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GGI, Florence , 14 September 200 6 Julien Lesgourgues (LAPTH , Annecy )

cosmological constraints on neutrinos and other light relics. GGI, Florence , 14 September 200 6 Julien Lesgourgues (LAPTH , Annecy ). Cosmological perturbations offer two types of constraints on DM. If still relativistic around photon decoupling: contribution to radiation density

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GGI, Florence , 14 September 200 6 Julien Lesgourgues (LAPTH , Annecy )

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  1. cosmological constraints on neutrinos and other light relics GGI, Florence, 14 September 2006 Julien Lesgourgues (LAPTH, Annecy)

  2. Cosmological perturbations offer two types of constraints on DM • If still relativistic around photon decoupling: • contribution to radiation density • CMB anisotropies (complementary to BBN) • If <p> large enough: • damping of structures during MD caused by free-streaming • galaxy redshift surveys • lyman alpha forests in quasar spectra • (potentially also CMB, but not for most realistic candidates) • Non-trivial entanglement between the two • e.g. for scenarios with Nn light neutrinos: Nn bounds depend on Smn

  3. Cosmological perturbations offer two types of constraints on DM • If still relativistic around photon decoupling: • contribution to radiation density • CMB anisotropies (complementary to BBN) • If <p> large enough: • damping of structures during MD caused by free-streaming • galaxy redshift surveys • lyman alpha forests in quasar spectra • (potentially also CMB, but not for most realistic candidates) • Non-trivial entanglement between the two • e.g. for scenarios with Nn light neutrinos: Nn bounds depend on Smn NOT AS TRIVIAL AS USUALLY THOUGHT: -rich phenomenology -effect not so simple, not degenerate with other params -spectacular sensitivity increase with future techniques (weak lensing)

  4. accélération décélération lente décélération rqpide accélération inflation radiation matière énergie noire Theory accélération décélération lente décélération rqpide accélération ?

  5. Free-streaming and structure formation • Pure CDM • Einstein + conservation: • dcdm+ H dcdm = 4pG rcdmdcdm dcdm a during MD • expansion gravitational forces linear growth factor neglect small velocities: NO FREE STREAMING . .. P = dcdm2 LCDM power spectrum k

  6. Free-streaming and structure formation • Pure HDM (or WDM) • Einstein + Vlasov equation: •  particles with velocities cannot cluster below a diffusion length: • lFS= a(t) ∫ <v> dt/a ≤ a(t) ∫ c dt/a ~ RH(t) • relativistic: <v> c constant lFS/agoes through maximum • non-relativistic: <v> = <p>/m decays at non-relativistic transition: • lnr

  7. Free-streaming and structure formation • Pure HDM (or WDM) • lnr P HDM (standard neutrinos) WDM (smaller momenta) k

  8. Free-streaming and structure formation • mixed CDM+HDM(like standard cosmological scenario) • Einstein + conservation above free-streaming scale: • ddm+ H ddm = 4pG rdmddm ddm=dcdm = dhdm a • expansion gravitational forces linear growth factor • Einstein + conservation below free-streaming scale: • dcdm+ H dcdm = 4pG rcdmdcdm dcdm a1-3/5 fn • expansion gravitational forces scale-dependent linear growth factor • (includes rn) • with fn = rn/rm ≈ (Smn)/(15 eV) • Bond, Efstathiou & Silk 1980 . .. .. .

  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 dn J.L. & S. Pastor, Physics Reports [astro-ph/0603494] dg metric

  11. Free-streaming and structure formation • mixed CDM+HDM(like standard cosmological scenario) P -8fn (from 3% to 60% for 0.05eV to 1eV) k

  12. Free-streaming and structure formation • mixed WDM+HDM (sterile + ordinary neutrinos) P k

  13. Free-streaming and structure formation • mixed CDM+WDM+HDM (cold + sterile neutrino + light neutrinos, • axion + gravitino + light neutrinos, …) P k

  14. accélération décélération lente décélération rqpide accélération inflation radiation matière énergie noire Current bounds accélération décélération lente décélération rqpide accélération ?

  15. Minimal LCDM+3n

  16. Bounds on neutrino mass • mass bounds for 3-n scenarios : 7-parameter fits J.L. & S. Pastor, Physics Reports [astro-ph/0603494]

  17. extra parameters  degeneracies bounds grow by factor < 2 (e.g. extra rel. d.o.f., tilt running, w …) Bounds on neutrino mass • mass bounds for 3-n scenarios : 7-parameter fits J.L. & S. Pastor, Physics Reports [astro-ph/0603494]

  18. LCDM+more light n’s

  19. (Neff-1) massless n + 1 massive n Hannestad & Raeffelt astro-ph/0607086 WMAP + otherCMB + SDSS + BAO…

  20. LWDM (early decoupled thermal relic)

  21. in the approximation where fns ≈ (sinq)2 fFD(Tn) 7210eV 4430eV 2970eV 1440eV P(k)WDM ms=180eV P(k)CDM free-streaming linear galaxy correlation function Lyman-a forests

