Particle Physics and Cosmology Dark Matter

What is our universe made of ? quintessence ! fire, air, water, soil !

Dark Energy dominates the Universe Energy - density in the Universe Energy - density in the Universe = Matter + Dark Energy Matter + Dark Energy 25 % + 75 % 25 % + 75 %

Composition of the universe Ω b = Ω b = Ω dm = Ω dm = Ω h = 0.73 Ω h = 0.73

critical density ρ c =3 H² M² ρ c =3 H² M² critical energy density of the universe critical energy density of the universe ( M : reduced Planck-mass, H : Hubble parameter ) ( M : reduced Planck-mass, H : Hubble parameter ) Ω b =ρ b /ρ c Ω b =ρ b /ρ c fraction in baryons fraction in baryons energy density in baryons over critical energy density energy density in baryons over critical energy density

~60,000 of >300,000 Galaxies Baryons/Atoms Dust Dust Ω b =0.045 Ω b =0.045 Only 5 percent of our Universe consist of known Only 5 percent of our Universe consist of known matter ! matter ! SDSS

Abell 2255 Cluster ~300 Mpc

Ω b =0.045 from nucleosynthesis, cosmic background radiation

Abell 2255 Cluster ~300 Mpc Matter : Everything that clumps

Dark Matter Ω m = 0.25 total “matter” Ω m = 0.25 total “matter” Most matter is dark ! Most matter is dark ! So far tested only through gravity So far tested only through gravity Every local mass concentration gravitational potential Every local mass concentration gravitational potential Orbits and velocities of stars and galaxies measurement of gravitational potential Orbits and velocities of stars and galaxies measurement of gravitational potential and therefore of local matter distribution and therefore of local matter distribution

gravitational lens, HST Ω m = 0.25

Gravitationslinse,HST

Abell 2255 Cluster ~300 Mpc Matter : Everything that clumps Ω m = 0.25

spatially flat universe theory (inflationary universe ) theory (inflationary universe ) Ω tot =1.0000……….x Ω tot =1.0000……….x observation ( WMAP ) observation ( WMAP ) Ω tot =1.02 (0.02) Ω tot =1.02 (0.02) Ω tot = 1

Dark Energy Ω m + X = 1 Ω m + X = 1 Ω m : 25% Ω m : 25% Ω h : 75% Dark Energy Ω h : 75% Dark Energy h : homogenous, often Ω Λ instead of Ω h

dark matter candidates WIMPS WIMPS weakly interacting massive particles weakly interacting massive particles Axions Axions many others … many others …

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

bullet cluster

How many dark matter particles are around ?

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

cosmic abundance of relic particles rough estimate for present number density n : n a 3 constant after decoupling n a 3 constant after decoupling n/s approximately constant after decoupling n/s approximately constant after decoupling compute na 3 at time of decoupling compute na 3 at time of decoupling roughly given by Boltzmann factor for temperature at time of decoupling roughly given by Boltzmann factor for temperature at time of decoupling and z dec and z dec

cosmic abundance of relic particles number density for WIMPS much less than for neutrinos number density for WIMPS much less than for neutrinos (Boltzmann factor at time of decoupling ) (Boltzmann factor at time of decoupling ) ρ = m n ρ = m n large mass : Ω m > Ω ν possible large mass : Ω m > Ω ν possible

computation of time evolution of particle number central aspects : decoupling of one species from thermal bath decoupling of one species from thermal bath other particles in equilibrium other particles in equilibrium Boltzmann equation Boltzmann equation occupation numbers occupation numbers book : Kolb and Turner

occupation numbers ρ inequilibrium

Boltzmann equation squared scattering amplitude phase space integrals

dimensionless inverse temperature dimensionless time variable in units of particle mass m m : particle mass small x : particle is relativistic x<3 large x : particle is non-relativistic x>3

particle number per entropy

Boltzmann equation for Y

2 – 2 - scattering as dominant annihilation and creation process particle X in thermal equilibrium ( classical approximation ) energy conservation detailed balance ( also for large T )

annihilation cross section

Boltzmann equation in terms of cross section.

particle number per entropy in equilibrium non – relativistic relativistic

annihilation rate freeze out when annihilation rate drops below expansion rate

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

hot relics x f : freeze out inverse temperature Y EQ is constant, approach to fixed point !

approach to fixed point Y > Y EQ : Y decreases towards Y EQ. Y < Y EQ : Y increases towards Y EQ.

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

neutrinos neutrino background radiation Ω ν = Σm ν / ( 91.5 eV h 2 ) Ω ν = Σm ν / ( 91.5 eV h 2 ) Σm ν present sum of neutrino masses m ν ≈ a few eV or smaller comparison : electron mass = eV comparison : electron mass = eV proton mass = eV proton mass = eV

cold relics n=0 for s-wave scattering ( n=1 p-wave ) x f > 3 s ~ T 3 ~ x -3

approximate solution of Boltzmann equation early time x < 3

late time solution YEQ strongly Boltzmann suppressed stoppingsolution

freeze out temperature x f set by matching of x f set by matching of early and late time solutions early and late time solutions Δ ≈Δ ≈Δ ≈Δ ≈ ≈ Y EQ ( x f ) f

cold relic abundance

cold relic fraction

not necessarily order one !

cold relic abundance, mass and cross section m (m,σ A ) inversely proportional to cross section, plus logarithmic dependence of x f plus logarithmic dependence of x f

baryon relics in baryon symmetric Universe observed : Y ≈

anti-baryons in baryon asymmetric Universe

relic WIMPS only narrow range in m vs. σ gives acceptable dark matter abundance !

relic WIMP fraction strong dependence on mass and cross section

Wimp bounds

relic stable heavy neutrinos stable neutrinos with mass > 4-5 GeV allowed

next week no lecture