A Review of Dark Energy

Johns Hopkins UniversityC. W. KimKorea Institute for Advanced Study

Cosmology Birth, Evolution, and Fate of the Universe IntroductionDiscovery of Dark EnergyDark EnergyCosmological ConstantQuintessence (K-essence)Extra DimensionsOthersSummary

Three Major Miracles1) Creation of the Universe~ 14 billion years ago2) Appearance of life on the Earth~ 3.5 billion years ago3)Anthropic Principle ?Why do we live now?Nancy Kerrigan: Why me, Why now ?

Genesis: 4004 B.C., October 26 (King James Version) Even Newton believed it. Hindu-Buddhism : Eternal existence Modern Cosmology : Born 14 B ys agoHow? 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

100 101 102 103 104 108 1012 1016 , , 1020 1024 1028 1032 1036 1040 1044 , 1048 10561064 , , , 1072 , , 1080 or101201088 or 10128 100 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-10 10-11 10-12 () 10-13 , 10-14 , 10-15 , 10-16 , 10-17 10-18 10-19 = , , , , , 10-20 , 10-21 , . 10-16 10-9 . , 10-24 , 10-32 , ,

, ,ksana

Big Bang CosmologyExperimental Evidence: Expansion,CMB, Element formation,.

Einsteins Gravity (1915)

Cosmological PrincipleHomogeneous and isotropic

(No center)Equation of State (current density) (critical density)ooc ~ 10 g/cmc-293 Modified by Inflation(Flat Universe)= 1

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 createdInflation

Fate of the Universet = 0 t0= 15 BystRk = -1, 0 < 1k = 0, 0 = 1k = 1, 0 > 1

Matter in The Universe?10 % Ordinary Matter ( proton, neutron, )< 1 % (Visible) DarkMatter 0 = 1

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

Accelerating Universe Rt

Accelerating Universet=0t0=14b.yk = -1, 0 < 1k = 0, 0 = 1k = 1, 0 > 1

0.50.50.270.0110.73LSSGLXmatterSN Type IaBOOMERANG Maxima (CMB)

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 0.04m 8Gm3H2L~

0.50.50.270.0110.73LSSGLmatterSN Type IaBOOMERANG Maxima (CMB)

Hydrogen Atom: electron: proton: photon t ~ 380,000 ys : T ~ 3000 K Universe then was 10001ininin size

First LightExpansion of the Universe ( 103)Microwaves

WMAP

Best Cosmological parameters : Wilkinson Microwave Anisotropy Probe(WMAP) Observations :Preliminary Resulta 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 -uncertaintyTotal density tot 1.02 0.02 0.02Age of universe (Gyr) t 0 13.7 0.2 0.2 Hubble constant h 0.71 0.04 0.03Equation of state of quintessence < -0.78 95%CL - Dark energy density 0.73 0.04 0.04 Matter density m 0.27 0.04 0.04Baryon density bh2 0.0224 0.0009 0.0009Baryon density b 0.044 0.004 0.004Baryon density(m-3) nb 0.25 0.1 0.01Matter density mh2 0.135 0.008 0.009Light neutrino density h2

Curvature of the UniverseCMB = 1, k = 0 ( flat )0 > 1, k = + 1 ( Closed )0 < 1, k = 1 ( Open )0(Observer)1Horizon size = 1o

The Power Spectrum30 degree1 degree0.1 degree

4/30/01 New York TimesRelative amplitude6420710.50.30.250.2................Main toneharmonicsAngular scale : degree(Latest BOOMERANG DATA)

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

0.50.50.270.0110.73LSSGLmatterSN Type IaBOOMERANG Maxima (CMB)

Standard Candle (SN)dL = H01[ Z + 21(1 - q) Z2 + . ]Hubbles LawCorrectionsDeviation from Hubbles Law can tellvalues of q (deceleration parameter).q RH2> 0 : deceleration< 0 : accelerationDirect measurement

Z = 0.2Z = 0.5Z = 1.0Z = 1.7mmmm 0SN Type Ia (Standard candle)

Chandra X-Ray Satellite

1 b years ago3.5 b years ago6.7 b years agoClusters seen by X-rays

Recent Independent Confirmation from CHANDRA X-ray ObsevatoryAbout 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 ~ 8blyClusters : Hundreds of Galaxies + Dark Matter + Hot Gasesd = f (z, q) q (deceleration Parameter)Consistent with SN Ia datameasured

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

Standard Matter (Including Energy)

Satisfy: 3 p + > 0 Define :W (Equation of state func)3 p + > 0 -31w>Universe with Standard Matter and Energy with deceleration

Usual expansion:

( Including dark matter)q - (3 p + )

X ~ R-3(1+W) Equation of State Func. WX =

Non-relativistic matter : WM = ~ 0 M ~ R-3

pMMCosmological constant:W = - 1 ~ R0= constantBehavior of as a function of W

W of Dark Energy

= +

(matter dominated)

Experiment : = 0.73

acceleration W < -0.46Data shows : W < -0.78 (95% C.L.) Significant acceleration!

