings are ruled out! Possible Candidates for X

43. Most attractive Interpretation as of now  X =  : Vacuum Energy  Break down of something? (Friedmann Equation, Gravity, … )  New models: Ads/CFT inspired, Non- Riemannian, Bimetric, Time varying cosmological constant, ….  Graviton leak to Extra dimension * Unexpected surprise? Why so small?

44. Einstein ’ s Equation of Gravity (1915) R  - Rg  -  g  = 8  GT  2 1 Space-time Cosmological Constant   0  Negative Pressure Vacuum energy matter (1917 ) 

45. Basic Equation (Einstein) T + V = E 1 2 R2R2. -  m R 3 44 3 G R -  R 2 = - k 2 1 6 1917, to make UniverseStatic.  R R. 2 = G  m R 2 +  R 2 - k 33 8 1 3 ~ 1 R k = 0 : flat Universe  > 0 : Repulsive force ! ( force =  R  < 0 : Attractive force Because of E = mc 2,  term acts as mass with gravity in Cosmology. But ordinary matter does not feel the effect since it is pulled by every direction equally.   “only” affects expansion of the Universe. 1 3

46. 1917 : Introduced by Einstein to make a static Universe “Biggest Blunder in my Life !” 1917 : de Sitter 1922 : Friedman Cosmology (Standard) 1929 : Hubble : Hubble’s Law (d, z) 1931 : Lemaitre Cosmology (alternative to Friedman Cosmology) 1980 : Guth : Inflation;  o = 1, : Hoyle, Bondi, Gold : to solve an age crisis : Solved by Sandage (1987) by a small H o (h 0 =0.42) 1997~98 : Perlmutter, Schmidt and Riess found independently an indication of an accelerating Universe (   0 ? ) using SN type Ia (z ~ 0.5) 1998 : BOOMERANG :  o ~ 1,  m < 1     0 2001 : Established ?! BOOMERANG, MAXIMA, COBE, … New SN Type Ia data, Large scale structure Data, CMB DATA New Cosmology (   0)  

47. Observed Cosmological Constant  c = = 1.9  10 -29 h 2 g/cm 3 3H 0 2 8G8G ~ 9.6  10 -30 g/cm 3 for h = 0.71   = 0.73  = 5.7  10 -30 g/cm 3  c  =   8G8G   = 1.05  10 -56 /cm 2 ~ 10 -35 /sec 2 ~ 10 -82 m  2 ~ 10 -84 (GeV) 2 ~ 10 -122 M p 2 Smallest number known in Science ! No SDSS data included Hard to explain!

48.  now t mm   was not important Already,   >  m (becoming de Sitter Universe) Eventually  ~   = const : de Sitter Universe 

49. R 2 -  R 2 = 0 H  : Hubble parameter  +(  +p) 3 ( ) = 0 q  - : deceleration parameter t =  0  dx, x = : R ~ t 2/3 Present : q 0 =,  0 = 1 t 0 =   dx = H 0 = h : h = 0.65 (± 0.05)  t 0 = 10.25 By for h = 0.65 Age of the oldest globular clusters, white dwarf 13 ~ 15 By 8G8G 3 R R R R RR R2R2 3H 2 8G8G  cc 1 1 H0H0 H0H0 100Km Mpc sec Standard (k=0,  =0) Cosmology x 1....... 1 H0H0 x x R RoRo  c = :   = 2q R. 3 2 2 0

50. Cosmology with k = 0,   0 R 2 -  R 2 - R 2 = 0 3 8  G 3    =,  =  m +  , 8  G   =  m +   = 1  m = = sech 2 (  t ) 3H 2 8  G  m 2 3   = = tanh 2 (  t ) 3H 2 8  G   2 3 R(t) = ,oRo,oRo  3 sinh 2 3 (  t ) q = (1 - ) = (  m - 2   ) 2 1 2 1   H2H2  3H 2 = q = 0 when  m =   : Inflexion Point q = (1 - 3   ) = 0 :  = H 2 or Z = - 1 2 1.     3  mm 3 2  m, 0 2  , 0 3 1  c = 8  G 3H 2 Deceleration  Acceleration 2 1

