Particle Physics and Cosmology
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Transcript of Particle Physics and Cosmology
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Particle PhysicsParticle Physicsand Cosmologyand Cosmology
cosmological cosmological neutrino abundanceneutrino abundance
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relic particlesrelic particles
examples:examples:
neutrinosneutrinos
baryonsbaryons
cold dark matter ( WIMPS )cold dark matter ( WIMPS )
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neutrinosneutrinos
neutrino background radiationneutrino background radiation
ΩΩνν = = ΣΣmmνν / ( 91.5 eV h/ ( 91.5 eV h22 ) )
ΣΣmmνν present sum of neutrino massespresent sum of neutrino massesmmνν ≈ a few eV or smaller ≈ a few eV or smaller
comparison : electron mass = 511 003 comparison : electron mass = 511 003 eVeV
proton mass = 938 279 600 eVproton mass = 938 279 600 eV
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experimental experimental determination of determination of
neutrino massneutrino massKATRIN neutrino-less KATRIN neutrino-less
double beta decay double beta decay
GERDAGERDA
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experimental bounds on experimental bounds on neutrino massneutrino mass
from neutrino oscillations :from neutrino oscillations :
largest neutrino mass must be larger than largest neutrino mass must be larger than 5 105 10-2-2 eV eV
direct tests ( endpoint of spectrum in direct tests ( endpoint of spectrum in tritium decay )tritium decay )
electron-neutrino mass smaller 2.3 eVelectron-neutrino mass smaller 2.3 eV
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cosmological neutrino cosmological neutrino abundanceabundance
How many neutrinos do we have in How many neutrinos do we have in the present Universe ?the present Universe ?
neutrino number density n neutrino number density n νν
for m for m νν > 10 > 10 - 3- 3 eV: eV:
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estimate of neutrino estimate of neutrino number in present Universenumber in present Universe
early cosmology: early cosmology:
neutrino numbers from thermal neutrino numbers from thermal equilibriumequilibrium
““initial conditions”initial conditions”
follow evolution of neutrino number follow evolution of neutrino number until todayuntil today
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decoupling of neutrinosdecoupling of neutrinos
…….from thermal equilibrium when.from thermal equilibrium when
afterwards conserved neutrino afterwards conserved neutrino number densitynumber density
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neutrinos in thermal neutrinos in thermal equilibriumequilibrium
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decay rate vs. Hubble decay rate vs. Hubble parameterparameter
neutrino decoupling temperature:neutrino decoupling temperature:
TTνν,d ,d ≈ a few MeV≈ a few MeV
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hot dark matterhot dark matter
particles which are relativistic during particles which are relativistic during decoupling :decoupling :
hot relicshot relics
nana3 3 conserved during decoupling ( and conserved during decoupling ( and also before and afterwards )also before and afterwards )
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neutrino and entropy neutrino and entropy densitiesdensities
neutrino number density nneutrino number density nνν ~ a ~ a -3-3
entropy density s ~ a entropy density s ~ a -3-3
ratio remains constantratio remains constant compute ratio in early thermal Universecompute ratio in early thermal Universe estimate entropy in present Universeestimate entropy in present Universe
(mainly photons from background (mainly photons from background radiation )radiation )
infer present neutrino number densityinfer present neutrino number density
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conserved entropyconserved entropy
entropy in comoving volume entropy in comoving volume of present size a=1of present size a=1
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entropy variationentropy variation
from energy momentum conservation :from energy momentum conservation :
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entropy conservationentropy conservation
use : use : S dT + N dS dT + N dμμ – V dp = 0 – V dp = 0
for for μμ = 0 : = 0 :
dp/dT = S / V = ( dp/dT = S / V = ( ρρ + p ) / T + p ) / T
adiabatic expansion : dS / adiabatic expansion : dS / dt = 0dt = 0
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conserved entropyconserved entropy
S = s a S = s a 33 conserved conserved
entropy density s ~ entropy density s ~ a a -3-3
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neutrino number density neutrino number density and entropyand entropy
( = Y( = Yνν ) )
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present neutrino fractionpresent neutrino fraction
s( ts( t0 0 ) known from background radiation) known from background radiation
ΩΩνν = = ΣΣmmνν
/ ( 91.5 eV / ( 91.5 eV hh22 ) )
ttνν : time before ( during , after ) : time before ( during , after ) decoupling of neutrinosdecoupling of neutrinos
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neutrino density in thermal neutrino density in thermal equilibriumequilibrium
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neutrinosneutrinos
neutrino background radiationneutrino background radiation
ΩΩνν = = ΣΣmmνν / ( 91.5 eV h/ ( 91.5 eV h22 ) )
ΣΣmmνν present sum of neutrino massespresent sum of neutrino massesmmνν ≈ a few eV or smaller ≈ a few eV or smaller
comparison : electron mass = 511 003 comparison : electron mass = 511 003 eVeV
proton mass = 938 279 600 eVproton mass = 938 279 600 eV
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evolution of neutrino evolution of neutrino number densitynumber density
σσ ~ total annihilation cross section ~ total annihilation cross section
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neutrino density per neutrino density per entropyentropy
attractive fixed point if Y has equilibrium valueattractive fixed point if Y has equilibrium value
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conservation of nconservation of nνν / s/ s
in thermal equilibriumin thermal equilibrium after decouplingafter decoupling during decoupling more complicatedduring decoupling more complicated
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ingredients for neutrino ingredients for neutrino mass boundmass bound
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cosmological neutrino mass cosmological neutrino mass boundbound
ΣΣmmνν = 91.5 eV = 91.5 eV ΩΩνν hh22
or mor mνν > 2 GeV> 2 GeVor neutrinos are unstableor neutrinos are unstable
other , more severe cosmological bounds other , more severe cosmological bounds arise from formation of cosmological arise from formation of cosmological structuresstructures
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cosmological neutrino mass cosmological neutrino mass boundbound
cosmological neutrino mass bound is cosmological neutrino mass bound is very robustvery robust
valid also for modified gravitational valid also for modified gravitational equationsequations, as long as , as long as
a) entropy is conserved for T < 10 MeVa) entropy is conserved for T < 10 MeV b) present entropy dominated by b) present entropy dominated by
photonsphotons