Particle PhysicsParticle Physicsand Cosmologyand Cosmology

Dark MatterDark Matter

What is our universe made of ?What is our universe made of ?

quintessence !fire , air,

water, soil !

Dark Energy Dark Energy dominates the Universedominates the Universe

Energy Energy -- density in the Universedensity in the Universe==

Matter + Dark EnergyMatter + Dark Energy

25 % + 75 %25 % + 75 %

Composition of the universeComposition of the universe

ΩΩb b = 0.045= 0.045

ΩΩdmdm= 0.225= 0.225

ΩΩh h = 0.73= 0.73

critical densitycritical densityρρcc =3 H=3 H²² MM²²critical energy density of the universe critical energy density of the universe ( M : reduced Planck( M : reduced Planck--mass , H : Hubble parameter )mass , H : Hubble parameter )

ΩΩbb==ρρbb//ρρcc

fraction in baryons fraction in baryons energy density in baryons over critical energy density in baryons over critical energy densityenergy density

Baryons/AtomsBaryons/Atoms

DustDustΩΩbb=0.045=0.045Only 5 Only 5 percent of percent of our Universe our Universe consist of consist of known known matter !matter !

SDSS

~60,000 of >300,000Galaxies

Abell 2255 Cluster~300 Mpc

Ωb=0.045

from nucleosynthesis,cosmic background radiation

Abell 2255 Cluster~300 Mpc

Matter : Everything that clumpsMatter : Everything that clumps

Dark MatterDark MatterΩΩmm = 0.25 total = 0.25 total ““mattermatter””Most matter is dark !Most matter is dark !So far tested only through gravitySo far tested only through gravityEvery local mass concentration Every local mass concentration gravitational potentialgravitational potentialOrbits and velocities of stars and galaxies Orbits and velocities of stars and galaxies measurement of gravitational potential measurement of gravitational potential and therefore of local matter distributionand therefore of local matter distribution

gravitational lens , HST

ΩΩmm= 0.25= 0.25

Gravitationslinse,HST

Gravitationslinse,HST

Abell 2255 Cluster~300 Mpc

Matter : Everything that clumpsMatter : Everything that clumps

ΩΩmm= 0.25= 0.25

spatially flat universespatially flat universe

ΩΩtottot = 1= 1theory (inflationary universe )theory (inflationary universe )

ΩΩtottot =1.0000=1.0000……………….x.xobservation ( WMAP )observation ( WMAP )

ΩΩtottot =1.02 (0.02)=1.02 (0.02)

ΩΩtottot=1=1

Dark EnergyDark Energy

ΩΩmm + X = 1+ X = 1

ΩΩmm : 25%: 25%

ΩΩhh : 75% : 75% Dark EnergyDark Energy

h : homogenous , often ΩΛ instead of Ωh

dark matter candidatesdark matter candidates

WIMPSWIMPSweakly interacting massive particlesweakly interacting massive particles

AxionsAxions

many others many others ……

WIMPSWIMPS

stable particlesstable particlestypical mass : 100 typical mass : 100 GeVGeVtypical cross section : weak interactionstypical cross section : weak interactionscharge : neutralcharge : neutralno electromagnetic interactions , no strong no electromagnetic interactions , no strong interactionsinteractionsseen by gravitational potentialseen by gravitational potential

bullet clusterbullet cluster

How many How many dark matter particles dark matter particles

are around ?are around ?

cosmic abundance of relic particlescosmic abundance of relic particles

early cosmology : present in high temperature early cosmology : present in high temperature equilibriumequilibriumannihilation as temperature drops below massannihilation as temperature drops below massannihilation not completed since cosmic dilution annihilation not completed since cosmic dilution prevents interactionsprevents interactionsdecoupling , similar to neutrinosdecoupling , similar to neutrinosrelic particles remain and contribute to cosmic relic particles remain and contribute to cosmic energy densityenergy density

cosmic abundance of relic particlescosmic abundance of relic particles

rough estimate for present number density n :rough estimate for present number density n :n an a3 3 constant after decouplingconstant after decouplingn/sn/s approximately constant after decouplingapproximately constant after decouplingcompute nacompute na3 3 at time of decouplingat time of decouplingroughly given by Boltzmann factor for roughly given by Boltzmann factor for temperature at time of decoupling temperature at time of decoupling and and zzdecdec

cosmic abundance of relic particlescosmic abundance of relic particles

number density for WIMPS much less than for number density for WIMPS much less than for neutrinos neutrinos (Boltzmann factor at time of decoupling )(Boltzmann factor at time of decoupling )ρρ = m n= m nlarge mass : large mass : ΩΩm m > > ΩΩνν possiblepossible

computation of time evolution of computation of time evolution of particle numberparticle number