51. t t q 2 1 0 2 1 Deceleration Deceleration Parameter 0.48 t 0t 0 Z ~ 0.55 q = [  m - 2   ] 2 1 – Acceleration (1997 ~ 2000) Z=1.7 (2001)...  = H 2 -

52. Miracle  m ~ sech 2 (  t ) 2 3   ~ tanh 2 (  t ) 2 3 R(t) ~ sinh 2 3 (  t ) 3 2     ~ 10 -17 /sec 3  t o ~ 10 17 sec 3   t ~ O (1) : Miracle ! Anthropic Principle ?

53.  =  m +   = 1  m m 10 Byt o = 14 By t  ( z ~ 0.23)  3.4 By (z =1.7)  = 1

54. The Fifth element (Greek philosophy) Air, Earth, Fire, Water and Quintessence Perfect Substance Quintessence as Dark Energy: Caldwell, Dave, Steinhardt (1998) Quantum Field( ) with a very long wavelength (about the size the visible Universe) In the context of Super string theory L = g - V( ) → + 3H + V’( ) = 0 P = - V( ) = + V( ) W = = : - Quintessence

55. V( ) : Extremely long wavelength and period << │V( )│ → W ~ -1 Few - Examples Pure exponential : V e Tracker : M /, M e Modified exponential : V ( ) e Tracker field > : mimics radiation > : mimics matter (due to Hubble damping) Some mechanism locks to be nearly a constant. (Kinetic – energy – driven quintessence k-essence)

56. Cosmological Constant Quintessence W = -1 -1 ≤ W ≤ 1 Recent epoch W ≠ W (t) W = W (t) W ≠ W (x) W = W (x) ripple in CMB Universe accelerates forever could decay into new forms of matter and radiation → Universe with new structures Future: Large – Aperture Synoptic Survey Telescope (LSST) Super Nova Acceleration Project (SNAP) ~ 2000 Deep Extragalactic Evolutionary Probe (DEEP) Planck Satellite (2007) Can they really distinguish?

57. Calabi-Yau Extra-dimensions 4 5 9 Extra- Dimensions

58. Extra-dimensions  Not seen because  curled up in a small world (~10 -33 cm).  may not be curled up but we live on our 3-D world. Everything is confined to our 3-D world (Brane), except gravitons (g). Virtual 6 ~ 7 dimensions are Gravitons: real Gravitational waves from SN, collision of galaxies, … String theory e, , q, …. Leaks out Tied to a brane graviton : : MM'M' g Super String : 11 dim.

59. Changes in Gravity

60. Zero - Point Energy of Reheating Potential V( ) Inflation Reheating + 3H + 3V’( ) = 0 V ( ) : Harmonic Oscillator H ( ) : ∼ ⇒ Power – law suppressed damped H.O. Boundary Conditions: Reheating starts at t ∼ 10 sec Energy Scale ∼ 10 GeV Quantum Mechanical Solution: Zero-point energy (t = t ) ∼ 10 g/cm ( ∼ ! )

61. What Next ?  Need more accurate value of  X (To a few % accuracy)  Crucial to know if W(t,z) or W = constant and space dependence  CMB Experiments (Boomerang, WMAP, Maxima, Plank, …) May not reach to ~ 0.05  Super Nova / Acceleration Probe : Satellite 4 years to construct, 3 year mission Expect to see ~2000 SN (z = 0.2 ~ 1.7) So far, Supernova Cosmology Project (Perlmutter) High – Z Supernova Search (Schmidt) HST (Riess) ~ 100 SN (6 at z > 1.25)  SDSS (Galaxy, Cluster counts), … May not be enough to see w(t)

62. z Weller and Albrecht 2001

64. Accelerating Universe R t de Sitter universe t=0 t 0 =15b.y k = -1,  0 < 1 k = 0,  0 = 1 k = 1,  0 > 1 W ( t ) will eventually determine the fate!

