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

This presentation explores constraints on dark matter from cosmological perturbations and the entanglement between neutrinos and relics. It delves into radiation density contributions, CMB anisotropies, damping of structures, and galaxy surveys. The non-trivial entwining of these elements offers rich phenomenology and potential sensitivity increases with advanced techniques.

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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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