1. DESY, 30 September 2008 Julien Lesgourgues (CERN & EPFL)

2. MAIN STREAM DM = CDM + 3 flavor neutrinos, with 2 or 3 massive eigenstates 2 unknown “cosmological parameters”:  m , IH or NH detectable negligible SIDE WAYS Sterile, non-thermal, coupled, decaying, mass-varying, …

3. accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire ? Effect of neutrino mass

4.   Background effect: parameter  different from  cdm (also DM today, but radiation in the past) e.g. increase  with fixed  dm decrease  cdm postpone M/R equality change CMB peak height (and position) and shape of matter power spectrum P(k) non-degenerate effect for flat  CDM   Effect on perturbations: free-streaming slows down structure formation

5. Perfect versus free-streaming fluid   Perfect fluid = strongly coupled particles with bulk velocity (in the linear regime: single-valued velocity field)   Free-streaming particles = collisionless particles with f(x,p,t) ≈ f(p,t) x p x p  |v|  =  |p|  /m = velocity dispersion CDM (WIMPS) in the approximation  v  << c HDM (light neutrinos) with 0.01 <  v  /c < 1

6. Free-streaming scale distances time   a inflation RADIATION DOMINATION eq MATTER DOMINATION acausal causal RHRH perturbation wavelength

7. Free-streaming scale distances time   a inflation RADIATION DOMINATION eq MATTER DOMINATION acausal causal RHRH perturbation wavelength maximum comoving f.s.s. free-streaming scale (10 -4 eV < m < 1 eV) nr heavylight

8. Effect of neutrino masses on (linear) structure formation  m + H  m = 4  G  m  m expansion gravitational force Below critical scale, neutrinos contribute to expansion but not to gravitational force:  m (a) slows down, [ d ln  m / d ln a – 1 ]   m...

9.  cdm bb   metric a J.L. & S. Pastor, Physics Reports [astro-ph/0603494] Free-streaming and structure formation

10.  cdm bb   metric a 1-3/5f a J.L. & S. Pastor, Physics Reports [astro-ph/0603494] Free-streaming and structure formation (f =  /  m )

11. A. A.characteristic shape of matter power spectrum today Signature of massive neutrinos on P(k) P(k) =  m 2  (today) k Light neutrinos step-like suppression -8f (from 3% to 60% for 0.05eV to 1eV) for 0.05eV to 1eV)

12. B. B.linear growth factor Signature of massive neutrinos on P(k) P(k,a)/a 2 = (1+z) 2 P(k,z) k sCDM no linear growth factor sCDM (no DE, no m )

13. B. B.linear growth factor Signature of massive neutrinos on P(k) P(k,a)/a 2 = (1+z) 2 P(k,z) k DE+CDM scale-independent linear growth factor sCDM (no DE, no m ) DE+CDM (no m )

14. B. B.linear growth factor Signature of massive neutrinos on P(k) P(k,a)/a 2 = (1+z) 2 P(k,z) k DE+CDM+m scale-dependent linear growth factor sCDM (no DE, no m ) DE+CDM+HDM

15. accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire ? current observations till 2007: best constraints from free-streaming since WMAP-5yr: background effect better seen future: free-streaming more powerful

16. mass bounds from 7-parameter fits (  MDM = minimal  CDM+M ) Bounds on neutrino mass Adapted from J.L. & S. Pastor, Physics Reports 06 (95% CL) + SNIa / BAO + Ly 

17. mass bounds from 7-parameter fits (  MDM = minimal  CDM+M ) Bounds on neutrino mass Adapted from J.L. & S. Pastor, Physics Reports 06 (95% CL) + SNIa / BAO + Ly  CMB only WMAP5 Dunkley et al. 08

18. mass bounds from 7-parameter fits (  MDM = minimal  CDM+M ) Bounds on neutrino mass Adapted from J.L. & S. Pastor, Physics Reports 06 WMAP5 + BAO (SDSS, 2dF) + + SNIa (SNLS, ESSENCE) Komatsu et al. 08 + SNIa / BAO + Ly  + background (d A, d L ) (95% CL)

