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

2. Cosmology and neutrino masses Sergio Pastor (IFIC Valencia) Universidad de Buenos Aires Febrero 2009 ν Picture from Hubble ST

3. 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

4. At least 2 species are NR today Relativistic neutrinos T~m

5. 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

6. 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 !

7. Mixing Parameters... From present evidences of oscillations from experiments measuring atmospheric, solar, reactor and accelerator neutrinos Mixing matrix U

8. Mixing Parameters... Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122 [hep-ph/0405172 v6]

9. 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 v6]

10. ... and neutrino masses Data on flavour oscillations do not fix the absolute scale of neutrino masses eV atm solar NORMAL INVERTED eV m0m0 What is the value of m 0 ?

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

12. The Cosmic Neutrino Background 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

13. 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 Neutrino Free Streaming Φ b, cdm ν

14. 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

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

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

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

18. Cosmological observables 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

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

20. Galaxy Redshift Surveys SDSS 2dFGRS ~ 1300 Mpc

21. Cosmological observables: LSS 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 0<z<0.2 matter power spectrum P(k) galaxy redshift surveys linear non-linear δρ/ρ<1 δρ/ρ ~ 1 60 Mpc bias uncertainty Distribution of large-scale structures at low z

22. Power spectrum of density fluctuations Bias b 2 (k)=P g (k)/P m (k) k ma x SDSS 2dFGRS Non-linearity

23. Cosmological observables : LSS 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 2<z<3 Lyman- α forests in quasar spectra matter power spectrum P(k) various systematics Distribution of large-scale structures at medium z

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

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

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

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

28. growth of  (k,t) fixed by « gravity vs. expansion » balance    a Structure formation after equality baryons and CDM experience gravitational clustering

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

30. Structure formation after equality baryon and CDM experience gravitational clustering baryons and CDM experience gravitational clustering neutrinos experience free-streaming with v = c or /m

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

32. Structure formation after equality baryon and CDM experience gravitational clustering baryons and CDM experience gravitational clustering neutrinos experience free-streaming with v = c or /m

33. J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/0603494] Structure formation after equality d cdm dbdb dgdg dndn metric a Massless neutrinos

34. J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/0603494] d cdm dbdb dgdg dndn metric a 1-3/5f n a Massive neutrinos f ν =0.1 Structure formation after equality

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

36. Cosmological observables: CMB 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 z≈1100  photon power spectra CMB temperature/polarization anisotropies Anisotropies of the Cosmic Microwave Background

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

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

39. CMB Polarization DATA TT TE EE BB WMAP 3

40. CMB Polarization DATA

41. Effect of massive neutrinos on the CMB spectra 1)Direct effect of sub-eV massive neutrinos on the evolution of the baryon-photon coupling is very small 2)Impact on CMB spectra is indirect: non-zero Ω ν today implies a change in the spatial curvature or other Ω i. The background evolution is modified Ex: in a flat universe, keep Ω Λ +Ω cdm +Ω b +Ω ν =1 constant

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

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

44. How to get a bound (measurement) of neutrino masses from Cosmology DATA Fiducial cosmological model: (Ω b h 2, Ω m h 2, h, n s, τ, Σm ν ) PARAMETER ESTIMATES

45. Cosmological Data CMB Temperature: WMAP plus data from other experiments at large multipoles (CBI, ACBAR, VSA…) CMB Polarization: WMAP,… Large Scale Structure: * Galaxy Clustering (2dF,SDSS) * Bias (Galaxy, …): Amplitude of the Matter P(k) (SDSS,σ 8 ) * Lyman-α forest: independent measurement of power on small scales * Baryon acoustic oscillations (SDSS) Bounds on parameters from other data: SNIa (Ω m ), HST (h), …

46. Cosmological Parameters: example SDSS Coll, PRD 69 (2004) 103501

47. Cosmological bounds on neutrino mass(es) A unique cosmological bound on m ν DOES NOT exist ! ν

48. Cosmological bounds on neutrino mass(es) A unique cosmological bound on m ν DOES NOT exist ! Different analyses have found upper bounds on neutrino masses, since they depend on The combination of cosmological data used The assumed cosmological model: number of parameters (problem of parameter degeneracies) The properties of relic neutrinos

