GGI Florence 14 September 200 6 Julien Lesgourgues

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

Cosmological perturbations offer two types of constraints on DM 1) If still relativistic around photon decoupling: 2) contribution to radiation density 3) CMB anisotropies (complementary to BBN) 2) If <p> large enough: 3) damping of structures during MD caused by freestreaming 4) galaxy redshift surveys 5) lyman alpha forests in quasar spectra 6) (potentially also CMB, but not for most realistic candidates)

Cosmological perturbations offer two types of constraints on DM 1) If still relativistic around photon decoupling: 2) contribution to radiation density 3) CMB anisotropies (complementary to BBN) 2) If <p> large enough: 3) damping of structures during MD caused by freestreaming 4) galaxy redshift surveys 5) lyman alpha forests in quasar spectra NOT AS TRIVIAL AS USUALLY THOUGHT: -rich phenomenology 6) (potentially also CMB, but not for most realistic -effect not so simple, not degenerate with other candidates) params -spectacular sensitivity increase with future techniques (weak lensing)

? non réartaitoi é l l é é acaccc inflation de rqrpqipdie n n o o i i t t a a r r dcéécléélé dé nte ononlele titi rara élé dcééclé dé artaitoinon acaccécléélré Theory radiation matière énergie noire

Free-streaming and structure formation 1) Pure CDM neglect small velocities: 2) Einstein + conservation: . . . 3) dcdm+ H dcdm = 4 p. G rcdmdcdm NO FREE STREAMING dcdm a during MD expansion P= gravitational forces dcdm 2 linear growth factor LCDM power spectrum k

Free-streaming and structure formation 2) Pure HDM (or WDM) Einstein + Vlasov equation: particles with velocities cannot cluster below a diffusion length: l. FS = a(t) ∫ <v> • relativistic: <v> dt/a c ≤ a(t) ∫ c dt/a ~ R H(t) constant l. FS/a goes through maximum • non-relativistic : <v> = <p>/m transition: decays at non-relativistic

Free-streaming and structure formation 2) Pure HDM (or WDM) lnr P HDM (standard neutrinos) WDM (smaller momenta ) k

Free-streaming and structure formation 3) mixed CDM+HDM (like standard cosmological scenario) Einstein + conservation above free-streaming scale: . . . ddm+ H ddm = 4 p. G rdmddm ddm= dcdm = dhdm a expansion gravitational forces linear growth factor 1) Einstein + conservation below free-streaming scale: . . . 2) dcdm+ H dcdm = 4 p. G rcdmdcdm a 1 -3/5 fn expansion factor (includes gravitational forces rn ) ≈ (Smn)/(15 e. V) scale-dependent linear growth with fn = rn /rm Bond, Efstathiou & Silk 1980

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

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

Free-streaming and structure formation 3) mixed CDM+HDM (like standard cosmological scenario) P -8 f n (from 3% to 60% for 0. 05 e. V to 1 e. V) k

Free-streaming and structure formation 4) mixed WDM+HDM (sterile + ordinary neutrinos) P k

Free-streaming and structure formation 5) mixed CDM+WDM+HDM (cold + sterile neutrino + light neutrinos, P neutrinos, …) axion + gravitino + light k

? non réartaitoi é l l é é acaccc inflation Current bounds de rqrpqipdie n n o o i i t t a a r r dcéécléélé dé radiation nte ononlele titi rara élé dcééclé dé matière artaitoinon acaccécléélré énergie noire

Minimal LCDM+3 n

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

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

LCDM+mor e light n’s

(Neff-1) massless n + 1 massive n Hannestad & Raeffelt astro-ph/0607086 WMAP + other. CMB

LWDM (early decoupled thermal relic)

in the approximation where fns ≈ (sin q)2 f. FD(Tn) 40 14 e. V m s= e. V 180 P(k)WDM P(k)CDM 721 443 0 e. V 29 0 e. V 70 e. V free-streaming linear galaxy correlation function Lyman- a forests

LCDM LWDM msterile = 30 comoving Mpc/h, 200 3 1. 75 ke. V particules, z=3 § Viel et al. 2005 - LUQAS data (few QSO, high res, conservative errorbars ) - full hydro-dynamical simulations (GADGET 2) with 60 com. Mpc/h 400 3 particles m > 0. 5 ke. V § Seljak et al. 2005 m > 2. 5 § Viel et al. 2006 m>2 ke. V (SDSS Ly- a + their method) ke. V (SDSS Ly a + our method)

