Neutrinos in Cosmology (II) Sergio Pastor (IFIC Valencia) Cinvestav 8-12 June 2015
Outline Prologue: the physics of (massive) neutrinos IntroducAon: neutrinos and the history of the Universe Basics of Cosmology 1st ProducAon and decoupling of relic neutrinos
Outline The radiaaon content of the Universe (N eff ) Neutrinos and Primordial Nucleosynthesis Neutrino oscillaaons in the Early Universe Massive neutrinos as Dark MaMer
ProducAon and decoupling of relic neutrinos
Neutrinos coupled by weak interacaons T~MeV t~sec
Equilibrium thermodynamics Distribution function of particle momenta in equilibrium Thermodynamical variables VARIABLE BOSE RELATIVISTIC FERMI NON REL. Particles in equilibrium when T are high and interactions effective T~1/a(t)
Neutrinos in Equilibrium 1MeV. T. m µ T = T e ± = T $ $ e ± $ e ± $ e + e
Neutrino decoupling As the Universe expands, par:cle densi:es are diluted and temperatures fall. Weak interac:ons become ineffec:ve to keep neutrinos in good thermal contact with the e.m. plasma Rough, but quite accurate es:mate of the decoupling temperature W Rate of weak processes ~ Hubble expansion rate W v n, H 2 = 8 rad 3M 2 P! G 2 F T 5 s 8 rad 3M 2 P! T dec ( ) 1MeV Since e have both CC and NC interac:ons with e ± T dec ( e ) ' 2MeV T dec ( µ, ) ' 3MeV
Neutrino decoupling f = Weak Processes Effec:ve: in eq (thermal spectrum) 1 exp(p/t )+1 Collisions less and less important: decouple (spectrum keeps th. form) Expansion of the Universe
Neutrinos coupled by weak interacaons 1 f (p, T ) = exp(p/t ) + 1 T~MeV t~sec
Free- streaming neutrinos (decoupled): Cosmic Neutrino Background Neutrinos coupled by weak interacaons 1 f (p, T ) = exp(p/t ) + 1 Neutrinos keep the energy spectrum of a rela:vis:c fermion with eq form T~MeV t~sec
Neutrino and photon (CMB) temperatures At T~m e, electronpositron pairs annihilate e + e - γγ heating photons but not the decoupled neutrinos T = T 11 4 1/3 f (p, T )= 1 exp(p/t )+1
Neutrino decoupling and e ± annihilaaons f = Weak Processes Effec:ve: in eq (thermal spectrum) 1 exp(p/t )+1 Collisions less and less important: decouple (spectrum keeps th. form) f = T = 11 1/3 T 4 1 exp(p/t )+1 + - e e γγ Expansion of the Universe
Neutrino and Photon (CMB) temperatures At T~m e, electronpositron pairs annihilate Photon temp falls slower than 1/a(t) e + e - γγ heating photons but not the decoupled neutrinos T = T 11 4 1/3 f (p, T )= 1 exp(p/t )+1
Number density Energy density The Cosmic Neutrino Background Neutrinos decoupled at T~MeV, keeping a spectrum as that of a rela:vis:c species Z n n = = ( 2π) 11 = 3 dd 3 p 3 6ζ (3) 3 f 3 (p,t ) = nγ T 2 CMB (2 ) 3 f (p, T )= 3 11 n = 6 (3) 11π f (p, T )= 11 2 T 3 CMB 1 exp(p/t )+1 i = Z q p 2 + m 2 i d 3 p (2 ) 3 f (p, T )! 7 2 120 m i n 4/3 4 TCMB 4 11 Massless Massive m >>T
Number density The Cosmic Neutrino Background Neutrinos decoupled at T~MeV, keeping a spectrum as that of a rela:vis:c species 3 d p 3 n = ( f 3 + ) (p,t ) = nγ = ( 2π) 11 At present 112 6ζ (3) T 2 11π cm -3 per flavour f (p, T )= 3 CMB 1 exp(p/t )+1 Energy density Contribution to the energy density of the Universe Massless Massive m >>T
Evolu:on of the background densi:es: 1 MeV now photons neutrinos i = i / crit Λ m =1 ev cdm baryons m =0.05 ev m =0.009 ev m 0 ev a eq : ρ r =ρ m
VERY LOW Energy Neutrinos Non-relativistic? 2 Δm 21 2 Δm 31 Low Energy Neutrinos
The radiaaon content of the Universe (N eff )
RelaAvisAc paracles in the Universe At T>>m e, the radia:on content of the Universe is ρ r = ρ γ + ρ = π 2 15 T 4 + 3 7 8 π 2 15 T ' 4 = 1+ 7 ( ) 8 3 * +, ρ γ At T<m e, the radia:on content of the Universe is ρ r 2 2 4/3 π π 4 7 4 7 4 = ργ + ρ = Tγ + 3 T = 1 + 3 ρ 15 8 15 8 11 γ # of flavour neutrinos: N = 2.984 ± T 4 T γ 4 0.008 (LEP data)
RelaAvisAc paracles in the Universe At T<m e, the radia:on content of the Universe is EffecAve number of relaavisac neutrino species Tradi:onal parametriza:on of ρ stored in rela:vis:c par:cles N eff is a way to measure the ra:o + x Ø standard neutrinos only: N eff 3 (3.046) Bounds on N eff from Primordial Nucleosynthesis and other cosmological observables (CMB+LSS) Ø N eff > 3 (delays equality :me) from addi:onal rela:vis:c par:cles (scalars, pseudoscalars, decay products of heavy par:cles, ) or non- standard neutrino physics (primordial neutrino asymmetries, totally or par:ally thermalized light sterile neutrinos, non- standard interac:ons with electrons, )
Neutrinos and Primordial Nucleosynthesis
Primordial abundances of light elements: Big Bang Nucleosynthesis (BBN) BBN: last epoch sensi:ve to neutrino flavour Bound on N eff (typically N eff <4)
