Particle%20Physics%20and%20Cosmology

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Particle Physicsand Cosmology

• Dark Matter

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What is our universe made of ?
fire , air, water, soil !
quintessence !
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Dark Energy dominates the Universe

• Energy - density in the Universe
• Matter Dark Energy
• 25 75

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Composition of the universe

• Ob 0.045
• Odm 0.225
• Oh 0.73

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critical density

• ?c 3 H² M²
• critical energy density of the universe
• ( M reduced Planck-mass , H Hubble
  parameter )
• Ob?b/?c
• fraction in baryons
• energy density in baryons over critical energy
  density

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Baryons/Atoms

• Dust
• Ob0.045
• Only 5 percent of our Universe consist of known
  
• matter !

SDSS
60,000 of gt300,000 Galaxies
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Abell 2255 Cluster 300 Mpc
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Ob0.045 from nucleosynthesis, cosmic
background radiation
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Matter Everything that clumps
Abell 2255 Cluster 300 Mpc
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Dark Matter

• Om 0.25 total matter
• Most matter is dark !
• So far tested only through gravity
• Every local mass concentration
  gravitational potential
• Orbits and velocities of stars and galaxies
  measurement of gravitational potential
• and therefore of local matter distribution

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Om 0.25
gravitational lens , HST
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Gravitationslinse,HST
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Gravitationslinse,HST
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Matter Everything that clumps
Om 0.25
Abell 2255 Cluster 300 Mpc
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spatially flat universe
Otot 1

• theory (inflationary universe )
• Otot 1.0000.x
• observation ( WMAP )
• Otot 1.02 (0.02)

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Otot1
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Dark Energy

• Om X 1
• Om 25
• Oh 75 Dark Energy

h homogenous , often O? instead of Oh
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dark matter candidates

• WIMPS
• weakly interacting massive particles
• Axions
• many others

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WIMPS

• stable particles
• typical mass 100 GeV
• typical cross section weak interactions
• charge neutral
• no electromagnetic interactions , no strong
  interactions
• seen by gravitational potential

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bullet cluster
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How many dark matter particles are around ?
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cosmic abundance of relic particles

• early cosmology present in high temperature
  equilibrium
• annihilation as temperature drops below mass
• annihilation not completed since cosmic dilution
  prevents interactions
• decoupling , similar to neutrinos
• relic particles remain and contribute to cosmic
  energy density

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cosmic abundance of relic particles

• rough estimate for present number density n
• n a3 constant after decoupling
• n/s approximately constant after decoupling
• compute na3 at time of decoupling
• roughly given by Boltzmann factor for temperature
  at time of decoupling
• and zdec

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cosmic abundance of relic particles

• number density for WIMPS much less than for
  neutrinos
• (Boltzmann factor at time of decoupling )
• ? m n
• large mass Om gt O? possible

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computation of time evolution of particle number

• central aspects
• decoupling of one species from thermal bath
• other particles in equilibrium
• Boltzmann equation
• occupation numbers

book Kolb and Turner
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occupation numbers
in equilibrium
?
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Boltzmann equation
squared scattering amplitude
phase space integrals
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dimensionless inverse temperature
m particle mass
small x particle is relativistic
xlt3 large x particle is non-relativistic
xgt3
dimensionless time variable in units of particle
mass m
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particle number per entropy
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Boltzmann equation for Y
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2 2 - scattering
as dominant annihilation and creation process
particle X in thermal equilibrium ( classical
approximation )
energy conservation
detailed balance ( also for large T )
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annihilation cross section
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Boltzmann equation in terms of cross section
.
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particle number per entropy in equilibrium
non relativistic
relativistic
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annihilation rate
freeze out when annihilation rate drops below
expansion rate
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hot and cold relics

• hot relics freeze out when they are relativistic
• hot dark matter , neutrinos
• cold relics freeze out when they are
  non-relativistic
• cold dark matter

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hot relics
xf freeze out inverse temperature
YEQ is constant , approach to fixed point !
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approach to fixed point
Y gt YEQ Y decreases towards YEQ . Y lt YEQ Y
increases towards YEQ .
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hot relics

• for hot relics
• Y does not change ,
• independently of details
• robust predictions

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neutrinos

• neutrino background radiation
• O? Sm? / ( 91.5 eV h2 )
• Sm? present sum of neutrino masses
• m? a few eV or smaller
• comparison electron mass
  511 003 eV
• proton
  mass 938 279 600 eV

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cold relics
xf gt 3
n0 for s-wave scattering ( n1 p-wave )
s T3 x-3
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approximate solution of Boltzmann equation
early time x lt 3
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late time solution
YEQ strongly Boltzmann suppressed
stopping solution
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freeze out temperature

• xf set by matching of
• early and late time solutions

?
YEQ ( xf )
f
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cold relic abundance
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cold relic fraction
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cold relic fraction
not necessarily order one !
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cold relic abundance ,mass and cross section
(m,sA)
m
inversely proportional to cross section , plus
logarithmic dependence of xf
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baryon relics in baryon symmetric Universe
observed Y 10 -10
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anti-baryons in baryon asymmetric Universe
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relic WIMPS
only narrow range in m vs. s gives acceptable
dark matter abundance !
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relic WIMP fraction
strong dependence on mass and cross section
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Wimp bounds
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relic stable heavy neutrinos
stable neutrinos with mass gt 4-5 GeV allowed
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