49. Cosmological bounds on neutrino masses using WMAP Fogli et al., PRD 75 (2007) 053001 Dependence on the data set used. Fogli et al., PRD 78 (2008) 033010 With WMAP3 With WMAP5

50. Neutrino masses in 3-neutrino schemes CMB + galaxy clustering + HST, SNI-a…+ BAO and/or bias + including Ly- α Strumia & Vissani, hep-ph/0606054

51. Direct laboratory bounds on m ν Searching for non-zero neutrino mass in laboratory experiments Tritium beta decay: measurements of endpoint energy m( ν e ) < 2.2 eV (95% CL) Mainz Future experiments (KATRIN) m( ν e ) ~ 0.2-0.3 eV Neutrinoless double beta decay: if Majorana neutrinos experiments with 76 Ge, 130 Te and other isotopes: Im ee I < 0.23-0.85 eV, depending on NME

52. Absolute mass scale searches Neutrinoless double beta decay < 0.2-0.8 eV Tritium β decay  2.2 eV < 0.2-2.0 eV Cosmology

53. Tritium  decay, 0 2  and Cosmology Fogli et al., PRD 75 (2007) 053001

54. 0 2  and Cosmology Fogli et al., PRD 78 (2008) 033010

55. 0 2  and Cosmology Fogli et al., PRD 78 (2008) 033010

56. 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 Constraints on N eff from BBN and from CMB+LSS

57. Effect of N eff at later epochs N eff modifies the radiation content: Changes the epoch of matter-radiation equivalence

58. CMB+LSS: allowed ranges for N eff Set of parameters: ( Ω b h 2, Ω cdm h 2, h, n s, A, b, N eff ) DATA: WMAP + other CMB + LSS + HST (+ SN-Ia) Flat Models Non-flat Models Recent result Pierpaoli, MNRAS 342 (2003) L63 95% CL Crotty, Lesgourgues & SP, PRD 67 (2003) 123005 95% CL Hannestad, JCAP 0305 (2003) 004 Hannestad & Raffelt, JCAP 0611 (2006) 016 95% CL

59. Allowed ranges for N eff Mangano et al, JCAP 0703 (2007) 006 Using cosmological data (95% CL) 1.9 < N eff < 7.8 (WMAP5+BAO+SN+HST) WMAP Coll., arXiv:0803.0547

60. Future bounds on N eff Next CMB data from WMAP and PLANCK (other CMB experiments on large l’s) temperature and polarization spectra Forecast analysis in Ω Λ =0 models Lopez et al, PRL 82 (1999) 3952 WMAP PLANCK

61. Future bounds on N eff Updated analysis: Larger errors Bowen et al 2002 ΔN eff ~ 3 (WMAP) ΔN eff ~ 0.2 (Planck) Bashinsky & Seljak 2003

62. The bound on Σm ν depends on the number of neutrinos Example: in the 3+1 scenario, there are 4 neutrinos (including thermalized sterile) Calculate the bounds with N ν > 3 Abazajian 2002, di Bari 2002 Hannestad JCAP 0305 (2003) 004 (also Elgarøy & Lahav, JCAP 0304 (2003) 004) 3 ν 4 ν 5 ν Hannestad 95% CL WMAP + Other CMB + 2dF + HST + SN-Ia

63. Σm ν and N eff degeneracy (0 eV,3) (0 eV,7) (2.25 eV,7) (0 eV,3) (0 eV,7) (2.25 eV,7)

64. Analysis with Σm ν and N eff free Hannestad & Raffelt, JCAP 0404 (2004) 008 Crotty, Lesgourgues & SP, PRD 69 (2004) 123007 2σ upper bound on Σm ν ( eV) WMAP + ACBAR + SDSS + 2dF Previous + priors (HST + SN-Ia) BBN allowed region

