Neutrinos in Cosmology (I)

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

2. Neutrinos in Cosmology 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. T~m Relativistic neutrinos At least 2 species are NR today • 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. Neutrinos in Cosmology 1st lecture Introduction: neutrinos and the History of the Universe Basics of cosmology: background evolution Relic neutrino production and decoupling Neutrinos and Primordial Nucleosynthesis

8. Neutrinos in Cosmology 2nd lecture 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 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. 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 fν=fFD(p,Tν)[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 νe ν,

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

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

36. 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

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 WMAP5 ΩBh2=0.02265±0.00059 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, JCAP 0703 (2007) 006

42. Exercises: try to calculate… • The present number density of massive/massless neutrinosnn0 in cm-3 • The present energy density of massive/massless neutrinos Wn0 and find the limits on the total neutrino mass from Wn0<1 and Wn0 <Wm0 • The final ratio Tg/Tnusing the conservation of entropy density before/after e± annihilations • The decoupling temperature of relic neutrinos using GH • The evolution of W(n,g,b,cdm)with the expansion for (3,0,0), (1,1,1) and (0.05,0.009,0) [masses in eV] • The value of Neff if neutrinos decouple at Tdec in [5,0.2] MeV

43. End of 1st lecture