1. Neutrinos in Cosmology (I) Sergio Pastor (IFIC Valencia) Universidad de Buenos Aires Febrero 2009 ν

2. Neutrinos in Cosmology 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 2 species are NR today Relativistic neutrinos T~m 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 Introduction: neutrinos and the History of the Universe Relic neutrino production and decoupling Neutrinos in Cosmology Neutrinos and Primordial Nucleosynthesis 1st lecture

8. Neutrinos in Cosmology 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 2nd lecture

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 Ann. Rev. Nucl. Part. Sci. 56 (2006) 137-161 [hep-ph/0602058] Primordial Nucleosynthesis: from precision cosmology to fundamental physics F. Iocco et al, arXiv:0809.0631

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 ν =f FD (p,T ν )[1+δf(p)]

29. Momentum-dependent Boltzmann equation 9-dim Phase SpaceProcess  P i conservation Statistical Factor + evolution of total energy density:

30. νeνe ν,ν, δf x10

31. N eff Instantaneous decoupling 1.401023 SM+3 ν mixing (θ 13 =0) 1.39783.046 Mangano et al, NPB 729 (2005) 221 Non-instantaneous neutrino decoupling Dolgov, Hansen & Semikoz, NPB 503 (1997) 426 Mangano et al, PLB 534 (2002) 8

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

33. Neff varying the neutrino decoupling temperature

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

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

36. 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

37. 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

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. Fields & Sarkar PDG 2006 BBN: Predictions vs Observations after WMAP5 Ω B h 2 =0.02265±0.00059

40. 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

41. BBN: allowed ranges for N eff Mangano et al, JCAP 0703 (2007) 006 Using 4 He + D data (95% CL)

42. Exercises: try to calculate… The present number density of massive/massless neutrinos n  in cm -3 The present energy density of massive/massless neutrinos   and find the limits on the total neutrino mass from    and    m 0 The final ratio T  /T  using the conservation of entropy density before/after e ± annihilations The decoupling temperature of relic neutrinos using  The evolution of  b,cdm)  with the expansion for (3,0,0), (1,1,1) and (0.05,0.009,0) [masses in eV] The value of N eff if neutrinos decouple at T dec in [5,0.2] MeV

43. End of 1st lecture