Neutrinos in Cosmology ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν Sergio Pastor (IFIC Valencia) ISAPP 2017 Arenzano, 22-23 June Where do neutrinos come from? ü Nuclear reactors Sun ü Supernovae Particle accelerators ü SN 1987A ü Accelerators in ü Earth Atmosphere (Cosmic rays) astrophysical sources ?ü Early Universe ü Earth interior (today 336 ν/cm3) (Natural Radioactivity) Indirect evidence History of the Universe Role of neutrinos? VERY LOW Energy Neutrinos Low Energy Neutrinos IntroducGon: neutrinos and the history of the Universe Neutrinos coupled by weak interacons T~MeV t~sec Decoupled neutrinos Neutrinos coupled (Cosmic Neutrino by weak interacons Background or CNB) T~MeV t~sec ν m ~ T Neutrino cosmology is interesng because Relic neutrinos are very abundant: • The CNB contributes to radiaon at early mes and to maer at late mes (info on the number of neutrinos and their masses) • Cosmological observables can be used to test standard or non-standard neutrino properes Outline IntroducGon: neutrinos and the history of the Universe ν ν ν ν ν ν ν ν ν Basics of Cosmology ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν Producon and decoupling of relic neutrinos Outline The radiaon content of the Universe (Neff) ν ν ν ν ν ν ν Neutrinos and Primordial ν ν ν ν ν ν ν ν ν ν Nucleosynthesis ν ν ν ν ν ν ν Neutrino oscillaons in the Early Universe Outline Massive neutrinos as Dark Maer Effects of neutrino masses ν ν ν ν ν ν ν on cosmological observables ν ν ν ν ν ν ν ν ν ν ν ν Present bounds on neutrino ν ν ν ν ν properGes from cosmology Future sensivies on neutrino physics from cosmology Basics of Cosmology Eqs in the SM of Cosmology The FLRW Model describes the evoluon of the isotropic and homogeneous expanding Universe ⎛ dr 2 ⎞ ds 2 g dx µdx ν dt 2 a(t)2 ⎜ r 2dθ 2 r 2 sin2 θdφ2 ⎟ = µν = − ⎜ 2 + + ⎟ ⎝1− kr ⎠ a(t) is the scale factor and k=-1,0,+1 the curvature 1 Einstein eqs Gµν = Rµν − gµν R = 8πGTµν +- Λgµν 2 Energy-momentum tensor of a perfect T = ( p + ρ)u u − pg fluid µν µ ν µν Eqs in the SM of Cosmology 00 component a˙ 2 8⇡G k H(t)2 = = ⇢ (Friedmann eq) a 3 − a2 ✓ ◆ ρ=ρM+ρR+ρΛ H(t) is the Hubble parameter k = ⌦ 1 Ω= ρ/ρ H(t)2a2 − crit d⇢ ⇢˙ = = 3H(⇢ + p) 2 dt − ρcrit=3H /8πG is the crical density Eq of state p=αρ ρ = const a -3(1+α) Radiaon α=1/3 Maer α=0 Cosmological constant α=-1 4 3 ρR~1/a ρM~1/a ρΛ~const Evoluon of the Universe a¨ 4⇡G ⇤ = (⇢ +3P )+ a − 3 3 accaccéléeleélérationration dslowécélédécélé decelerationrationration lente lente eceleration dfastécélédécélé d rationration rqpide rqpide accaccéléeleélérationration ? .. a 4πG inflationinflation RD (radiationradiation= − (ρ +domination)3p) MD mati(matterère domination) édarknergie energy noire domination a 3 a(t)~eHt a(t)~t1/2 a(t)~t2/3 Evoluon of the background densies: 1 MeV → now Three neutrino species with different masses Background densies: 1 MeV → now ν b cdm γ ν photons DE neutrinos Λ mν=1 eV crit ρ / cdm i ρ mν=50 meV = baryons i Ω mν=9 meV mν≈ 0 eV aeq: ρr=ρm Producon and decoupling of relic neutrinos Neutrinos coupled by weak interacons T~MeV t~sec Distribution function of particle momenta in equilibrium Equilibrium thermodynamics Thermodynamical variables RELATIVISTIC VARIABLE NON REL. BOSE FERMI Particles in equilibrium when T are high and interactions effective T~1/a(t) Neutrinos in Equilibrium ⌫↵⌫β ⌫↵⌫β 1MeV. T . mµ $ ⌫ ⌫¯ ⌫ ⌫¯ ↵ β $ ↵ β T = T = T ⌫ e± γ ⌫ e± ⌫ e± ↵ $ ↵ + ⌫ ⌫¯ e e− ↵ ↵ $ Neutrino decoupling As the Universe expands, parcle densies are diluted and temperatures fall. Weak interacons become ineffecve to keep neutrinos in good thermal contact with the e.m. plasma Rough, but quite accurate esmate of the decoupling temperature Rate of weak processes ~ Hubble expansion rate 2 8⇡⇢rad 2 5 8⇡⇢rad ΓW σW v n, H = G T Tdec(⌫) 1MeV ⇡ | | 3M 2 ! F ⇡ 3M 2 ! ⇡ P s P Since ν have both CC and NC interacons with e± e T (⌫ ) 2MeV T (⌫ ) 3MeV dec e ' dec µ,⌧ ' Neutrino decoupling Weak Processes Collisions less Effecve: and less ν in eq important: (thermal ν decouple spectrum) (spectrum keeps th. form) 1 f = ν exp(p/T )+1 Expansion of the Universe Neutrinos coupled by weak interacons 1 f (p, T )= ⌫ exp(p/T )+1 T~MeV t~sec Free-streaming neutrinos Neutrinos coupled (decoupled): Cosmic by weak interacons Neutrino Background 1 f (p, T )= ⌫ exp(p/T )+1 Neutrinos keep the energy spectrum of a relavisc fermion with eq form T~MeV t~sec Neutrino and photon (CMB) temperatures At T~me, electron- positron pairs annihilate + - e e → γγ heating photons but not the decoupled neutrinos 1/3 Tγ 11 1 = f (p, T )= T 4 ⌫ ⌫ ✓ ◆ exp(p/T⌫ )+1 Neutrino decoupling and e± annihilaons T 11 1/3 Weak γ = Processes T 4 Collisions less ⇥ ⇥ Effecve: and less 1 ν in eq important: fν = (thermal ν decouple exp(p/Tν )+1 spectrum) (spectrum keeps th. form) 1 f = ν exp(p/T )+1 e+e- → γγ Expansion of the Universe Neutrino and Photon (CMB) temperatures Photon temp falls At T~me, slower than 1/a(t) electron- positron pairs annihilate + - e e → γγ heating photons but not the decoupled neutrinos 1/3 Tγ 11 1 = f (p, T )= T 4 ⌫ ⌫ ✓ ◆ exp(p/T⌫ )+1 The Cosmic Neutrino Background Neutrinos decoupled at T~MeV, keeping a 1 f⌫ (p, T )= spectrum as that of a relavisc species exp(p/T⌫ )+1 • Number density dd33pp 3 36ζ (3) 6⇣(3) n n== f (p,Tf (p,) T= )=n = n =T 3 T 3 ⌫ ν ∫ ((22π⇡)3)3ν ⌫ ν ⌫11 γ 1111γπ 2 CMB11⇡2 CMB Z • Energy density 2 4/3 7⇡ 4 4 TCMB 3 120 11 d p ⇢ = p2 + m2 f (p, T ) ✓ ◆Massless ⌫i ⌫i (2⇡)3 ⌫ ⌫ ! Z q m n ⌫i ⌫ Massive mν>>T The Cosmic Neutrino Background Neutrinos decoupled at T~MeV, keeping a 1 f⌫ (p, T )= spectrum as that of a relavisc species exp(p/T⌫ )+1 • Number density 3 d p 3 6ζ (3) 3 At presentn = 112 ( ν f +¯(p,T ν ) )cm= -3 pern =flavour T ν ∫ ( 2π)3 ν ν 11 γ 11π 2 CMB • Energy density Massless Contribution to the energy density of the Universe Massive mν>>T Evoluon of the background