Å rhus, 4 September 2007 Julien Lesgourgues (LAPTH , Annecy, France )

1. The Path to Neutrino Mass... ... goes to high redshift ! Århus, 4 September 2007 Julien Lesgourgues (LAPTH, Annecy, France)

2. Structure formation • dm + H dm = 4pG rmdm • expansion gravitational forces • 3H2=8pG SriSridi • linear growth factor • for LCDM : cdm, b cdm, b dcdma (MD) • for LMDM, large scales : cdm, b, n cdm, b, n  dcdm a • “ “ , small scales : cdm, b, n cdm, b dcdma1-3/5 fn .. .

3. smaller than free-streaming scale lFS = a(t) ∫ <v> dt/a signature of n free-streaming fn = rn/ rm ≈ (Smn)/(15 eV) Bond, Efstathiou & Silk 1980 Structure formation • dm + H dm = 4pG rmdm • expansion gravitational forces • 3H2=8pG SriSridi • linear growth factor • for LCDM : cdm, b cdm, b dcdma (MD) • for LMDM, large scales : cdm, b, n cdm, b, n  dcdm a • “ “ , small scales : cdm, b, n cdm, b dcdma1-3/5 fn .. .

4. Free-streaming and structure formation a dcdm db J.L. & S. Pastor, Physics Reports [astro-ph/0603494] dn dg metric

5. Free-streaming and structure formation a dcdm db 1-3/5fn a dn J.L. & S. Pastor, Physics Reports [astro-ph/0603494] dg metric

6. accélération décélération lente décélération rqpide accélération inflation radiation matière énergie noire Why is the signature of massive neutrinos non-degenerate with other cosmological parameters? accélération décélération lente décélération rqpide accélération ?

7. Why is the signature of massive neutrinos non-degenerate with other cosmological parameters? • characteristic shape of matter power spectrum today P(k) = dm2 -8fn (from 3% to 60% for 0.05eV to 1eV) k Light neutrinos step-like suppression

8. Why is the signature of massive neutrinos non-degenerate with other cosmological parameters? • characteristic shape of matter power spectrum today P dark energy k Light neutrinos step-like suppression

9. Why is the signature of massive neutrinos non-degenerate with other cosmological parameters? • characteristic shape of matter power spectrum today P primordial tilt k Light neutrinos step-like suppression

10. Why is the signature of massive neutrinos non-degenerate with other cosmological parameters? • characteristic shape of matter power spectrum today P primordial tilt tilt running k Light neutrinos step-like suppression

11. Why is the signature of massive neutrinos non-degenerate with other cosmological parameters? • linear growth factor sCDM (no DE, no mn) P(k,a)/a2 = (1+z2) P(k,z) k sCDM no linear growth factor

12. Why is the signature of massive neutrinos non-degenerate with other cosmological parameters? • linear growth factor sCDM (no DE, no mn) P(k,a)/a2 = (1+z2) P(k,z) DE+CDM (no mn) k DE+CDM scale-independent linear growth factor

13. Why is the signature of massive neutrinos non-degenerate with other cosmological parameters? • linear growth factor sCDM (no DE, no mn) P(k,a)/a2 = (1+z2) P(k,z) DE+CDM+HDM k DE+CDM+mn scale-dependent linear growth factor

14. Why is the signature of massive neutrinos non-degenerate with other cosmological parameters? • linear growth factor Large scale: D(z) = cst during MD, non-trivial during DED; Small scale:

17. Conclusion: For precise enough data, the effect of neutrino masses on CMB and LSS is clearly non-degenerate with that of any other ingredient

18. Current & future methods for detecting neutrino masses with cosmological perturbation theory • CMB (primary temperature anisotropies) Laurence • galaxy/cluster redshift surveys Ofer • galaxy weak lensing (cosmic shear surveys) Yvonne • CMB weak lensing (CMB lensing extraction) Laurence • quasar spectra (Lyman-alpha forests) • cluster counting • ISW effect

19. Possible probes of linear growth factor ? Direct study of dependence of LSS 2-point correlation function w.r.t z, using: • galaxy overdensity • cosmic shear

20. Galaxy redhsift surveys Current: 2dF, SDSS Future: SDSS-II, -III, cluster surveys … … possible to cut in redshift bins! probes this region P bias non-linear evolution -8fn (from 3% to 60% for 0.05eV to 1eV) k

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

22. Weak lensing: galaxy shear

23. CMB and late ISW • Primary CMB anisotropies not very sensitive to neutrino masses, • but various secondary effects sensitive to LSS: • weak lensing (Laurence’s talk) • Sunayev Zel’dovitch effect • late integrated Sachs Wolfe CMB photon gravitational potential

24. Late ISW and neutrino mass Valkenburg, JL & Gaztanaga, in prep. Poisson: (k2/a2)f = 4pG rmdm Massless neutrinos, MD: f= cst fvaries: - due to DE on all scales, small z - due to fn on small scales, all z late ISW What is the effect of mn? Suppression, or boost induced by ISW? CMB photon gravitational potential

25. CMB and late ISW Effect of fn :

26. CMB and late ISW

27. CMB and late ISW Ideal experiment:

28. CMB and late ISW

29. CMB and late ISW Ideal experiment:

30. CMB and late ISW Detailed error forecast for Planck + LSST Well-known sensitivity 80 gal. / sq arcmin 6 redshift bins Generate some mock data and fit it with 8-parameter model: LCDM + mn + w, using MCMC

31. CMB and late ISW 0.020 0.024