1. Cosmological Aspects of Neutrino Physics (I) Sergio Pastor (IFIC) 61st SUSSP St Andrews, August 2006 ν

2. Cosmological Aspects of Neutrino Physics 1st lecture Introduction: neutrinos and the History of the Universe

3. This is a neutrino!

4. T~MeV t~sec Primordial Nucleosynthesis Decoupled neutrinos (Cosmic Neutrino Background or CNB) Neutrinos coupled by weak interactions

5. At least 1 species is NR Relativistic neutrinos T~eV Neutrino cosmology is interesting because Relic neutrinos are very abundant: The CNB contributes to radiation at early times and to matter at late times (info on the number of neutrinos and their masses) Cosmological observables can be used to test non-standard neutrino properties

6. Relic neutrinos influence several cosmological epochs T < eVT ~ MeV Formation of Large Scale Structures LSS Cosmic Microwave Background CMB Primordial Nucleosynthesis BBN No flavour sensitivity N eff & m ν ν e vs ν μ,τ N eff

7. Basics of cosmology: background evolution 1st lecture Introduction: neutrinos and the History of the Universe Relic neutrino production and decoupling Cosmological Aspects of Neutrino Physics Neutrinos and Primordial Nucleosynthesis Neutrino oscillations in the Early Universe* * Advanced topic

8. Cosmological Aspects of Neutrino Physics 2nd & 3rd lectures Degenerate relic neutrinos (Neutrino asymmetries)* Massive neutrinos as Dark Matter Effects of neutrino masses on cosmological observables Bounds on m ν from CMB, LSS and other data Bounds on the radiation content (N ν ) Future sensitivities on m ν and N ν from cosmology * Advanced topic

9. Suggested References Books Modern Cosmology, S. Dodelson (Academic Press, 2003) The Early Universe, E. Kolb & M. Turner (Addison-Wesley, 1990) Kinetic theory in the expanding Universe, Bernstein (Cambridge U., 1988) Recent reviews Neutrino Cosmology, A.D. Dolgov, Phys. Rep. 370 (2002) 333-535 [hep-ph/0202122] Massive neutrinos and cosmology, J. Lesgourgues & SP, Phys. Rep. 429 (2006) 307-379 [astro-ph/0603494] Primordial Neutrinos, S. Hannestad hep-ph/0602058 BBN and Physics beyond the Standard Model, S. Sarkar Rep. Prog. Phys. 59 (1996) 1493-1610 [hep-ph/9602260]

10. Eqs in the SM of Cosmology The FLRW Model describes the evolution of the isotropic and homogeneous expanding Universe a(t) is the scale factor and k=-1,0,+1 the curvature Einstein eqs Energy-momentum tensor of a perfect fluid

11. Eqs in the SM of Cosmology Eq of state p=αρ ρ = const a -3(1+α) Radiation α =1/3 Matter α =0Cosmological constant α =-1 ρ R ~ 1/a 4 ρ M ~1/a 3 ρ Λ ~const 00 component (Friedmann eq) H(t) is the Hubble parameter ρ=ρM+ρR+ρΛρ=ρM+ρR+ρΛ ρ crit =3H 2 /8πG is the critical density Ω= ρ/ρ crit

12. Evolution of the Universe accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire acceleration slow deceleration fast deceleration ? inflation RD (radiation domination)MD (matter domination) dark energy domination a (t)~t 1/2 a (t)~t 2/3 a (t)~e Ht

13. Evolution of the background densities: 1 MeV → now 3 neutrino species with different masses

14. Evolution of the background densities: 1 MeV → now photons neutrinos cdm baryons Λ m 3 =0.05 eV m 2 =0.009 eV m 1 ≈ 0 eV Ω i = ρ i /ρ crit

15. Equilibrium thermodynamics 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. BOSEFERMI

16. T~MeV t~sec Primordial Nucleosynthesis Neutrinos coupled by weak interactions (in equilibrium)

17. T ν = T e = T γ 1 MeV  T  m μ Neutrinos in Equilibrium

18. Neutrino decoupling As the Universe expands, particle densities are diluted and temperatures fall. Weak interactions become ineffective to keep neutrinos in good thermal contact with the e.m. plasma Rate of weak processes ~ Hubble expansion rate Rough, but quite accurate estimate of the decoupling temperature Since ν e have both CC and NC interactions with e ± T dec ( ν e ) ~ 2 MeV T dec ( ν μ,τ ) ~ 3 MeV

19. T~MeV t~sec Free-streaming neutrinos (decoupled) Cosmic Neutrino Background Neutrinos coupled by weak interactions (in equilibrium) Neutrinos keep the energy spectrum of a relativistic fermion with eq form

20. At T~m e, electron- positron pairs annihilate heating photons but not the decoupled neutrinos Neutrino and Photon (CMB) temperatures

21. At T~m e, electron- positron pairs annihilate heating photons but not the decoupled neutrinos Neutrino and Photon (CMB) temperatures Photon temp falls slower than 1/a(t)

