A Review of Dark Energy

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

2. Cosmology Birth, Evolution, and Fateof 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) Why do we live now? Anthropic Principle ? Nancy Kerrigan: Why me, Why now ?

4. Birth of Universe  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)

5. 東洋의 十進法 일 一100 십 十 101열 십 백 百102온 백 천 千103즈 믄 천 만 萬104일만 만 억 億108억 억 조 兆 1012조 조 경 京1016 서울 경, 클 경, 경 경 해 垓1020땅 가장자리 해 자 秭1024만 억 억 양 壤1028 부드러운 흙 양 구 溝1032 도랑 구 간 澗1036산골 물 간 정 正1040바를 정 재 載1044실을 재, 해 재 극 極1048 지극할 극 항하사 恒河沙 아승기 阿僧祇 나유타 那由他 불가사의 不可思議 무량수 無量數 일 一100 분 分10-1나눌 분 리 厘10-2리 리 모 毛10-3털 모 사 絲10-4실 사 홀 忽10-5문득 홀 미 微10-6작을 미 섬 纖10-7가늘 섬 사 沙10-8모래 사 애 埃10-10 묘 渺10-11 막 漠10-12사막(아득할) 막 모호 摸湖10-13 법 모, 호수 호 준순 浚巡10-14물러갈 준, 순행할 순 수유 須臾 10-15잠깐 수, 잠깐 유 순식 瞬息10-16눈깜짝할 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10-20빌 허, 빌 공 청정 淸淨10-21맑을 청, 깨끗할 정 티끌 진. 10-16이란 해석도 있음 진 塵 10-9 티끌 애. 진의 억분의 일, 즉 10-24이란 해석도 있음 아득할 묘, 10-32이란 해석도 있음 갠지스 강의 무수한 모래라는 뜻 1056 언덕 아, 중 승, 땅귀신 기, 헤아릴수 없는 수 1064 탄알 탄, 손가락 지, 손가락을 튀김 어찌 나, 말미암을 유, 무량의 수 절 찰, 어찌 나, ksana의 음역 1072 1080 or 10120 불가사의 1088 or 10128 불가사의의 억배

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

7. Inflation SHBBM:  Horizon Problem Flatness Problem, Age Problem  Problem,...   Inflation : Expansion by more than 1030 10-35 sec 10-32 sec all problems solved Predictions : • O = 1 : Flat Universe • created  

8. Fate of the Universe R k = -1, 0 < 1 k = 0, 0 = 1 k = 1, 0 > 1 ○ t t = 0 t0= 15 Bys

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

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

11. Accelerating Universe Accelerating Universe R k = -1, 0 < 1 k = 0, 0 = 1 k = 1, 0 > 1 t t0=14b.y t=0

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

13. m = 0.27 ± 0.04 Rotation Curves Hot Gas Galaxy Halos Gravitational Lensing Large Scale structure M m L 8G m  3H2 B = 0.044 ± 0.004 L = 0.005 < 0.015 (no degeneracy) ~ ~

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

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

17. First Light Expansion of the Universe (  103) Microwaves

19. WMAP

24. “Best” Cosmological parameters : Wilkinson Microwave Anisotropy Probe(WMAP) Observations : Preliminary Result Description Symbol Value + uncertainty -uncertainty Total density tot 1.02 0.02 0.02 Age of universe (Gyr) t0 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 bh2 0.0224 0.0009 0.0009 Baryon density b 0.044 0.004 0.004 Baryon density(m-3) nb 0.25 0.1 0.01 Matter density mh2 0.135 0.008 0.009 Light neutrino density h2 <0.0076 95% CL - CMB temperature (K)a Tcmb 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) tdec 379 8 7 Decoupling time interval (kyr) tdec 118 3 2 Redshift of matter-energy equality zeq 3233 194 210 • 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)

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

26. 30 degree 1 degree 0.1 degree The Power Spectrum

27. 4/30/01 New York Times (Latest BOOMERANG DATA) 6 Main tone . harmonics . . 4 . . Relative amplitude . . . . . . . . 2 . . . 0 7 1 0.5 0.3 0.25 0.2 Angular scale : degree

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

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

32. ‥ R Standard Candle (SN) Direct measurement 1 1 (1 - q) Z2 + ……. ] dL = [ Z + 2 H0 Hubble’s Law Corrections Deviation from Hubble’s Law can tell values of q (deceleration parameter). > 0 : deceleration – q RH2 < 0 : acceleration

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

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 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 Emit X-ray d = f (z, q) measured  q (deceleration Parameter) About 6 Billion years ago the Universe began to accelerate. “Consistent with SN Ia data”

38. Dark Energy • Characteristic of space-time (?) • Uniformly distributed (?) Changes very slowly in time (?) • No interference with formation of • structures (?) • Acceleration of Expansion: Negative p • E = mc2 gravity  • ~ 10-29 g/㎤ ~ 0.73 x total density X

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

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

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. Vacuum Energy (Cosmological Constant, ) W = –1 : Satisfies all requirements  = constant • Quintessence (Rolling, Dynamic Scalar Field) • • 1 2 1 2 — 2 – V() — 2 + V() 1 for strings 2 for walls WQ = : –1 < WQ < 1 N 3 N = WT = – —  Topological defects Possible Candidates for X Some changes in time Clusters slightly on very large scale Strings are ruled out!

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

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

45. Basic Equation (Einstein) T + V = E . k 4 G 1 - m R3 1 = - - R2 R2 2 3 R 6 2 1917, to make Universe Static. . 3 1 = G mR2 + R2 - k  R 2 8 3 1 ~ k = 0 : flat Universe R 1  > 0 : Repulsive force ! ( force =  R 3  < 0 : Attractive force Because of E = mc2,  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.

46. New Cosmology (  0) 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 Ho (h0=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

47. Observed Cosmological Constant 3H0 2  = = 1.9  10-29 h2 g/cm3 c 8G ~ 9.6  10-30 g/cm3for h = 0.71   = 0.73  = 5.7  10-30 g/cm3  c  No SDSS data included  =  8G   = 1.05  10-56 /cm2 ~ 10-35 /sec2 ~ 10-82 m 2  ~ 10-84 (GeV)2 ~ 10-122 Mp 2 Smallest number known in Science ! Hard to explain!

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

49. Standard (k=0, =0) Cosmology . . . R R 8G R2 - R2 = 0 H  : Hubble parameter R 3 . .. . R RR +(+p)3 ( ) = 0 q  - : deceleration parameter . R R2  3H2 c = :  = 2q c 8G 1 R x t = 0 dx , x = : R ~ t 2/3 x H0 Ro 1 Present : q0 = , 0 = 1 2 1 2 1 x t0 = dx = H0 0 3 H0 100Km H0 = h : h = 0.65 (± 0.05) Mpc sec t0 =10.25 By for h = 0.65 Ageof the oldest globular clusters , white dwarf 13 ~ 15 By

50. Cosmology with k = 0 ,   0 .  8 G R2 - R2 - R2 = 0 3 3 3H2   = ,  = m +  ,  c = 8 G 8 G  =  m +  = 1     3 8 G m 3  m = = sech 2 (  t ) 3H2 2 8 G  3  = = tanh 2 (  t ) 3H2 2 2 3 m R(t) = (  t )  3 ,oRo sinh 3 2   1 1 q = (1 - ) = ( m - 2 ) 2 H2 2   = 3H2 1 q = 0 when  m =  : Inflexion Point 2 Deceleration  Acceleration 1 2, 0 1 3 q = (1 - 3 ) = 0 :  = H2 or Z = - 1 m, 0 2