  22. LCDM LWDM msterile = 1.75 keV 30 comoving Mpc/h, 2003 particules, z=3 • Viel et al. 2005 - LUQAS data (few QSO, high res, conservative errorbars) • - full hydro-dynamical simulations (GADGET2) with 60 com. Mpc/h, • 4003 particles • m > 0.5 keV • Seljak et al. 2005 m > 2.5 keV (SDSS Ly-a + their method) • Viel et al. 2006 m > 2 keV (SDSS Lya + our method)

  23. LWDM (sub-case of sterile n)

  24. … when fns proportional to fna • Viel et al. 2005 - LUQAS data (few QSO, high res, conservative errorbars) • - full hydro-dynamical simulations (GADGET2) with 60 com. Mpc/h, • 4003 particles • m > 2 keV • Seljak et al. 2005 m > 15 keV (SDSS Ly-a + their method) • Viel et al. 2006 m > 10 keV (SDSS Lya + our method)

  25. LCWDM (light gravitino)

  26. Thermal relics… … decoupling from thermal equilibrium when relativistic, then collisionless : fn = [ep/T+1]-1 g* e.g. 106 for SM 100 QCD phase transition 10.75 e-e+ annihilation 10 light gravitino (LSP in gauge-mediated SUSY breaking) v decoupling 1 103 1 10-3 10-6 T (GeV)

  27. m3/2~ 100eV ( ~ 100% of gravitino DM ) EXCLUDED light gravitinos gauge-mediated SUSY breaking: LSP = ½ helicity component of gravitino, decouples while relativistic W3/2 h2= 0.117 (100/g*) (m3/2/100eV) with g* function of m3/2 and other masses Pierpaoli, Borgani, Masiero, Yamaguchi 97: 10 eV < m3/2 < 100 eV  g* ~ 100 (±10%) • m3/2 > 100 eV : overclose Universe • m3/2 < 10 eV : signature becomes small

  28. light gravitino Viel, JL, Haehnelt, Matarrese, Riotto 05 g*=100, (wCDM , m3/2 ) = free parameters (kFS, w3/2 ) = related parameters (CMB+LSS  wCDM+w3/2~0.125 ) • free-streaming effect:  no CMB effect (large scales : CDM=WDM) Lya sensitivity 10eV P(k)WDM 20eV 30eV P(k)CDM 50eV 70eV 100eV

  29. light gravitinos • WMAP + Lya analysis: m3/2 < 16 eV (2s) • gauge-mediated SUSY scenario: Lsusy ~ (m3/2 MP)1/2 < 260 TeV robust even for model with NSP  gravitino possible way out: entropy production after gravitino decoupling wDM Fujii & Yanagida 02; Baltz & Murayama 03

  30. Many more interesting cases… • Extra massive/massless relics interacting among themselves or with massless/massive bosons (Cirelli & Strumia) • MaVaNs (Mota et al., …) • Decaying neutrinos (Beacom et al., Hannestad et al., …) • Standard neutrinos with non-thermal corrections from decaying scalar (Cuoco et al., …) or low-scale reheating (Kawasaki et al., …) • Standard neutrinos with Bose-Einstein statistics (Dolgov et al.) • …

  31. accélération décélération lente décélération rqpide accélération inflation radiation matière énergie noire Prospects accélération décélération lente décélération rqpide accélération ?

  32. Prospects on neutrino mass bounds • future CMB+ galaxy redshift surveys

  33. Prospects on neutrino mass bounds • CMBweak lensing dT/Tobs(n)=dT/T(n+f) gravitational potential integrated along line-of-sight with window function probing up to z~3 • deflection field measurable statistically !! no bias uncertainty small scales much closer to linear regime makes CMB alone more sensitive to masses < 0.3eV

  34. Quadratic estimator : forecasts Hu & Okamoto, astro-ph/0511735 Lesgourgues, Perotto, Pastor, Piat, astro-ph/0511735

  35. Quadratic estimator : forecasts Lesgourgues, Perotto, Pastor, Piat, astro-ph/0511735

  36. s(Mn) in eV for future CMB experiments alone : Applications • sensitivity forecast in Lesgourgues, Perotto, Pastor, Piat, astro-ph/0511735 : • Fisher matrix analysis : gaussian approximation of L (qi) • derivatives dClff / dqi • results for Mn :

  37. Perotto, Lesgourgues, Hannestad, Tu, Wong, astro-ph/0606227

  38. Prospects on neutrino mass bounds • galaxy weak lensing deflection sensitive to gravitational potential integrated along line-of-sight with window function centered on d ~ dS/2 • deflection field measurable statistically !! no bias uncertainty small scales close to linear regime tomography: 3D reconstruction

  39. Prospects on neutrino mass bounds expected power spectrum of deflection field from sources at z ~ 1100 (CMB) (error for CMBpol) linear from sources at z ~ 0.2, 0.6, … 3.0 (error for LSST)

  40. Prospects on neutrino mass bounds summary of 2s expected errors on Smn(eV) : PLANCK + gal. lensing CMBpol lensing

  41. End

  42. 3 massless ns + DN massive n Cirelli & Strumia astro-ph/0607086 WMAP+otherCMB+SDSS+BAO…

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