densies: 1 MeV → now photons Ωi = ρi/ρcrit neutrinos Λ mν=1 eV m ⌦ h2 = ⌫i cdm ⌫ 93.2eV P m =0.05 eV baryons ν mν=0.009 eV mν≈ 0 eV aeq: ρr=ρm VERY LOW Energy Neutrinos Non-relativistic? Low Energy 2 m2 Δm21 Δ 31 Neutrinos € € The radiaon content of the Universe (Neff) Relavisc parGcles in the Universe At T>>me, the radiaon content of the Universe is π 2 7 π 2 ' 7 * ρ = ρ + ρ = T 4 + 3× × T 4 = 1+ × 3 ρ r γ ν 15 8 15 () 8 +, γ At T<me, the radiaon content of the Universe is 2 2 4/3 € π 4 7 π 4 ⎡ 7 ⎛ 4 ⎞ ⎤ ρr = ργ + ρν = Tγ + 3× × Tν = ⎢1+ ⎜ ⎟ 3⎥ργ 15 8 15 ⎣⎢ 8 ⎝11⎠ ⎦⎥ 4 Tν 4 Tγ # of flavour neutrinos: N = 2.984 ± 0.008 (LEP data) ν € Relavisc parGcles in the Universe At T<me, the radiaon content of the Universe is EffecGve number of relavisc neutrino species Tradional parametrizaon of ρ stored in relavisc parcles ρ + ρ ⇥ x Bounds on N from Neff is a way to measure the rao eff ργ Primordial Nucleosynthesis and other cosmological Ø standard neutrinos only: N 3 (3.045) eff observables (CMB+LSS) Ø Neff > 3 (delays equality me) from addional relavisc parcles (scalars, pseudoscalars, decay products of heavy parcles,…) or non-standard neutrino physics (primordial neutrino asymmetries, totally or parally thermalized light sterile neutrinos, non-standard interacons with electrons,…) Neutrinos and Primordial Nucleosynthesis BBN: last epoch sensive Primordial abundances of to neutrino flavour light elements: Big Bang Bound on Neff Nucleosynthesis (BBN) (typically Neff<4) Decoupled neutrinos Neutrinos coupled (Cosmic Neutrino by weak interactions Background or CNB) T~MeV t~sec BBN: Creaon of light elements Produced elements: D, 3He, 4He, 7Li and small abundances of others Theorecal inputs: BBN: Creaon of light elements Range of temperatures: from 0.8 to 0.01 MeV Phase I: 0.8-0.1 MeV n-p reacons n/p freezing and neutron decay BBN: Creaon of light elements Phase II: 0.1-0.01 MeV Formaon of light nuclei starng from D Photodesintegraon prevents earlier formaon for temperatures closer to nuclear binding energies 0.07 0.03 MeV MeV BBN: Creaon of light elements Phase II: 0.1-0.01 MeV Formaon of light nuclei starng from D Photodesintegraon prevents earlier formaon for temperatures closer to nuclear binding energies 0.03 MeV BBN: Creaon of light elements Phase II: 0.1-0.01 MeV Formaon of light nuclei starng from D Photodesintegraon prevents earlier formaon for temperatures closer to nuclear binding energies BBN: Measurement of Primordial abundances Difficult task: search in astrophysical systems with chemical evoluon as small as possible Deuterium: destroyed in stars. Any observed abundance of D is a lower limit to the primordial abundance. Data from high-z, low metallicity QSO absorpon line systems Helium-3: produced and destroyed in stars (complicated evolu5on) Data from solar system and galaxies but not used in BBN analysis Helium-4: primordial abundance increased by H burning in stars.