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

2. Cosmological aspects of neutrinos 3rd lecture Bounds on m ν from CMB, LSS and other data Bounds on the radiation content (N eff ) Future sensitivities on m ν from cosmology keV sterile neutrinos as Dark Matter

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

4. keV sterile neutrinos mixed with active species Consider 2 ν active-sterile mixing with  m 2 of order keV 2 and very small mixing angle Probability of conversion in the primordial plasma (active neutrinos still interacting) λ osc =oscillation length λ s =scattering length Mixing angle suppressed by medium effects until T falls below T≈130 MeV(  m 2 /keV 2 ) 1/6

5. The heavy state decays radiatively (with lifetime larger than the age of the Universe): search for X-ray photon line Abazajian et al 2001, Dolgov & Hansen 2002 Kusenko, Neutrino 2006 keV states created in partial equilibrium with the right DM density Would behave as Warm Dark Matter: lower limits from Structure Formation See e.g. Viel et al 2006 Dodelson & Widrow 1994 Shi & Fuller 1999 Abazajian et al 2001 Dolgov & Hansen 2002

6. Bounds on mν from CMB, LSS and other data

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

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

9. 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

10. 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), …

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

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

13. 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

14. Cosmological bounds on neutrino masses using WMAP3 Fogli et al., hep-ph/0608060 Dependence on the data set used. An example:

15. Neutrino masses in 3-neutrino schemes CMB + galaxy clustering + HST, SNI-a…+ BAO and/or bias + including Ly- α Lesgourgues & SP, Phys. Rep. 429 (2006) 307

16. Tritium  decay, 0 2  and Cosmology Fogli et al., hep-ph/0608060

17. 0 2  and Cosmology Fogli et al., hep-ph/0608060

18. 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

19. 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 on N eff from BBN and from CMB+LSS Extra relativistic particles

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

21. 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) 95% CL Crotty, Lesgourgues & SP, PRD 67 (2003) 95% CL Hannestad, JCAP 0305 (2003) Hannestad & Raffelt, astro-ph/0607101 95% CL

22. Allowed ranges for N eff Mangano et al, astro-ph/0612150 Using cosmological data (95% CL)

23. 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

24. 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

25. 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

26. 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)

27. 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

28. 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

29. 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

30. 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)

31. 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

32. 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…

33. 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

34. 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

35. 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

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

37. Summary of future sensitivities Lesgourgues & SP, Phys. Rep. 429 (2006) 307 Future cosmic shear surveys

38. End of 3rd lecture