Decoupled neutrinos (Cosmic Neutrino Background or CNB) Neutrinos coupled by weak interactions T~MeV t~sec
BBN: CreaAon of light elements Produced elements: D, 3 He, 4 He, 7 Li and small abundances of others Theore:cal inputs:
BBN: CreaAon of light elements Range of temperatures: from 0.8 to 0.01 MeV Phase I: 0.8-0.1 MeV n- p reac:ons n/p freezing and neutron decay
BBN: CreaAon of light elements Phase II: 0.1-0.01 MeV Forma:on of light nuclei star:ng from D Photodesintegra:on prevents earlier forma:on for temperatures closer to nuclear binding energies 0.07 MeV 0.03 MeV
BBN: CreaAon of light elements Phase II: 0.1-0.01 MeV Forma:on of light nuclei star:ng from D Photodesintegra:on prevents earlier forma:on for temperatures closer to nuclear binding energies 0.03 MeV
BBN: Measurement of Primordial abundances Difficult task: search in astrophysical systems with chemical evoluaon 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 absorp:on line systems Helium- 3: produced and destroyed in stars (complicated evolu:on) Data from solar system and galaxies but not used in BBN analysis Helium- 4: primordial abundance increased by H burning in stars. Data from low metallicity, extragala:c HII regions Lithium- 7: destroyed in stars, produced in cosmic ray reac:ons. Data from oldest, most metal- poor stars in the Galaxy
BBN: PredicAons vs ObservaAons 10 = n B/n 10 10 ' 274 Bh 2 Baryon- to- photon ra:o F. Iocco et al, Phys. Rep. 472 (2009) 1
BBN: PredicAons vs ObservaAons Planck 2015, arxiv:1502.01589
Effect of neutrinos on BBN 1. N eff fixes the expansion rate during BBN s H = 8 3M 2 p 3.4 3.2 3.0 ρ(n eff )>ρ 0 4 He Burles, Noller & Turner 1999 2. Direct effect of electron neutrinos and an:neutrinos on the n- p reac:ons e + n $ p + e e + + n $ p + e
BBN: allowed ranges for N eff Conserva:ve approach: upper bound on 4 He Mangano & Serpico, PLB 701 (2011) 296 Planck 2015, arxiv:1502.01589 ΔN eff < 1 (95% CL)
Neutrino oscillaaons in the Early Universe
Neutrino oscillaaons in the Early Universe Neutrino oscilla:ons are effec:ve when medium effects get small enough Coupled neutrinos Compare oscilla:on term with effec:ve poten:als Oscilla:on terms prop. to Δm 2 /2E Second order marer effects prop. to G F (E/M Z 2 )[ρ(e - )+ρ(e + )] First order marer effects prop. to G F [n(e - )- n(e + )] Expansion of the Universe Strumia & Vissani, hep- ph/0606054
Flavour neutrino oscillaaons in the Early Universe Standard case: all neutrino flavours equally populated oscillations are effective below a few MeV, but have no effect (except for mixing the small distortions δf ) Cosmology is insensitive to neutrino flavour after decoupling! Non-zero neutrino asymmetries: flavour oscillations lead to (approximate) global flavour equilibrium the restrictive BBN bound on the asymmetry applies to all flavors, but fine-tuned initial asymmetries always allow for a large surviving neutrino excess radiation that may show up in precision cosmological data (value depends on θ 13 ) SP, Pinto & Raffelt, PRL 102 (2009) 241302
AcAve- sterile neutrino oscillaaons What if additional, light sterile neutrino species are mixed with the flavour neutrinos? If oscillations are effective before decoupling: the additional species can be brought into equilibrium: N eff =4 If oscillations are effective after decoupling: N eff =3 but the spectrum of active neutrinos is distorted (direct effect of e and anti- e on BBN) Results depend on the sign of Δm 2 (resonant vs non- resonant case)
N eff & AcAve- sterile neutrino oscillaaons Weak Processes Effec:ve: in eq (thermal spectrum) Collisions less and less important: decouple (spectrum keeps th. form) Oscilla:ons effec:ve BEFORE decoupling: the addi:onal species can be brought into eq: N eff =4 Oscilla:ons effec:ve AFTER decoupling: spectrum of ac:ve neutrinos distorted but N eff =3 + - e e γγ Expansion of the universe
N eff & AcAve- sterile neutrino oscillaaons /ev 2 ) log 10 ( δm s 2 ) 1 0.5 0 0.5 1 1.5 2 2.5 1 0.8 0.6 0.4 0.2 Addi:onal neutrino in full eq, N eff =4 Contribu:on of addi:onal to ρ rad in N eff units 3 4 3.5 3 2.5 2 1.5 1 log 10 (sin 2 2θ s ) Hannestad, Tamborra & Tram, JCAP 07 (2012) 025 0
N eff & AcAve- sterile neutrino oscillaaons Addi:onal neutrino fully in eq Flavour neutrino spectrum depleted Dolgov & Villante, NPB 679 (2004) 261
Active-sterile neutrino oscillations Kirilova, astro- ph/0312569 Addi:onal neutrino fully in eq Flavour neutrino spectrum depleted Dolgov & Villante, NPB 679 (2004) 261
End of 2nd lecture