65. Analysis with Σm ν and N eff free Crotty, Lesgourgues & SP, PRD 69 (2004) 123007 WMAP + ACBAR + SDSS + 2dF Hannestad & Raffelt, JCAP 0611 (2006) 016 BBN allowed region

66. Parameter degeneracy: Neutrino mass and w In cosmological models with more parameters the neutrino mass bounds can be relaxed. Ex: quintessence-like dark energy with ρ DE =w p DE WMAP Coll, astro-ph/0603449 Λ

67. Non-standard relic neutrinos The cosmological bounds on neutrino masses are modified if relic neutrinos have non-standard properties (or for non-standard models) Two examples where the cosmological bounds do not apply Massive neutrinos strongly coupled to a light scalar field: they could annihilate when becoming NR Neutrinos coupled to the dark energy: the DE density is a function of the neutrino mass (mass-varying neutrinos)

68. Non-thermal relic neutrinos The spectrum could be distorted after neutrino decoupling Example: decay of a light scalar after BBN Cuoco, Lesgourgues, Mangano & SP, PRD 71 (2005) 123501 Thermal FD spectrum Distortion from Φ decay * CMB + LSS data still compatible with large deviations from a thermal neutrino spectrum (degeneracy NT distortion – N eff ) * Better expectations for future CMB + LSS data, but model degeneracy NT- N eff remains

69. Future sensitivities to Σm ν CMB (Temperature & Polarization anis.) Galaxy redshift surveys Galaxy cluster surveys Weak lensing surveys CMB lensing Future cosmological data will be available from WMAP, SPT, ACT, BICEP, QUaD, BRAIN, ClOVER, PLANCK, SAMPAN, Inflation Probe, SDSS, SDSS-II, ALHAMBRA, KAOS, DES, CFHTLS, SNAP, LSST, Pan-STARRS, DUO…

70. PLANCK+SDSS Lesgourgues, SP & Perotto, PRD 70 (2004) 045016 Σm detectable at 2σ if larger than 0.21 eV (PLANCK+SDSS) 0.13 eV (CMBpol+SDSS) Fiducial cosmological model: (Ω b h 2, Ω m h 2, h, n s, τ, Σm ν ) = (0.0245, 0.148, 0.70, 0.98, 0.12, Σm ν ) Fisher matrix analysis: expected sensitivities assuming a fiducial cosmological model, for future experiments with known specifications

71. Future sensitivities to Σm ν : new ideas weak gravitational and CMB lensing lensing No bias uncertainty Small scales much closer to linear regime Tomography: 3D reconstruction Makes CMB sensitive to smaller neutrino masses

72. Future sensitivities to Σm ν : new ideas sensitivity of future weak lensing survey (4000º) 2 to m ν σ(m ν ) ~ 0.1 eV Abazajian & Dodelson PRL 91 (2003) 041301 sensitivity of CMB (primary + lensing) to m ν σ(m ν ) = 0.15 eV (Planck) σ(m ν ) = 0.044 eV (CMBpol) Kaplinghat, Knox & Song PRL 91 (2003) 241301 weak gravitational and CMB lensing lensing

73. CMB lensing: recent analysis σ(M ν ) in eV for future CMB experiments alone : Lesgourgues et al, PRD 73 (2006) 045021

74. “Measuring” even m ν =0.05 eV ? New cosmological observable as a potential probe of fluctuations at intermediate redshifts (6<z<20)  study of fluctuations in the 21cm line emitted by neutral H Karttunen et al. 2007

75. “Measuring” even m ν =0.05 eV ? New cosmological observable as a potential probe of fluctuations at intermediate redshifts (6<z<20)  study of fluctuations in the 21cm line emitted by neutral H 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 20>z>6 Redshifted line: 2.1 m at redshift 10 power spectrum of 21 cm brightness fluctuations P 21 (k)

76. Future sensitivities on  m from 21cm exps. Pritchard & Pierpaoli, arXiv:0805.1920 Future Low- ν radio telescopes

77. Summary of future sensitivities Lesgourgues & SP, Phys. Rep. 429 (2006) 307 Future cosmic shear surveys Future high-z 21cm observations