NeutrinosinCosmology(II)
Sergio Pastor (IFIC Valencia)
29thIndian-SummerSchoolofPhysics,Prague
4-8Sep2017
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Outline
IntroducEon:neutrinosandthehistoryoftheUniverse
Prologue:thephysicsof(massive)neutrinos
ProducEonanddecouplingofrelicneutrinos
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1st
Outline
NeutrinooscillaEonsintheEarlyUniverse
NeutrinosandPrimordialNucleosynthesis
TheradiaEoncontentoftheUniverse(Neff)
MassiveneutrinosasDarkMaOer
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ProducEonanddecouplingofrelicneutrinos
T~MeV t~sec
NeutrinoscoupledbyweakinteracEons
Equilibriumthermodynamics
Particles in equilibrium when T are high and interactions effective
T~1/a(t)
Distribution function of particle momenta in equilibrium Thermodynamical variables
VARIABLE RELATIVISTIC
NON REL. BOSE FERMI
NeutrinosinEquilibrium
⌫↵⌫� $ ⌫↵⌫�
⌫↵⌫̄� $ ⌫↵⌫̄�
⌫↵e± $ ⌫↵e
±
⌫↵⌫̄↵ $ e+e�
1 MeV . T . mµ
T⌫ = Te± = T�
Neutrinodecoupling
As the Universe expands, par:cle densi:es are diluted andtemperatures fall.Weak interac:ons become ineffec:ve to keepneutrinosingoodthermalcontactwiththee.m.plasma
Rateofweakprocesses~Hubbleexpansionrate
Rough,butquiteaccuratees:mateofthedecouplingtemperature
SinceνehavebothCCandNCinterac:onswithe±
�W ⇡ �W |v|n, H2 =8⇡⇢rad3M2
P
! G2FT
5 ⇡
s8⇡⇢rad3M2
P
! Tdec(⌫) ⇡ 1 MeV
Tdec(⌫e) ' 2 MeV Tdec(⌫µ,⌧ ) ' 3 MeV
Neutrinodecoupling
ExpansionoftheUniverse
WeakProcessesEffec:ve:ν ineq(thermalspectrum)
Collisionslessandlessimportant:ν decouple(spectrumkeepsth.form)
f� =1
exp(p/T ) + 1
T~MeV t~sec
NeutrinoscoupledbyweakinteracEons
f⌫(p, T ) =1
exp(p/T ) + 1
T~MeV t~sec
NeutrinoscoupledbyweakinteracEons
f⌫(p, T ) =1
exp(p/T ) + 1
Free-streamingneutrinos(decoupled):CosmicNeutrinoBackground
Neutrinoskeeptheenergyspectrumofarela:vis:cfermionwitheqform
At T~me, electron-positron pairs annihilate heating photons but not the decoupled neutrinos
γγ→+ -ee
Neutrinoandphoton(CMB)temperatures
f⌫(p, T ) =1
exp(p/T⌫) + 1
T�
T⌫=
✓11
4
◆1/3
Neutrinodecouplingande±annihilaEons
ExpansionoftheUniverse
WeakProcessesEffec:ve:ν ineq(thermalspectrum)
Collisionslessandlessimportant:ν decouple(spectrumkeepsth.form)
γγ→+ -ee
T�
T⇥=
�11
4
⇥1/3
f� =1
exp(p/T�) + 1
f� =1
exp(p/T ) + 1
At T~me, electron-positron pairs annihilate heating photons but not the decoupled neutrinos
γγ→+ -ee
Photontempfallsslowerthan1/a(t)
NeutrinoandPhoton(CMB)temperatures
f⌫(p, T ) =1
exp(p/T⌫) + 1
T�
T⌫=
✓11
4
◆1/3
TheCosmicNeutrinoBackground
• Numberdensity
• Energydensity
323
3
113(6
113
2 CMBγννν Tπ)ζn)(p,Tf
π)(pdn === ∫
NeutrinosdecoupledatT~MeV,keepingaspectrumasthatofarela:vis:cspecies
f⌫(p, T ) =1
exp(p/T⌫) + 1
n⌫ =
Zd3p
(2⇡)3f⌫(p, T⌫) =
3
11n� =
6⇣(3)
11⇡2T 3CMB
Massless
Massivemν>>T
⇢⌫i =
Z qp2 +m2
⌫i
d3p
(2⇡)3f⌫(p, T⌫) !
m⌫in⌫
7⇡2
120
✓4
11
◆4/3
T 4CMB
TheCosmicNeutrinoBackground
• Numberdensity
• Energydensity
323
3
113(6
113
2 CMBγννν Tπ)ζn)(p,Tf
π)(pdn === ∫At present 112 cm-3 per flavour
Contribution to the energy density of the Universe
NeutrinosdecoupledatT~MeV,keepingaspectrumasthatofarela:vis:cspecies
(� + �̄)
Massless
Massive
mν>>T
f⌫(p, T ) =1
exp(p/T⌫) + 1
photons
neutrinos
cdm
baryons
Λ
mν=0.05eV
mν=0.009eV
mν≈0eV
mν=1eV
Evolu:onofthebackgrounddensi:es:1MeV→now
�i = �i/�crit
aeq:ρr=ρm
⌦⌫h2 =
Pm⌫i
93.2 eV
LowEnergyNeutrinos
VERYLOWEnergyNeutrinos
Non-relativistic?