19. mass bounds from 7-parameter fits (  MDM = minimal  CDM+M ) Bounds on neutrino mass Adapted from J.L. & S. Pastor, Physics Reports 06 WMAP3 + SDSS-LRG/BAO + 2dF + SNIa Hannestad et al. 07, Kristiansen et al. 07 + SNIa / BAO + Ly  + galaxy power spectrum (95% CL)

20. mass bounds from 7-parameter fits (  MDM = minimal  CDM+M ) Bounds on neutrino mass Adapted from J.L. & S. Pastor, Physics Reports 06 WMAP3 + SDSS-LRG/BAO + 2dF + SNIa Hannestad et al. 07, Kristiansen et al. 07 + SNIa / BAO + Ly  + galaxy power spectrum (95% CL) limited to scales still linear today: suppression effect in power spectrum P(k)

21. mass bounds from 7-parameter fits (  MDM = minimal  CDM+M ) Bounds on neutrino mass Adapted from J.L. & S. Pastor, Physics Reports 06 WMAP5 + other CMB + SDSS-LRG/BAO + SNIa + SDSS-Ly  Fogli et al. 08 + SNIa / BAO + Lyman-  forest (95% CL)

22. accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire ? future techniques

23. Weak lensing: galaxy shear Future: many dedicated surveys (CFHTLS, DES, SNAP, Pan-STARRS, LSST, Dune, …) Map of gravitational potential projected along line-of-sight COSMOS Massey et al., Nature 05497, 7 january 2007 tomography

24. Weak lensing: CMB deflection map of gravitational potential map of gravitational potential projected along line-of-sight, especially around z~3

25. Weak lensing: theoretical prediction Lensing spectrum (= convergence spectrum) expected power spectrum of lensing potential from sources at z ~ 0.2, 0.6, … 3.0 (error for LSST) from sources at z ~ 1100 (CMB) (error for CMBpol) linear Song & Knox [astro-ph/0312175]

26. Weak lensing: theoretical prediction Lensing potential spectrum

27. Weak lensing: observation with Planck JL, Perotto, Pastor, Piat Phys.Rev.D73:045021,2006

28. Weak lensing: forecasts J.L. & S. Pastor, Physics Reports [astro-ph/0603494] LSST SNAP Planck+DUNE Kitching et al 08 Perotto et al. 06 Lesgourgues et al. 05 Song & Knox 2003

29. Other promising techniques   ISW effect induced by free-streaming during MD/DED Detectable with CMB x LSS cross-correlation Ichikawa & Takahashi 05 Lesgourgues, Valkenburg & Gaztanaga 07   Cluster redshift surveys Wang et al. 05   21cm surveys (21cm line emission by residual cosmic hydrogen after reionization) Wyithe & Loeb 08  =0.006 eV (differentiate NH / IH) Pritchard & Pierpaoli 08   Ly  forests in quasar spectra Gratton et al. 07

30. Impact of massive neutrinos on non-linear gravitational clustering … is a crucial to understand, in order to: - Extend analysis of galaxy / cluster/ cosmic shear surveys to larger k - Perform proper analysis of Ly-  / BAO / 21cm data - Properly extract / interpret CMB foregrounds (thermal SZ) - Precisely address small-scale CDM distribution problem (satellites)

31. Impact of massive neutrinos on non-linear gravitational clustering Brandbyge et al. 0802.3700 [astro-ph] N-body simulations including thermal velocities

32. Impact of massive neutrinos on non-linear gravitational clustering Saito, Takada, Taruya 0801.0607 [astro-ph] Semi-analytical method (approximation to one-loop order) z=0

33. Impact of massive neutrinos on non-linear gravitational clustering Y.Y.Y.Wong 0809.0693 [astro-ph] Semi-analytical method (one-loop order)

34. accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire ? The end