22. Number density Energy density Massless Massive m ν >>T Neutrinos decoupled at T~MeV, keeping a spectrum as that of a relativistic species The Cosmic Neutrino Background

23. Number density Energy density Massless Massive m ν >>T Neutrinos decoupled at T~MeV, keeping a spectrum as that of a relativistic species At present 112 per flavour Contribution to the energy density of the Universe

24. At T<m e, the radiation content of the Universe is Relativistic particles in the Universe

25. At T<m e, the radiation content of the Universe is Effective number of relativistic neutrino species Traditional parametrization of the energy density stored in relativistic particles Relativistic particles in the Universe # of flavour neutrinos:

26. Extra radiation can be: scalars, pseudoscalars, sterile neutrinos (totally or partially thermalized, bulk), neutrinos in very low-energy reheating scenarios, relativistic decay products of heavy particles… Particular case: relic neutrino asymmetries Constraints from BBN and from CMB+LSS Extra relativistic particles

27. At T<m e, the radiation content of the Universe is Effective number of relativistic neutrino species Traditional parametrization of the energy density stored in relativistic particles N eff is not exactly 3 for standard neutrinos Relativistic particles in the Universe # of flavour neutrinos:

28. But, since T dec ( ν ) is close to m e, neutrinos share a small part of the entropy release At T~m e, e + e - pairs annihilate heating photons Non-instantaneous neutrino decoupling f =f FD (p,T )[1+δf(p)]

29. Boltzmann Equation 9-dim Phase SpaceProcess  P i conservation Statistical Factor

30. e ,  δf x10

31. ρ( e ) 0.73% larger ρ(  ) 0.52% larger f ν =f FD (p,T ν )[1+δf(p)] Mangano et al 2002 Non-instantaneous neutrino decoupling Non-instantaneous decoupling + QED corrections to e.m. plasma + Flavor Oscillations N eff =3.046 T.Pinto et al, NPB 729 (2005) 221

32. Produced elements: D, 3 He, 4 He, 7 Li and small abundances of others BBN: Creation of light elements Theoretical inputs:

33. Range of temperatures: from 0.8 to 0.01 MeV BBN: Creation of light elements n/p freezing and neutron decay Phase I: 0.8-0.1 MeV n-p reactions

34. BBN: Creation of light elements 0.03 MeV 0.07 MeV Phase II: 0.1-0.01 MeV Formation of light nuclei starting from D Photodesintegration prevents earlier formation for temperatures closer to nuclear binding energies

35. BBN: Creation of light elements 0.03 MeV 0.07 MeV Phase II: 0.1-0.01 MeV Formation of light nuclei starting from D Photodesintegration prevents earlier formation for temperatures closer to nuclear binding energies

36. BBN: Measurement of Primordial abundances Difficult task: search in astrophysical systems with chemical evolution 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 absorption line systems Helium-3: produced and destroyed in stars (complicated evolution) 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, extragalatic HII regions Lithium-7: destroyed in stars, produced in cosmic ray reactions. Data from oldest, most metal-poor stars in the Galaxy

37. Fields & Sarkar PDG 2004 BBN: Predictions vs Observations after WMAP Ω B h 2 =0.023±0.001

38. Effect of neutrinos on BBN 1. N eff fixes the expansion rate during BBN  (N eff )>  0   4 He Burles, Nollett & Turner 1999 3.43.2 3.0 2. Direct effect of electron neutrinos and antineutrinos on the n-p reactions

39. BBN: allowed ranges for N eff Cuoco et al, IJMP A19 (2004) 4431 [astro-ph/0307203] Using 4 He + D data (2σ)

40. Neutrino oscillations in the Early Universe Neutrino oscillations are effective when medium effects get small enough Compare oscillation term with effective potentials Strumia & Vissani, hep-ph/0606054 Oscillation term prop. to Δm 2 /2E First order matter effects prop. to G F [n(e - )-n(e + )] Second order matter effects prop. to G F (E/M Z ) 2 [n(e - )+n(e + )] Coupled neutrinos

41. Flavor neutrino oscillations 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 ν ) Cosmology is insensitive to neutrino flavour after decoupling! Non-zero neutrino asymmetries: flavour oscillations lead to (almost) equilibrium for all μ ν

42. What if additional, 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 ν e and anti- ν e on BBN) Active-sterile neutrino oscillations Results depend on the sign of Δm 2 (resonant vs non-resonant case)

43. Active-sterile neutrino oscillations Dolgov & Villante, NPB 679 (2004) 261 Additional neutrino fully in eq Flavour neutrino spectrum depleted

44. Active-sterile neutrino oscillations Dolgov & Villante, NPB 679 (2004) 261 Additional neutrino fully in eq Flavour neutrino spectrum depleted Kirilova, astro-ph/0312569

45. Active-sterile neutrino oscillations Dolgov & Villante, NPB 679 (2004) 261 Additional neutrino fully in eq Flavour neutrino spectrum depleted

46. Active-sterile neutrino oscillations Dolgov & Villante, NPB 679 (2004) 261 Additional neutrino fully in eq

47. End of 1st lecture