€
Δm312
€
Δm212
TheradiaEoncontentoftheUniverse(Neff)
AtT>>me,theradia:oncontentoftheUniverseisAtT<me,theradia:oncontentoftheUniverseis
RelaEvisEcparEclesintheUniverse
γνγνγ ρππ
ρρρ⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛+=××+=+= 3114
871
15873
15
3/44
24
2
r TT€
ρr = ργ + ρν =π 2
15T 4 + 3× 7
8×π 2
15T 4 = 1+
78× 3
'
( ) *
+ , ργ
€
Tν4
Tγ4
data) (LEP 008.0984.2 ±=νN# of flavour neutrinos:
RelaEvisEcparEclesintheUniverseAtT<me,theradia:oncontentoftheUniverseis
EffecEvenumberofrelaEvisEcneutrinospeciesTradi:onalparametriza:onofρ storedinrela:vis:cpar:cles
Neffisawaytomeasurethera:oØ standardneutrinosonly:Neff3(3.045)
Ø Neff>3(delaysequality:me)fromaddi:onalrela:vis:cpar:cles(scalars,pseudoscalars,decayproductsofheavypar:cles,…)ornon-standardneutrinophysics(primordialneutrinoasymmetries,totallyorpar:allythermalizedlightsterileneutrinos,non-standardinterac:onswithelectrons,…)
�⇥ + �x
��
�
BoundsonNefffromPrimordialNucleosynthesisandothercosmologicalobservables(CMB+LSS)
RelaEvisEcparEclesintheUniverseAtT<me,theradia:oncontentoftheUniverseis
EffecEvenumberofrelaEvisEcneutrinospeciesTradi:onalparametriza:onofρ storedinrela:vis:cpar:cles
Neffisawaytomeasurethera:oØ standardneutrinosonly:Neff3(3.045)
Ø Neff>3(delaysequality:me)fromaddi:onalrela:vis:cpar:cles(scalars,pseudoscalars,decayproductsofheavypar:cles,…)ornon-standardneutrinophysics(primordialneutrinoasymmetries,totallyorpar:allythermalizedlightsterileneutrinos,non-standardinterac:onswithelectrons,…)
�⇥ + �x
��
�
BoundsonNefffromPrimordialNucleosynthesisandothercosmologicalobservables(CMB+LSS)
Neff>3:smallneutrinoheaEng
Expansionoftheuniverse
WeakProcessesEffec:ve:ν ineq(thermalspectrum)
ν decouplingdependsonν momentum(smallspectraldistorsions)
γγ→+ -ee
f� =1
exp(p/T ) + 1
T�
T 0�
<
✓11
4
◆1/3
f⌫ = f eq⌫ + �f⌫↵
Ne↵ = 3.045
Neffinthestandardcase
PabloFernándezdeSalas&SP,JCAP07(2016)051
T�/T0�
contribu:onofdistor:onstoρν
z0
NeutrinosandPrimordialNucleosynthesis
Primordialabundancesoflightelements:BigBangNucleosynthesis(BBN)
BBN:lastepochsensi:vetoneutrinoflavour
BoundonNeff(typicallyNeff<4)
T~MeVt~sec
Decoupledneutrinos(CosmicNeutrinoBackgroundorCNB)
Neutrinos coupled by weak interactions
Producedelements:D,3He,4He,7Liandsmallabundancesofothers
BBN:CreaEonoflightelements
Theore:calinputs:
Rangeoftemperatures:from0.8to0.01MeV
BBN:CreaEonoflightelements
n/pfreezingandneutrondecay
PhaseI:0.8-0.1MeVn-preac:ons
0.03 MeV
0.07 MeV
PhaseII:0.1-0.01MeVForma:onoflightnucleistar:ngfromD
Photodesintegra:onpreventsearlierforma:onfortemperaturesclosertonuclearbindingenergies
BBN:CreaEonoflightelements
PhaseII:0.1-0.01MeVForma:onoflightnucleistar:ngfromD
Photodesintegra:onpreventsearlierforma:onfortemperaturesclosertonuclearbindingenergies
BBN:CreaEonoflightelements
0.03 MeV
PhaseII:0.1-0.01MeVForma:onoflightnucleistar:ngfromD
Photodesintegra:onpreventsearlierforma:onfortemperaturesclosertonuclearbindingenergies
BBN:CreaEonoflightelements
BBN:MeasurementofPrimordialabundancesDifficulttask:searchinastrophysicalsystemswithchemicalevoluEonassmallaspossible
Deuterium:destroyedinstars.AnyobservedabundanceofDisalowerlimittotheprimordialabundance.Datafromhigh-z,lowmetallicityQSOabsorp:onlinesystemsHelium-3:producedanddestroyedinstars(complicatedevolu:on)DatafromsolarsystemandgalaxiesbutnotusedinBBNanalysisHelium-4:primordialabundanceincreasedbyHburninginstars.Datafromlowmetallicity,extragala:cHIIregionsLithium-7:destroyedinstars,producedincosmicrayreac:ons.Datafromoldest,mostmetal-poorstarsintheGalaxy
Fields,Molaro&Sarkar,PDG2016
BBN:PredicEonsvsObservaEons
⌘10 =nB/n�
10�10' 274⌦Bh
2
BBN:PredicEonsvsObservaEons
Planck2015,arXiv:1502.01589
EffectofneutrinosonBBN1.NefffixestheexpansionrateduringBBN
ρ(Neff)>ρ0 → ↑ 4He
3.4 3.2 3.0
2.Directeffectofelectronneutrinosandan:neutrinosonthen-preac:ons
Burles,Nolles&Turner1999
H =
s8⇡⇢
3M2p
⌫e + n $ p+ e� e+ + n $ p+ ⌫̄e
BBN:allowedrangesforNeff
Planck2015,arXiv:1502.01589Deuterium-onlyboundsMarcuccietal,PRL116(2016)102501
[arXiv:1510.07877]
Endof2ndlecture