LWDM (sub-case of sterile n)

… when f ns proportional to fna § Viel et al. 2005 - LUQAS data (few QSO, high res, conservative errorbars ) - full hydro-dynamical simulations (GADGET 2) with 60 com. Mpc/h 400 3 particles m>2 ke. V § Seljak et al. 2005 m > 15 § Viel et al. 2006 m > 10 ke. V (SDSS Ly- a + their method) ke. V (SDSS Ly a + our method)

LCWDM (light gravitino)

Thermal relics… … decoupling from thermal equilibrium when relativistic, then collisionless : fn = [e g* p/T+1] -1 e. g. 106 for SM 100 QC e has p D t 10. 75 light gravitino (LSP in gaugemediated SUSY breaking ) 10 1 10 3 1 ion t i s ran ion at l i h i n - e+ an e v decoupling T ( Ge. V) 10 -3 10 -6

light gravitinos gauge-mediated SUSY breaking: LSP = ½ helicity component of gravitino, decouples while relativistic W 3/2 h 2 = 0. 117 (100/g*) (m 3/2/100 e. V) with g* function of m 3/2 and other masses Pierpaoli, Borgani, Masiero, Yamaguchi 97: 10 e. V < m 3/2 < 100 e. V g* ~ 100 (± 10%) m 3/2 ~ 100 e. V § m 3/2 > 100 e. V : overclose Universe( ~ 100% of gravitino DM ) § m 3/2 < 10 e. V : signature becomes small EXCLUDED

light gravitino Viel, JL, Haehnelt, Matarrese, Riotto 05 g*=100, (w. CDM , m 3/2 ) = free parameters (k. FS, w 3/2 ) = related parameters (CMB+LSS w. CDM+w 3/2~0. 125 ) Lya sensitivity free-streaming effect: e. V 50 V 70 e 100 e. V no CMB effect (large scales : CDM=WDM) P(k)WDM P(k)CDM 10 e. V 20 e V 30 e V

light gravitinos WMAP + Lya analysis: m 3/2 < 16 e. V (2 s) q w. DM q gauge-mediated SUSY scenario: Lsusy ~ (m 3/2 MP)1/2 < 260 Te. V robust even for model with NSP gravitino possible way out: entropy production after gravitino Fujii & Yanagida 02; Baltz & Murayama 03 decoupling

Many more interesting cases… § Extra massive/ massless relics interacting among themselves or with massless/massive bosons (Cirelli & Strumia) § Ma. Va. Ns (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. )

? non réartaitoi é l l é é acaccc inflation de rqrpqipdie n n o o i i t t a a r r dcéécléélé dé nte ononlele titi rara élé dcééclé dé artaitoinon acaccécléélré Prospects radiation matière énergie noire

1) Prospects on neutrino mass bounds future CMB + galaxy redshift surveys

Prospects on neutrino mass bounds 2) CMB weak lensing d. T/Tobs(n)= d. T/T(n+ f) gravitational potential integrated along line-of-sight with window function probing up to z~3 Ø deflection field measurable statistically !! no bias uncertainty small scales much closer to linear regime makes CMB alone more sensitive to masses < 0. 3 e. V

Quadratic estimator : forecasts Hu & Okamoto, astroph/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 : Ø Fisher matrix analysis : gaussian approximation of L (qi) Ø derivatives d. Clff / dqi Ø results for Mn : s(Mn) in e. V for future CMB experiments alone :

h/0606227 erotto, Lesgourgues, Hannestad, Tu, Wong, astro-

Prospects on neutrino mass bounds 3) galaxy weak lensing deflection sensitive to gravitational potential along function d. S/2 integrated line-of-sight with window centered on d~

Prospects on neutrino mass bounds expected power spectrum of deflection field from sources at z ~ 1100 (CMB) (error for CMBpol) ar e lin from sources at z ~ 0. 2, 0. 6, … 3. 0 (error for LSST)

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

End

3 massless ns + DN massive n Cirelli & Strumia astro-ph/0607086 WMAP+other. CM