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

Structure formation  m + H  m = 4  G  m  m expansion gravitational forces 3H 2 =8  G  i   i  i linear growth factor   for  CDM : cdm, b cdm, b   cdm  a (MD)   for  MDM, large scales : cdm, b, cdm, b,    cdm  a   “ “, small scales : cdm, b, cdm, b   cdm  a 1-3/5 f.....

Structure formation  m + H  m = 4  G  m  m expansion gravitational forces 3H 2 =8  G  i   i  i linear growth factor   for  CDM : cdm, b cdm, b   cdm  a (MD)   for  MDM, large scales : cdm, b, cdm, b,    cdm  a   “ “, small scales : cdm, b, cdm, b   cdm  a 1-3/5 f..... smaller than free-streaming scale FS = a(t) ∫ dt/a signature of free-streaming f =  /  m ≈ (  m )/(15 eV) Bond, Efstathiou & Silk 1980

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

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

accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire ? Why is the signature of massive neutrinos non-degenerate with other cosmological parameters?

A. A.characteristic shape of matter power spectrum today Why is the signature of massive neutrinos non-degenerate with other cosmological parameters? P(k) =  m 2  k Light neutrinos step-like suppression -8f (from 3% to 60% for 0.05eV to 1eV) for 0.05eV to 1eV)

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

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

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

B. B.linear growth factor Why is the signature of massive neutrinos non-degenerate with other cosmological parameters? P(k,a)/a 2 = (1+z 2 ) P(k,z) k sCDM no linear growth factor sCDM (no DE, no m )

B. B.linear growth factor Why is the signature of massive neutrinos non-degenerate with other cosmological parameters? 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 )

B. B.linear growth factor Why is the signature of massive neutrinos non-degenerate with other cosmological parameters? 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

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

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

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

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

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

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

Weak lensing: galaxy shear

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

Late ISW and neutrino mass CMB photon gravitational potential Poisson: (k 2 /a 2 )  = 4  G  m  m Massless neutrinos, MD:  = cst   varies: - due to DE on all scales, small z - due to f on small scales, all z late ISW What is the effect of m? Suppression, or boost induced by ISW? What is the effect of m ? Suppression, or boost induced by ISW? Valkenburg, JL & Gaztanaga, in prep.

CMB and late ISW Effect of f :

CMB and late ISW

Ideal experiment:

CMB and late ISW

Ideal experiment:

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:  CDM + m  + w, using MCMC

CMB and late ISW