central aspects :central aspects :decoupling of one species from thermal bathdecoupling of one species from thermal bathother particles in equilibriumother particles in equilibriumBoltzmann equationBoltzmann equationoccupation numbersoccupation numbers

book : Kolb and Turnerbook : Kolb and Turner

occupation numbersoccupation numbers

ininequilibriumequilibrium ρρ

Boltzmann equationBoltzmann equation

squared scattering amplitudesquared scattering amplitude

phase space integralsphase space integrals

dimensionless inverse temperaturedimensionless inverse temperature

m : particle massm : particle mass

small x : particle is relativistic x<3small x : particle is relativistic x<3large x : particle is nonlarge x : particle is non--relativistic x>3relativistic x>3

dimensionlessdimensionlesstime variable time variable in units ofin units ofparticle mass m particle mass m

particle number per entropyparticle number per entropy

Boltzmann equation for YBoltzmann equation for Y

2 2 –– 2 2 -- scatteringscattering

as dominant annihilationas dominant annihilationand creation processand creation process

particle X in thermal equilibriumparticle X in thermal equilibrium( classical approximation )( classical approximation )

energy conservationenergy conservation

detailed balancedetailed balance( also for large T )( also for large T )

annihilation cross sectionannihilation cross section

Boltzmann equation in terms of Boltzmann equation in terms of cross sectioncross section

..

particle number per entropy particle number per entropy in equilibriumin equilibrium

non non ––relativisticrelativistic

relativisticrelativistic

annihilation rateannihilation rate

freeze outfreeze out when annihilation rate when annihilation rate drops below expansion ratedrops below expansion rate

hot and cold relicshot and cold relics

hot relics hot relics freeze out when they are freeze out when they are relativisticrelativistic

hot dark matter , neutrinoshot dark matter , neutrinoscold relics cold relics freeze out when they are nonfreeze out when they are non--relativisticrelativistic

cold dark mattercold dark matter

hot relicshot relics

xxff : freeze out inverse temperature: freeze out inverse temperature

YYEQ EQ is constant , approach to fixed point !is constant , approach to fixed point !

approach to fixed pointapproach to fixed point

Y > YY > YEQEQ : Y decreases towards Y: Y decreases towards YEQEQ ..Y < YY < YEQEQ : Y increases towards Y: Y increases towards YEQEQ ..

hot relicshot relics

for hot relics :for hot relics :

Y does not change , Y does not change , independently of detailsindependently of detailsrobust predictionsrobust predictions

neutrinosneutrinos

neutrino background radiationneutrino background radiation

ΩΩνν = = ΣΣmmνν / ( 91.5 / ( 91.5 eVeV hh22 ))

ΣΣmmνν present sum of neutrino massespresent sum of neutrino massesmmνν ≈≈ a few a few eVeV or smalleror smaller

comparison : electron mass = 511 003 comparison : electron mass = 511 003 eVeVproton mass = 938 279 proton mass = 938 279 600 600 eVeV

cold relicscold relics xxff > 3> 3

n=0 for sn=0 for s--wave scattering wave scattering ( n=1 p( n=1 p--wave )wave )

s ~ Ts ~ T3 3 ~ x~ x--33

approximate solution approximate solution of Boltzmann equationof Boltzmann equation

early time x < 3early time x < 3

late time solutionlate time solution

YEQ strongly YEQ strongly Boltzmann suppressedBoltzmann suppressed

stopping stopping solutionsolution

freeze out temperaturefreeze out temperature

xxff set by matching of set by matching of early and late time solutionsearly and late time solutions

∆∆ ≈≈ ≈≈ YYEQ EQ ( ( xxff ))ff

cold relic abundancecold relic abundance

cold relic fractioncold relic fraction

cold relic fractioncold relic fraction

not necessarily order one !not necessarily order one !

cold relic abundance ,cold relic abundance ,mass and cross sectionmass and cross section

mm(m,(m,σσAA))

inversely proportional to cross section ,inversely proportional to cross section ,plus logarithmic dependence of plus logarithmic dependence of xxff

baryon relics in baryon relics in baryon symmetric Universebaryon symmetric Universe

observed : Y observed : Y ≈≈ 10 10 --1010

antianti--baryons in baryons in baryon asymmetric Universebaryon asymmetric Universe

relic WIMPSrelic WIMPS

only narrow range in m vs. only narrow range in m vs. σσ gives gives acceptable dark matter abundance !acceptable dark matter abundance !

relic WIMP fractionrelic WIMP fraction

strong dependence on mass and cross sectionstrong dependence on mass and cross section

Wimp boundsWimp bounds

relic stable heavy neutrinosrelic stable heavy neutrinos

stable neutrinos with mass > 4stable neutrinos with mass > 4--5 5 GeVGeV allowedallowed

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