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Neutrino Cosmology: Effects on Structure Formation and Constraints on Neutrino Mass

This paper explores the impact of neutrino mass on structure formation in the universe and provides constraints on the mass of neutrinos using various observational techniques. It discusses the effects of neutrino mass on the matter power spectrum and linear growth factor, as well as future techniques for studying neutrino cosmology.

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Neutrino Cosmology: Effects on Structure Formation and Constraints on Neutrino Mass

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  1. Neutrino cosmology 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”: Smn , IH or NH detectable negligible SIDE WAYS Sterile, non-thermal, coupled, decaying, mass-varying, …

  3. accélération décélération lente décélération rqpide accélération inflation radiation matière énergie noire Effect of neutrino mass accélération décélération lente décélération rqpide accélération ?

  4. Effect of neutrino mass • Background effect: parameter Wn different from Wcdm (also DM today, but radiation in the past) e.g. increase Wn with fixed Wdm decrease Wcdm postpone M/R equality change CMB peak height (and position) and shape of matter power spectrum P(k) non-degenerate effect for flat LCDM • 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) p CDM (WIMPS) in the approximation v << c x p |v| = |p| /m = velocity dispersion x HDM (light neutrinos) with 0.01 < v/c < 1

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

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

  8. Effect of neutrino masseson (linear) structure formation dm + H dm = 4pG rmdm expansion gravitational force Below critical scale, neutrinos contribute to expansion but not to gravitational force: dm(a) slows down, [d lndm/d ln a – 1] aSmn .. .

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

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

  11. Signature of massive neutrinos on P(k) • characteristic shape of matter power spectrum today P(k) = dm2 (today) -8fn (from 3% to 60% for 0.05eV to 1eV) k Light neutrinos step-like suppression

  12. Signature of massive neutrinos on P(k) • linear growth factor sCDM (no DE, no mn) P(k,a)/a2 = (1+z)2 P(k,z) k sCDM no linear growth factor

  13. Signature of massive neutrinos on P(k) • linear growth factor sCDM (no DE, no mn) P(k,a)/a2 = (1+z)2 P(k,z) DE+CDM (no mn) k DE+CDM scale-independent linear growth factor

  14. Signature of massive neutrinos on P(k) • linear growth factor sCDM (no DE, no mn) P(k,a)/a2 = (1+z)2 P(k,z) DE+CDM+HDM k DE+CDM+mn scale-dependent linear growth factor

  15. accélération décélération lente décélération rqpide accélération inflation radiation matière énergie noire currentobservations accélération décélération lente décélération rqpide accélération ? till 2007: best constraints from free-streaming since WMAP-5yr: background effect better seen future: free-streaming more powerful

  16. Bounds on neutrino mass (95% CL) mass bounds from 7-parameter fits (LMDM = minimal LCDM+Mn) + SNIa / BAO + Lya Adapted from J.L. & S. Pastor, Physics Reports 06

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

  18. Bounds on neutrino mass (95% CL) mass bounds from 7-parameter fits (LMDM = minimal LCDM+Mn) + background (dA, dL) WMAP5 + BAO (SDSS, 2dF) + + SNIa (SNLS, ESSENCE) Komatsu et al. 08 + SNIa / BAO + Lya Adapted from J.L. & S. Pastor, Physics Reports 06

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

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

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

  22. accélération décélération lente décélération rqpide accélération inflation radiation matière énergie noire futuretechniques accélération décélération lente décélération rqpide accélération ?

  23. 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

  24. Weak lensing: CMB deflection 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 ~ 1100 (CMB) (error for CMBpol) linear from sources at z ~ 0.2, 0.6, … 3.0 (error for LSST) 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 Perotto et al. 06 Lesgourgues et al. 05 J.L. & S. Pastor, Physics Reports [astro-ph/0603494] Planck+DUNE Kitching et al 08 SNAP Song & Knox 2003 LSST

  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 s=0.006 eV (differentiate NH / IH) Pritchard & Pierpaoli 08 • Lya 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-a / 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 z=0 Saito, Takada, Taruya 0801.0607 [astro-ph] Semi-analytical method (approximation to one-loop order)

  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 inflation radiation matière énergie noire The end accélération décélération lente décélération rqpide accélération ?

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