Some changes in time Clusters slightly on very large scaleStrings are ruled out!Possible Candidates for X

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?

Einsteins Equation of Gravity(1915)R - Rg - g = 8 GT21Space-timeCosmological Constant 0 Negative PressureVacuum energymatter(1917 )

Basic Equation (Einstein) T + V = E12R2 .- m R343GR- R2= - k2161917, to make UniverseStatic. R.2= G m R2 + R2 - k3813~ 1Rk = 0 : flat Universe > 0 : Repulsive force ! ( force = R < 0 : Attractive forceBecause of E = mc2 , term acts asmass 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. 13

1917 : Introduced by Einstein to make a static Universe Biggest Blunder in my Life !1917 : de Sitter1922 : Friedman Cosmology (Standard)1929 : Hubble : Hubbles 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 New Cosmology ( 0)

Observed Cosmological Constantc= = 1.9 10-29 h2 g/cm3 3H028G~ 9.6 10-30 g/cm3 for h = 0.71 = 0.73 = 5.7 10-30 g/cm3c = 8G = 1.05 10-56 /cm2~ 10-35 /sec2 ~ 10-82 m2~ 10-84 (GeV)2~ 10-122 Mp2Smallest number knownin Science !No SDSS data includedHard to explain!

nowtm was not importantAlready, > m (becoming de Sitter Universe)Eventually ~ = const : de Sitter Universe

R2 - R2 = 0 H : Hubble parameter +(+p) 3 ( ) = 0 q - : deceleration parameter t = 0 dx , x = : R ~ t 2/3 Present : q0 = , 0 = 1 t0 = dx = H0 = h : h = 0.65 ( 0.05) t0 = 10.25 By for h = 0.65Age of the oldest globular clusters , white dwarf 13 ~ 15 By8G3RRRRRRR23H28Gc11H0H0100KmMpc secStandard (k=0, =0) Cosmologyx1 .......1H0xxRRoc = : = 2qR.3220

Cosmology with k = 0 , 0R2 - R2 - R2 = 0 38 G3 = , = m + ,8 G = m + = 1 m = = sech 2 ( t )3H28 G m 23 = = tanh 2 ( t )3H28 G 23R(t) =,oRo3sinh 23( t ) q = (1 - ) = ( m - 2 ) 21 21 H23H2=q = 0 when m = : Inflexion Point q = (1 - 3 ) = 0 : = H2 or Z = - 1 21. 3m32 m, 02, 031 c =8 G3H2Deceleration Acceleration21

ttq21021-1DecelerationDeceleration Parameter 0.48t 0Z ~ 0.55 q = [ m - 2 ] 21 Acceleration(1997 ~ 2000)Z=1.7(2001). .. = H2-

Miracle m ~ sech 2 ( t )23 ~ tanh 2 ( t )23 R(t) ~sinh 23( t )32 ~ 10 -17/sec 3 t o ~ 10 17 sec3t ~ O (1) : Miracle !Anthropic Principle ?

= m + = 1 m10 Byt o = 14 Byt (z ~ 0.23)3.4 By(z =1.7) = 1

The Fifth element (Greek philosophy)Air, Earth, Fire, Water and Quintessence

Perfect SubstanceQuintessence 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

V( ) : Extremely long wavelength and period : mimics radiation > : mimics matter (due to Hubble damping) Some mechanism locks to be nearly a constant. (Kinetic energy driven quintessence k-essence)

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?

Calabi-Yau Extra-dimensions459Extra- Dimensions

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 areGravitons:realGravitational waves from SN, collision of galaxies, String theorye, , q, .Leaks outTied to a branegraviton::MM'gSuper String : 11 dim.

Changes in Gravity

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 ( ! )

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) SDSS (Galaxy, Cluster counts), May not be enough to see w(t)

zWeller and Albrecht 2001

Accelerating Universe Rt

de Sitter universet=0t0=15b.yk = -1, 0 < 1k = 0, 0 = 1k = 1, 0 > 1W ( t ) will eventually determine the fate!

Comments on Vacuum Energy Maybe the most fundamentally mysteriousthing in basic Science. Every attempt to calculate it hasgotten an absurd answer. Basically, people dont have a clueas to how to solve the problem. Vacuum energy would be NO.1 on mylist of things to figure out. Right now, not only for cosmology but for elementary particle theory, this is the bone in our throat.

