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Particle Physics and Cosmology

Particle Physics and Cosmology. cosmological neutrino abundance. relic particles. examples: neutrinos baryons cold dark matter ( WIMPS ). neutrinos. neutrino background radiation Ω ν = Σ m ν / ( 91.5 eV h 2 ) Σ m ν present sum of neutrino masses m ν ≈ a few eV or smaller

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Particle Physics and Cosmology

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  1. Particle Physicsand Cosmology cosmological neutrino abundance

  2. relic particles examples: • neutrinos • baryons • cold dark matter ( WIMPS )

  3. neutrinos neutrino background radiation Ων= Σmν/ ( 91.5 eV h2 ) Σmνpresent sum of neutrino masses mν ≈ a few eV or smaller comparison : electron mass = 511 003 eV proton mass = 938 279 600 eV

  4. experimental determination of neutrino mass KATRIN neutrino-less double beta decay GERDA

  5. experimental bounds on neutrino mass from neutrino oscillations : largest neutrino mass must be larger than 5 10-2 eV direct tests ( endpoint of spectrum in tritium decay ) electron-neutrino mass smaller 2.3 eV

  6. cosmological neutrino abundance • How many neutrinos do we have in the present Universe ? • neutrino number density n ν for m ν > 10 - 3 eV:

  7. estimate of neutrino number in present Universe early cosmology: neutrino numbers from thermal equilibrium “initial conditions” follow evolution of neutrino number until today

  8. decoupling of neutrinos ….from thermal equilibrium when afterwards conserved neutrino number density

  9. neutrinos in thermal equilibrium

  10. decay rate vs. Hubble parameter neutrino decoupling temperature: Tν,d ≈ a few MeV

  11. hot dark matter particles which are relativistic during decoupling : hot relics na3 conserved during decoupling ( and also before and afterwards )

  12. neutrino and entropy densities • neutrino number density nν~ a -3 • entropy density s ~ a -3 • ratio remains constant • compute ratio in early thermal Universe • estimate entropy in present Universe (mainly photons from background radiation ) • infer present neutrino number density

  13. conserved entropy entropy in comoving volume of present size a=1

  14. entropy variation from energy momentum conservation :

  15. entropy conservation use : S dT + N dμ – V dp = 0 for μ = 0 : dp/dT = S / V = ( ρ + p ) / T adiabatic expansion : dS / dt = 0

  16. conserved entropy S = s a 3 conserved entropy density s ~ a -3

  17. neutrino number density and entropy ( = Yν )

  18. present neutrino fraction tν : time before ( during , after ) decoupling of neutrinos Ων= Σmν / ( 91.5 eV h2 ) s( t0 ) known from background radiation

  19. neutrino density in thermal equilibrium

  20. neutrinos neutrino background radiation Ων= Σmν/ ( 91.5 eV h2 ) Σmνpresent sum of neutrino masses mν ≈ a few eV or smaller comparison : electron mass = 511 003 eV proton mass = 938 279 600 eV

  21. evolution of neutrino number density σ ~ total annihilation cross section

  22. neutrino density per entropy attractive fixed point if Y has equilibrium value

  23. conservation of nν/ s • in thermal equilibrium • after decoupling • during decoupling more complicated

  24. ingredients for neutrino mass bound

  25. cosmological neutrino mass bound Σmν= 91.5 eV Ωνh2 or mν> 2 GeV or neutrinos are unstable other , more severe cosmological bounds arise from formation of cosmological structures

  26. cosmological neutrino mass bound cosmological neutrino mass bound is very robust valid also for modified gravitational equations, as long as • a) entropy is conserved for T < 10 MeV • b) present entropy dominated by photons

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