Cosmological Aspects of Neutrinos: Relic Neutrinos, Masses, and Dark Matter

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

2. 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

3. Degenerate relic neutrinos (relic neutrino asymmetries)

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

5. 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)

6.    /T Neutrinos coupled by weak interactions Primordial Nucleosynthesis T~MeV t~sec

7. Relic neutrino asymmetries Fermi-Dirac spectrum with temperature T and chemical potential  Raffelt More radiation

8. Degenerate Big Bang Nucleosynthesis If 0 , for any flavor ()>(0) 4He Plus thedirect effecton np if(e)0 e>0  4He Pairs (e,N)that produce the same observed abundances forlarger B Kang & Steigman 1992

9. Combined bounds BBN & CMB-LSS Degeneracy direction (arbitrary ξe) Hansen et al 2001 Hannestad 2003 In the presence of flavor oscillations ?

10. Flavor neutrino oscillations in the Early Universe • Density matrix • Mixing matrix • Expansion of the Universe • Charged lepton background (2nd order contribution) • Collisions (damping) • Neutrino background: diagonal and off-diagonal potentials Dominant term: Synchronized Neutrino Oscillations

11. Serpico & Raffelt 2005 Evolution of neutrino asymmetries BBN Dolgov et al 2002 Wong 2002 Abazajian et al 2002 Effective flavor equilibrium (almost) established 

12. Massive Neutrinos and Cosmology

13. 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

14. We know that flavour neutrino oscillations exist From present evidences of oscillations from experiments measuring atmospheric, solar, reactor and accelerator neutrinos Evidence of Particle Physics beyond the Standard Model !

15. Mixing Parameters... From present evidences of oscillations from experiments measuring atmospheric, solar, reactor and accelerator neutrinos Mixing matrix U Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122 [hep-ph/0405172 v5]

16. Mixing Parameters... From present evidences of oscillations from experiments measuring atmospheric, solar, reactor and accelerator neutrinos Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122 [hep-ph/0405172 v5]

17. eV eV solar m0 NORMAL INVERTED atm atm solar ... and neutrino masses Data on flavour oscillations do not fix the absolute scale of neutrino masses What is the value of m0 ?

18. Direct laboratory bounds on mν Searching for non-zero neutrino mass in laboratory experiments • Tritium beta decay: measurements of endpoint energy • m(νe) < 2.2 eV (95% CL) Mainz • Future experiments (KATRIN) m(νe) ~ 0.2-0.3 eV • Neutrinoless double beta decay: if Majorana neutrinos • experiments with 76Ge and other isotopes: ImeeI < 0.4hN eV

19. Cosmology < 0.3-2.0 eV Absolute mass scale searches

20. 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

21. 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

22. Neutrino Free Streaming ν Φ b, cdm Neutrinos as Dark Matter • Neutrinos are natural DM candidates • They stream freely until non-relativistic (collisionless phase mixing) Neutrinos are HOT Dark Matter • First structures to be formed when Universe became matter -dominated • Ruled out by structure formation CDM

23. Neutrinos as Dark Matter • Neutrinos are natural DM candidates • They stream freely until non-relativistic (collisionless phase mixing) Neutrinos are HOT Dark Matter • First structures to be formed when Universe became matter -dominated • HDM ruled out by structure formation CDM

24. Neutrinos as Hot Dark Matter • Effect of Massive Neutrinos: suppression of Power at small scales

25. Neutrinos as Hot Dark Matter • Effect of Massive Neutrinos: suppression of Power at small scales

26. Neutrinos as Hot Dark Matter Massive Neutrinos can still be subdominant DM: limits on mν from Structure Formation (combined with other cosmological data)

27. accélération décélération lente décélération rqpide accélération inflation radiation matière énergie noire Cosmological observables accélération acceleration décélération lente slow deceleration décélération rqpide fast deceleration accélération acceleration ? inflation RD (radiation domination) MD (matter domination) dark energy domination

28. Field of density Fluctuations Matter power spectrum is the Fourier transform of the two-point correlation function Power Spectrum of density fluctuations

