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GGI, Florence, 14 September 2006 Julien Lesgourgues (LAPTH, Annecy)
cosmological constraints on neutrinos and other light relics GGI, Florence, 14 September 2006 Julien Lesgourgues (LAPTH, Annecy)
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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
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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)
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Theory ? accélération décélération lente décélération rqpide inflation
radiation matière énergie noire accélération décélération lente décélération rqpide accélération ?
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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
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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/a goes through maximum non-relativistic: <v> = <p>/m decays at non-relativistic transition: lnr
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Free-streaming and structure formation
Pure HDM (or WDM) lnr P HDM (standard neutrinos) WDM (smaller momenta) k
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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 .. . .. .
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Free-streaming and structure formation
dcdm db J.L. & S. Pastor, Physics Reports [astro-ph/ ] dn dg metric
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Free-streaming and structure formation
dcdm db a 1-3/5fn dn J.L. & S. Pastor, Physics Reports [astro-ph/ ] dg metric
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Free-streaming and structure formation
mixed CDM+HDM (like standard cosmological scenario) P -8fn (from 3% to 60% for 0.05eV to 1eV) k
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Free-streaming and structure formation
mixed WDM+HDM (sterile + ordinary neutrinos) P k
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Free-streaming and structure formation
mixed CDM+WDM+HDM (cold + sterile neutrino + light neutrinos, axion + gravitino + light neutrinos, …) P k
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Current bounds ? accélération décélération lente décélération rqpide
inflation radiation matière énergie noire accélération décélération lente décélération rqpide accélération ?
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Minimal LCDM+3n
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Bounds on neutrino mass
mass bounds for 3-n scenarios : 7-parameter fits J.L. & S. Pastor, Physics Reports [astro-ph/ ]
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Bounds on neutrino mass
extra parameters degeneracies bounds grow by factor < 2 (e.g. extra rel. d.o.f., tilt running, w …) mass bounds for 3-n scenarios : 7-parameter fits J.L. & S. Pastor, Physics Reports [astro-ph/ ]
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LCDM+more light n’s
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(Neff-1) massless n + 1 massive n Hannestad & Raeffelt astro-ph/ WMAP + otherCMB + SDSS + BAO…
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LWDM (early decoupled thermal relic)
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P(k)WDM P(k)CDM in the approximation where fns ≈ (sinq)2 fFD(Tn)
7210eV 4430eV 1440eV 2970eV P(k)WDM ms=180eV P(k)CDM free-streaming linear galaxy correlation function Lyman-a forests
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- LUQAS data (few QSO, high res, conservative errorbars)
LCDM LWDM msterile = keV 30 comoving Mpc/h, 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 m > 2.5 keV (SDSS Ly-a + their method) Viel et al m > 2 keV (SDSS Lya + our method)
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LWDM (sub-case of sterile n)
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… 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 m > 15 keV (SDSS Ly-a + their method) Viel et al m > 10 keV (SDSS Lya + our method)
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LCWDM (light gravitino)
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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 10 light gravitino (LSP in gauge-mediated SUSY breaking) e-e+ annihilation v decoupling 1 103 1 10-3 10-6 T (GeV)
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light gravitinos gauge-mediated SUSY breaking:
LSP = ½ helicity component of gravitino, decouples while relativistic W3/2 h2 = (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 m3/2 ~ 100eV ( ~ 100% of gravitino DM ) EXCLUDED
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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
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light gravitinos Lsusy ~ (m3/2 MP)1/2 < 260 TeV
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
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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.) …
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Prospects ? accélération décélération lente décélération rqpide
inflation radiation matière énergie noire accélération décélération lente décélération rqpide accélération ?
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Prospects on neutrino mass bounds
future CMB + galaxy redshift surveys
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Prospects on neutrino mass bounds
CMB weak 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
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Quadratic estimator : forecasts
Hu & Okamoto, astro-ph/ Lesgourgues, Perotto, Pastor, Piat, astro-ph/
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Quadratic estimator : forecasts
Lesgourgues, Perotto, Pastor, Piat, astro-ph/
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Applications sensitivity forecast in Lesgourgues, Perotto, Pastor, Piat, astro-ph/ : Fisher matrix analysis : gaussian approximation of L (qi) derivatives dClff / dqi results for Mn : s(Mn) in eV for future CMB experiments alone :
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Perotto, Lesgourgues, Hannestad, Tu, Wong, astro-ph/0606227
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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
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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)
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Prospects on neutrino mass bounds
summary of 2s expected errors on Smn (eV) : PLANCK + gal. lensing CMBpol lensing
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End
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3 massless ns + DN massive n Cirelli & Strumia astro-ph/ WMAP+otherCMB+SDSS+BAO…
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