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)

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

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)

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

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

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

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

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 .. . .. .

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

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

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

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

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

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Minimal LCDM+3n

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

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/0603494]

LCDM+more light n’s

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

LWDM (early decoupled thermal relic)

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

- LUQAS data (few QSO, high res, conservative errorbars) 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)

LWDM (sub-case of sterile n)

… 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)

LCWDM (light gravitino)

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)

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 m3/2 ~ 100eV ( ~ 100% of gravitino DM ) EXCLUDED

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

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

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 on neutrino mass bounds future CMB + galaxy redshift surveys

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

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

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

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 : s(Mn) in eV for future CMB experiments alone :

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

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

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)

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

End

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