29. 2dFGRS Galaxy Redshift Surveys SDSS ~ 1300 Mpc

30. accélération décélération lente décélération rqpide accélération bias uncertainty 60 Mpc inflation radiation matière énergie noire linear non-linear δρ/ρ<1 δρ/ρ~ 1 matter power spectrum P(k)  Cosmological observables: LSS accélération acceleration décélération lente slow deceleration décélération rqpide fast deceleration accélération acceleration 0<z<0.2 ? inflation RD (radiation domination) MD (matter domination) dark energy domination Distribution of large-scale structures at low z galaxy redshift surveys

31. Non-linearity 2dFGRS SDSS kmax Power spectrum of density fluctuations Bias b2(k)=Pg(k)/Pm(k)

32. accélération décélération lente décélération rqpide accélération various systematics inflation radiation matière énergie noire matter power spectrum P(k)  Cosmological observables : LSS accélération acceleration décélération lente slow deceleration décélération rqpide fast deceleration accélération acceleration ? 2<z<3 inflation RD (radiation domination) MD (matter domination) dark energy domination Distribution of large-scale structures at medium z Lyman-α forests in quasar spectra

33. fν Neutrinos as Hot Dark Matter Massive Neutrinos can still be subdominant DM: limits on mν from Structure Formation (combined with other cosmological data) • Effect of Massive Neutrinos: suppression of Power at small scales

34. Structure formation after equality baryons and CDM experience gravitational clustering

35. Structure formation after equality baryons and CDM experience gravitational clustering • growth ofdr/r (k,t)fixed by • « gravity vs. expansion » balance •  dr/ra

36. Structure formation after equality baryons and CDM experience gravitational clustering neutrinos experience free-streaming with v = c or <p>/m

37. Structure formation after equality baryon and CDM experience gravitational clustering baryons and CDM experience gravitational clustering neutrinos experience free-streaming with v = c or <p>/m neutrinos cannot cluster below a diffusion length l = ∫ v dt < ∫ c dt

38. for (2p/k) <l , • free-streaming supresses growth of structures during MD •  dr/r a1-3/5 fnwith fn = rn /rm ≈ (Smn)/(15 eV) Structure formation after equality baryon and CDM experience gravitational clustering baryons and CDM experience gravitational clustering neutrinos experience free-streaming with v = c or <p>/m • neutrinos cannot cluster below a diffusion length l = ∫ v dt < ∫ c dt

39. a dcdm Massless neutrinos db dn dg metric Structure formation after equality J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/0603494]

40. Structure formation after equality a dcdm db 1-3/5fn a Massive neutrinos fν=0.1 dn dg metric J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/0603494]

41. Effect of massive neutrinos on P(k) Observable signature of the total mass on P(k) : P(k) massive P(k) massless various fν Lesgourgues & SP, Phys. Rep. 429 (2006) 307

42. accélération décélération lente décélération rqpide accélération inflation radiation matière énergie noire Cosmological observables: CMB accélération acceleration décélération lente slow deceleration décélération rqpide fast deceleration accélération acceleration ? z≈1100 inflation RD (radiation domination) MD (matter domination) dark energy domination Anisotropies of the Cosmic Microwave Background  photon power spectra CMB temperature/polarization anisotropies

43. Map of CMBR temperature Fluctuations Multipole Expansion Angular Power Spectrum CMB TT DATA

44. Map of CMBR temperature Fluctuations Multipole Expansion Angular Power Spectrum CMB TT DATA

45. TT TE EE BB WMAP 3 CMB Polarization DATA

46. Effect of massive neutrinos on the CMB spectra • Direct effect of sub-eV massive neutrinos on the evolution of the baryon-photon coupling is very small • Impact on CMB spectra is indirect: non-zero Ωνtoday implies a change in the spatial curvature or other Ωi . The background evolution is modified • Ex: in a flat universe, • keep ΩΛ+Ωcdm+Ωb+Ων=1 • constant

47. Effect of massive neutrinos on the CMB spectra Problem with parameter degeneracies: change in other cosmological parameters can mimic the effect of nu masses

48. Effect of massive neutrinos on the CMB and Matter Power Spectra Max Tegmark www.hep.upenn.edu/~max/

49. End of 2nd lecture