Dark Energy Vacuum Energy Vacuum Energy : Creation ?, Why so small? Most difficult problem in 21st Summary?Acceleration: No galaxies seen in the sky!Why do we live now?Life on Earth begins whenmatter density = dark energy densityCentury QuintessenceExtra dimensionChanges in Gravity

Galileos first Telescope1.33 m, X 14

1.2 meter Mt. Palomar TelescopeE. Hubble discovers the expanding Universe

Hubble Space Telescope

Keck 10 meter Telescopes

Chandre Chandra X-Ray Satellite

M = 0.3, = 0.7= 0m = 0.3Hubble Diagram = 1= 0m= 0.3= 0.7

Riess, 1998 Perlmutter, 1999(can tell q values)

R - Rg12- g = 8GTGravitational ConstantStatic Universe0 =Biggest blunder in my life!(1915)(1917)Cosmological Constant() : Vacuum(Dark) Energy (curvature, matter) + (Vacuum Energy)AccelerationR = RG + 34m3RDecreaseIncreaseExpansion RateRR= R2 km31( )2+38G+curvatureConstant Decrease

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 discoveredindependently by Perlmutter and Riess (1997~8) Acceleration is fairly recent !SN Type Ia 1997ff (Riess) with z=1.7 shows no acceleration !SN Type IaType ITypeII

How to calculate the age Rtime(t)14 ByNow (t )Present Rate(H )Einstein theoryH , density20 ByAge (t ) ~ H11 + density1

o= 1> 1o< 1o

Inflation Flat Universeo = 13 x 3 x 3

Inflation and Horizon ProblemSHBB Model10 28 cm 1 cm10 -24 cm10 23 cm......ABAB10 2510 3ABt =10 -35 secinft = 10 5 ydet = now0Causally connected(Same temperature)

How to Cure the Problems in SHBB CosmologyInflation !10 -24 cm10 6cm(10 -35 10 -34 sec)10 25Horizon problem solved ! > 10 30t = 10 5 ysPredictions..AB 0 0 = 1 + 10 -N : N very largeFlat Universe 10 25 cm

0 = 1 , m = 0.27 X = 0.73 SN Type Ia can tell us about m / X CMB 0 and B XAlso some cross - checking of CMB, LSS, SN X = 0.73 0.04 Nature of X(Nature unknown)

R - Rg12- g = 8GTGravitational ConstantStatic Universe0 =Biggest blunder in my life!(1915)(1917)Cosmological Constant() : Vacuum(Dark) Energy (curvature, matter) + (Vacuum Energy)AccelerationR = RG + 34m3RDecreaseIncreaseExpansion RateRR= R2 km31( )2+38G+curvatureConstant Decrease

Phase TransitionT > TcT = TcT < Tc

Creation of a Universe(Phase transition of vacuum)Quantum FluctuationUncertaintyPrincipleEnergy createdby the changeof natureof vacuum New Vacuum(New ground state)Ground stateor vacuum

A Brief History of the Universe t = 0 : Big Bang (No space time before) From singular Point ? ( > 0, P > 0 ) How? (why) : Quantum Fluctuation of Vacuum (nothing something)*Born as 11- dimensional Universe ? (string theory)

t ~ 10-43 sec : T ~ 1033 oK (~ 1019 GeV) ( Planck time ) Unified force Gravity + others Homogeneous. 11 dim. 4 (=3+1) dim.

t ~ 10-35 sec : T ~ 1030 oK (~1016 GeV)* strong force + others split Inflation : 10-35 sec - 10-32 sec Universe expands by > 1030 times Present Univ. was 1cm. * () Created (homogeneous until then) (observed now in CMBR) nB nB created We exist.

t ~ 10-10 sec : T ~ 1018 K (=250GeV) Weak and E/M interactions separated (W,Z became massive)

t ~ 10-4 sec : T ~ 1012 K (~MeV) p, n, , appear : Before this only leptons, quarks

t ~ 1 sec : T ~ 1010 K (~MeV) Neutrinos decoupled ( n ~ now)

t ~ 3 min : T ~ 109 K (0.1 MeV) Nucleosynthesis : d, He, Li, formed

t ~ 3,000 years : R = M

t ~ 380,000 years : T = 0.26eV ( ~3000 K) H atoms form. Photons decoupled : * First light !!! Carrying

340cm3

now n ~ 400/cm3, microwaves ~ 10-3 : dH = 1023 cm Our Univ. was 1025 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 k

R(t)R(t0)

>~

Present Universe1) Universe is expanding (Astronomy)V = H L : H = 71Mpcseckm1920s : Hubble2) Visible Size * ~ 1028 cm (~14 billion l.y.)* Age ~ 14 billion years old Uncertain due to H3) Visible Universe contains~100 billion (=1011) galaxiesEach galaxy contains ~100 billion stars* ~ 10-30 ~ 1 proton/m3Q0 , L 0 (Isotropic)3ooog/cm

5) 4He, d, Abundance (Nuclear Physics)M(p,n)M(4He)~ 0.24NucleosynthesisUniverse was once 109 K hot.4) 2.70 K Microwave BackgroundRadiation (Atomic Physics)N ~ 1090 : n 400 / cm3Uniform, isotropic to 10-5Universe was once 3000 K hot. TTT2.735 K*ooO

7) Relic Neutrinos (particle physics)N ~ 330 / cm3 : Hard to detect8) Evidence Big Bang !!6) Baryon number (Particle phyics)BaryogenesisNB ~ 1080 :=No B0=n n B~ 10~ 10Universe was once 1028 K hot.-10-19n n BNo confirmation, yet o

Inflation Flat Universeo = 13 x 3 x 3

Timeline of the Universe