Neutrinos in Cosmology (II)iss2017/ISS2017_files/pastor... · 2018. 9. 21. · Neutrinos and Primordial Nucleosynthesis The radiaon content ... neutrinos in good thermal contact with

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