Cosmological aspects of neutrinos (I)

1. Cosmological aspects of neutrinos (I) ν Sergio Pastor (IFIC Valencia) JIGSAW 2007 TIFR Mumbai, February 2007

2. Cosmological aspects of neutrinos 1st lecture Introduction: neutrinos and the History of the Universe

3. This is a neutrino!

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

5. Relativistic neutrinos At least 1 species is NR 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. Primordial Nucleosynthesis BBN Cosmic Microwave Background CMB Formation of Large Scale Structures LSS T ~ MeV T < eV νevsνμ,τ Neff No flavour sensitivityNeff & mν Relic neutrinos influence several cosmological epochs

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

8. Cosmological aspects of neutrinos 2nd & 3rd lectures Degenerate relic neutrinos (Neutrino asymmetries) Massive neutrinos as Dark Matter Effects of neutrino masses on cosmological observables Bounds on mν from CMB, LSS and other data Bounds on the radiation content (Nν) Future sensitivities on mν and Nνfrom cosmology

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. 00 component (Friedmann eq) ρ=ρM+ρR+ρΛ H(t) is the Hubble parameter Eq of state p=αρ ρ = const a-3(1+α) Radiation α=1/3 Matter α=0 Cosmological constantα=-1 ρR~1/a4ρM~1/a3ρΛ~const Eqs in the SM of Cosmology Ω= ρ/ρcrit ρcrit=3H2/8πG is the critical density

12. accélération acceleration décélération lente slow deceleration décélération rqpide fast deceleration accélération acceleration accélération ? décélération lente décélération rqpide accélération inflation RD (radiation domination) MD (matter domination) dark energy domination inflation radiation matière énergie noire Evolution of the Universe a(t)~eHt a(t)~t1/2 a(t)~t2/3

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

14. photons neutrinos Λ cdm m3=0.05 eV baryons m2=0.009 eV m1≈ 0 eV Evolution of the background densities: 1 MeV → now Ωi= ρi/ρcrit

15. Distribution function of particle momenta in equilibrium Thermodynamical variables Equilibrium thermodynamics Particles in equilibrium when T are high and interactions effective T~1/a(t)

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

17. Neutrinos in Equilibrium 1 MeV  T mμ Tν= Te = Tγ

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 Rough, but quite accurate estimate of the decoupling temperature Rate of weak processes ~ Hubble expansion rate Since νe have both CC and NC interactions withe± Tdec(νe) ~ 2 MeV Tdec(νμ,τ) ~ 3 MeV

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

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

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

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

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

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

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

26. Extra relativistic particles • 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

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

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

29. + evolution of total energy density: Momentum-dependent Boltzmann equation Statistical Factor 9-dim Phase Space Pi conservation Process

30. δf x10 e ,

31. Non-instantaneous neutrino decoupling Dolgov, Hansen & Semikoz, NPB 503 (1997) 426 Mangano et al, PLB 534 (2002) 8 Mangano et al, NPB 729 (2005) 221

32. Contribution of neutrinos to total energy density today (3 degenerate masses) Present neutrino number density Changes in CNB quantities

33. Neff varying the neutrino decoupling temperature

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

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

36. BBN: Creation of light elements 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 0.07 MeV 0.03 MeV

37. BBN: Creation of light elements 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 0.07 MeV 0.03 MeV

38. 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

39. BBN: Predictions vs Observations after WMAP ΩBh2=0.024±0.001 Fields & Sarkar PDG 2006

40. 1. Neff fixes the expansion rate during BBN 3.4 3.2 3.0 (Neff)>0 4He Burles, Nollett & Turner 1999 Effect of neutrinos on BBN 2. Direct effect of electron neutrinos and antineutrinos on the n-p reactions

41. Using 4He + D data (95% CL) BBN: allowed ranges for Neff Mangano et al, astro-ph/0612150

42. Neutrino oscillations in the Early Universe Neutrino oscillations are effective when medium effects get small enough Compare oscillation term with effective potentials Coupled neutrinos Oscillation term prop. to Δm2/2E Second order matter effects prop. to GF(E/MZ)2[n(e-)+n(e+)] First order matter effects prop. to GF[n(e-)-n(e+)] Strumia & Vissani, hep-ph/0606054

43. Standard case: all neutrino flavours equally populated oscillations are effective below a few MeV, but have no effect (except for mixing the small distortions δfν) Cosmology is insensitive to neutrino flavour after decoupling! Flavor neutrino oscillations in the Early Universe Non-zero neutrino asymmetries: flavour oscillations lead to (almost) equilibrium for all μν

44. Active-sterile neutrino oscillations • 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: Neff=4 • If oscillations are effective after decoupling: Neff=3but the spectrum of active neutrinos is distorted(direct effect of νe and anti-νe on BBN) Results depend on the sign of Δm2 (resonant vs non-resonant case)

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

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

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

48. End of 1st lecture