dark matter - thphys.uni-heidelberg.dewetterich/vorlesungen... · dark matter Ω m = 0.25 total...
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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
next week no lecturenext week no lecture
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