65. Comments on Vacuum Energy Maybe the most fundamentally mysterious thing in basic Science. Every attempt to calculate it has gotten an absurd answer. Basically, people don’t have a clue as to how to solve the problem. Vacuum energy would be NO.1 on my list of things to figure out. Right now, not only for cosmology but for elementary particle theory, this is the bone in our throat.

66.  Dark Energy Vacuum Energy  Vacuum Energy : Creation ?, Why so small? Most difficult problem in 21 st Summary ? Acceleration: No galaxies seen in the sky!  Why do we live now?  Life on Earth begins when matter density = dark energy density Century Quintessence Extra dimension Changes in Gravity

67. Galileo’s first Telescope 1.33 m, X 14

68. 1.2 meter Mt. Palomar Telescope E. Hubble discovers the expanding Universe

69. Hubble Space Telescope

70. Keck 10 meter Telescopes

71. ChandreChandre Chandra X-Ray Satellite

72.  M = 0.3,   = 0.7   = 0  m = 0.3 Hubble Diagram  = 1   = 0  m = 0.3   = 0.7 Riess, 1998 Perlmutter, 1999 ° (can tell q values)

73. R - Rg  1 2  -  g  = 8  GT  Gravitational Constant Static Universe 0 = “Biggest blunder in my life!” (1915) (1917) Cosmological Constant(  ) : Vacuum(Dark) Energy – (curvature, matter) + (Vacuum Energy) Acceleration R = RG  +  ‥  3 44 m 3 R Decrease Increase Expansion Rate R R =  R2R2 k m 3 1 ( ) 2 + 3 88 GG +  curvature Constant Decrease

75. Light Curves : Type Ia : Produces a lot of Fe Lack of H lines, Abundant in early Universe Standard Candles : distance measurements ( Not quite but correctable : colors and temperatures) Spectroscopy of various Bands : I, J, K,... A Hint that the Universe is accelerating lately (for small z (0.4~1)) was discovered independently by Perlmutter and Riess (1997~8) Acceleration is fairly recent ! SN Type Ia 1997ff (Riess) with z=1.7 shows no acceleration ! SN Type Ia Type ITypeII

77. How to calculate the age R time(t)  14 By Now (t ) ° Present Rate( H ) ° Einstein theory H, density ° 20 By Age (t ) ~ H ° 1 ° 1 + density 1

78. Ω o = 1 Ω > 1 o Ω < 1 o

79. Inflation  Flat Universe  o = 1 3 x 3 x 3

80. Inflation and Horizon Problem SHBB Model 10 28 cm 1 cm 10 -24 cm 10 23 cm...... A B A B 10 25 10 3 A B t =10 -35 sec inf t = 10 5 y de t = now 0  Causally connected (Same temperature)

81. How to Cure the Problems in SHBB Cosmology Inflation ! 10 -24 cm 10 6 cm (10 -35  10 -34 sec) 10 25 Horizon problem solved ! > 10 30 t = 10 5 ys Predictions .. A B   0    0 = 1 + 10 -N : N very large Flat Universe    10 25 cm

82.  0 = 1,  m = 0.27   X = 0.73  SN Type Ia can tell us about  m /  X  CMB  0 and  B   X Also some cross - checking of CMB, LSS, SN  X = 0.73 ± 0.04 Nature of X (Nature unknown)

83. R - Rg  1 2  -  g  = 8  GT  Gravitational Constant Static Universe 0 = “Biggest blunder in my life!” (1915) (1917) Cosmological Constant(  ) : Vacuum(Dark) Energy – (curvature, matter) + (Vacuum Energy) Acceleration R = RG  +  ‥  3 44 m 3 R Decrease Increase Expansion Rate R R =  R2R2 k m 3 1 ( ) 2 + 3 88 GG +  curvature Constant Decrease

