Neutrinos in Cosmology (II)

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1 Neutrinos in Cosmology (II) Sergio Pastor (IFIC Valencia) Cinvestav 8-12 June 2015

2 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

3 Outline The radiaaon content of the Universe (N eff ) Neutrinos and Primordial Nucleosynthesis Neutrino oscillaaons in the Early Universe Massive neutrinos as Dark MaMer

4 ProducAon and decoupling of relic neutrinos

5 Neutrinos coupled by weak interacaons T~MeV t~sec

6 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)

7 Neutrinos in Equilibrium 1MeV. T. m µ T = T e ± = T $ $ e ± $ e ± $ e + e

8 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

9 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

10 Neutrinos coupled by weak interacaons 1 f (p, T ) = exp(p/t ) + 1 T~MeV t~sec

11 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

12 Neutrino and photon (CMB) temperatures At T~m e, electronpositron pairs annihilate e + e - γγ heating photons but not the decoupled neutrinos T = T /3 f (p, T )= 1 exp(p/t )+1

13 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 ) e e γγ Expansion of the Universe

14 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 /3 f (p, T )= 1 exp(p/t )+1

15 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 )! m i n 4/3 4 TCMB 4 11 Massless Massive m >>T

16 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

17 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

18 VERY LOW Energy Neutrinos Non-relativistic? 2 Δm 21 2 Δm 31 Low Energy Neutrinos

19 The radiaaon content of the Universe (N eff )

20 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 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 = ργ + ρ = Tγ + 3 T = ρ γ # of flavour neutrinos: N = ± T 4 T γ (LEP data)

21 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, )

22 Neutrinos and Primordial Nucleosynthesis

23 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)

24 Decoupled neutrinos (Cosmic Neutrino Background or CNB) Neutrinos coupled by weak interactions T~MeV t~sec

25 BBN: CreaAon of light elements Produced elements: D, 3 He, 4 He, 7 Li and small abundances of others Theore:cal inputs:

26 BBN: CreaAon of light elements Range of temperatures: from 0.8 to 0.01 MeV Phase I: MeV n- p reac:ons n/p freezing and neutron decay

27 BBN: CreaAon of light elements Phase II: 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

28 BBN: CreaAon of light elements Phase II: 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

29 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

30 BBN: PredicAons vs ObservaAons 10 = n B/n ' 274 Bh 2 Baryon- to- photon ra:o F. Iocco et al, Phys. Rep. 472 (2009) 1

31 BBN: PredicAons vs ObservaAons Planck 2015, arxiv:

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.

32 Effect of neutrinos on BBN 1. N eff fixes the expansion rate during BBN s H = 8 3M 2 p ρ(n eff )>ρ 0 4 He Burles, Noller & Turner Direct effect of electron neutrinos and an:neutrinos on the n- p reac:ons e + n $ p + e e + + n $ p + e

33 BBN: allowed ranges for N eff Conserva:ve approach: upper bound on 4 He Mangano & Serpico, PLB 701 (2011) 296 Planck 2015, arxiv: ΔN eff < 1 (95% CL)

34 Neutrino oscillaaons in the Early Universe

35 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/

36 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)

37 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)

38 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

39 N eff & AcAve- sterile neutrino oscillaaons /ev 2 ) log 10 ( δm s 2 ) Addi:onal neutrino in full eq, N eff =4 Contribu:on of addi:onal to ρ rad in N eff units log 10 (sin 2 2θ s ) Hannestad, Tamborra & Tram, JCAP 07 (2012) 025 0

40 N eff & AcAve- sterile neutrino oscillaaons Addi:onal neutrino fully in eq Flavour neutrino spectrum depleted Dolgov & Villante, NPB 679 (2004) 261

41 Active-sterile neutrino oscillations Kirilova, astro- ph/ Addi:onal neutrino fully in eq Flavour neutrino spectrum depleted Dolgov & Villante, NPB 679 (2004) 261

42 End of 2nd lecture

Lecture 19 Nuclear Astrophysics. Baryons, Dark Matter, Dark Energy. Experimental Nuclear Physics PHYS 741

Lecture 19 Nuclear Astrophysics Baryons, Dark Matter, Dark Energy Experimental Nuclear Physics PHYS 741 heeger@wisc.edu References and Figures from: - Haxton, Nuclear Astrophysics - Basdevant, Fundamentals