84. Phase Transition T > Tc T = Tc T < Tc

85. Creation of a Universe (Phase transition of vacuum) Quantum Fluctuation Uncertainty Principle Energy created by the change of nature of vacuum New Vacuum (New ground state) Ground state or vacuum

86. A Brief History of the Universe t = 0 : Big Bang (No space – time before) From singular Point ? ( ρ > 0, P > 0 ) How? (why) : Quantum Fluctuation of Vacuum (nothing → something)* Born as 11- dimensional Universe ? (string theory) t ~ 10 -43 sec : T ~ 10 33 o K (~ 10 19 GeV) ( Planck time ) Unified force → Gravity + others Homogeneous. 11 dim. → 4 (=3+1) dim.

87. t ~ 10 -35 sec : T ~ 10 30 o K (~10 16 GeV)* strong force + others split Inflation : 10 -35 sec - 10 -32 sec Universe expands by > 10 30 times Present Univ. was 1cm. * (δρ ∕ ρ) Created (homogeneous until then) (observed now in CMBR) n B ≠ n B created → We exist. t ~ 10 -10 sec : T ~ 10 18 ºK (=250GeV) Weak and E/M interactions separated (W,Zº became massive) t ~ 10 -4 sec : T ~ 10 12 ºK (~MeV) p, n, π, … appear : Before this only leptons, quarks

88. t ~ 1 sec : T ~ 10 10 ºK (~MeV) Neutrinos decoupled ( n ν ~ now) t ~ 3 min : T ~ 10 9 ºK (0.1 MeV) Nucleosynthesis : d, He, Li, formed t ~ 3,000 years : ρ R = ρ M t ~ 380,000 years : T = 0.26eV ( ~3000 ºK) H atoms form. Photons decoupled : * First light !!! Carrying 340 cm 3 δρ ρ

89. now n γ ~ 400/cm 3, microwaves ~ 10 -3 : d H = 10 23 cm Our Univ. was 10 25 cm → horizon problem. t 1,000,000 years : Stars, Galaxies, Quasars, Black Holes Supernovae,…. t ~ (14 - 4.5) billion years (9.5 b years) Solar System formed from S.N. remnants t ~ (14 - 3) = 11 b years Life begins : Major Miracle t ~ 14 b years : Now T ~ 2.735 ºk R(t) R(t 0 ) >~>~

90. Present Universe 1) Universe is expanding (Astronomy) V = H  L : H = 71 Mpcsec km 1920’s : Hubble 2) “Visible” Size * ~ 10 28 cm (~14 billion l.y.)* Age ~ 14 billion years old Uncertain due to H 3) Visible Universe contains ~100 billion (=10 11 ) galaxies Each galaxy contains ~100 billion stars*  ~ 10 -30 ~ 1 proton/m 3 Q 0, L 0 (Isotropic) 3   oo o g/cm

91. 5) 4 He, d, …… Abundance (Nuclear Physics) M(p,n) M( 4 He) ~ 0.24 Nucleosynthesis Universe was once 10 9 K hot. 4) 2.7 0 K Microwave Background Radiation (Atomic Physics) N  ~ 10 90 : n   400 / cm 3 Uniform, isotropic to 10 -5 Universe was once 3000 K hot.   T TT T  2.735 K* o o O

92. 7) Relic Neutrinos (particle physics) N ~ 330 / cm 3 : Hard to detect 8) Evidence ↔ Big Bang !! 6) Baryon number (Particle phyics) Baryogenesis N B ~ 10 80 : =  No  B 0 = n  n B ~ 10 Universe was once 10 28 K hot. -10 -19 n  n B No confirmation, yet o

93. Inflation  Flat Universe  o = 1 3 x 3 x 3

94. Timeline of the Universe