Strasbourg , 11 July 200 6 Julien Lesgourgues (LAPTH , Annecy )

neutrinos in cosmology Strasbourg, 11 July 2006 Julien Lesgourgues (LAPTH, Annecy)

accélération décélération lente décélération rqpide accélération inflation radiation matière énergie noire The standard cosmological model accélération acceleration décélération lente slow deceleration décélération rqpide fast deceleration accélération acceleration ? inflation RD (radiation domination) MD (matter domination) dark energy domination

Neutrinos in the Universe • Early Universe: thermal plasma • left-handed neutrinos baryons, other leptons, … • weak interactions • 3 species share Fermi-Dirac distribution:fn= [eE/T+1]-1 • T>>m in early Universe, so neutrinos are ultra relativistic: v ~ c , E  p , p ~ T • same density as for photons: rn= rg • effect of expansion on ulltrarelativistic neutrinos: p ~ T  a-1 , rn = rg a-4

Neutrinos in the Universe • T < MeV: neutrino decoupling: • weak interaction rate < expansion rate : freezing-out • neutrinos abandoned to themselves (gravitational coupling only) • keep Fermi-Dirac distribution • keep diluting like rn a-4 • soon after: positron annihilation: • e+ + e-g • Tg, Tn unaffected, rn = 0.68 rg a-4 • T < ?? eV: non-relativistic regime • non relativistic regime: progressively p < m • so E = mc2 , rn a-3

ln r CDM & b (H0,q,k) ln a Neutrinos in the Universe 40% 0.1% to 1% total n g (Tg) <p>=3kBTn=mn today eq

How can we prove the existence of this cosmological neutrino background ?

How can we measure neutrino masses with cosmology ?

How can we prove the existence of a cosmological neutrino background ? • direct detection very difficult: n = 340 cm-3, E < 1 eV • indirect detection: effects in early Universe, when density = 40% • Big Bang Nucleosynthesis (BBN) • Cosmological perturbations: Cosmic Microwave Background (CMB) Large Scale Structure (LSS)

Big Bang Nucleosynthesis • ensemble of nuclear reactions: • p, n, e-, n H, D, He3, He4, Li … • freeze-out caused by expansion: • relative abundances constant until today • neutrinos contribute to expansion rate: • impact on relative abundances • observations (mainly of deuterium/hydrogen): • rn/rtot = 0.4 ± 0.1 (68% confidence level)

accélération décélération lente décélération rqpide accélération inflation radiation matière énergie noire Cosmological perturbations accélération acceleration décélération lente slow deceleration décélération rqpide fast deceleration • inhomogeneities decomposed in comobile Fourier space • physical wavelengths grow with scale factor : l(t) = (2p/k) a(t) • causal horizon during RD/MD grows with Hubble radius : d(t1,t2)  c/H  t gravity / photon pressure  acoustic oscillations of g , b inside horizon gravity only  gravitational clustering of b, CDM inside horizon accélération acceleration quantum fluctuations ? inflation RD (radiation domination) MD (matter domination) dark energy domination Theory :

accélération décélération lente décélération rqpide accélération inflation radiation matière énergie noire  photon power spectra Cosmological observations accélération acceleration décélération lente slow deceleration décélération rqpide fast deceleration accélération acceleration z ≈ 1100 ? inflation RD (radiation domination) MD (matter domination) dark energy domination • Best data available: • WMAP (3yrs) CMB temperature/polarization anisotropies

accélération décélération lente décélération rqpide accélération bias uncertainty … 60 Mpc inflation radiation matière énergie noire linear non-linear dr/r<1 dr/r~1 matter power spectrum P(k) Cosmological observations accélération acceleration décélération lente slow deceleration décélération rqpide fast deceleration accélération acceleration 0<z<0.2 ? inflation RD (radiation domination) MD (matter domination) dark energy domination • Best data available: • 2dF GRS • SDSS galaxy redshift surveys

Cosmological perturbationsand neutrinos • physics of acoustic oscillations and structure formation • sensitive to relative abundance of matter/radiation • combined analysis of CMB+LSS gives result consitent BBN with • similar errorbar (30% at the 68% confidence level) • error bar could shrink by factor ~10 in the future Existence of cosmic neutrino background proved indirectly by two independent methods!

How can we measure neutrino masses with cosmology ?

accélération décélération lente décélération rqpide accélération inflation radiation matière énergie noire How can we measure neutrino masses with cosmology? accélération acceleration décélération lente slow deceleration décélération rqpide fast deceleration gravity only  gravitational clustering of b, CDM inside horizon accélération acceleration ? inflation RD (radiation domination) MD (matter domination) dark energy domination structure formation after equality

Structure formation after equality baryon and CDM experience gravitational clustering

growth ofdr/r (k,t)fixed by • « gravity vs. expansion » balance •  dr/ra Structure formation after equality baryon and CDM experience gravitational clustering

Structure formation after equality baryon and CDM experience gravitational clustering neutrinos experience free-streaming at v = c or <p>/m

Structure formation after equality baryon and CDM experience gravitational clustering neutrinos experience free-streaming at v = c or <p>/m • neutrinos cannot cluster below a diffusion length l = ∫ v dt < ∫ c dt

for (2p/k) <l , • free-streaming prevents growth of structure during MD : •  dr/r a1-3/5 fnwith fn = rn /rm ≈ (Smn)/(15 eV) Structure formation after equality baryon and CDM experience gravitational clustering neutrinos experience free-streaming at v = c or <p>/m • neutrinos cannot cluster below a diffusion length l = ∫ v dt < ∫ c dt

Structure formation after equality a dcdm db J.L. & S. Pastor, Physics Reports, in press [astro-ph/0603494] dn dg metric

Structure formation after equality a dcdm db 1-3/5fn a J.L. & S. Pastor, Physics Reports, in press [astro-ph/0603494] dn dg metric

Effect of neutrino mass • observable signature of the total mass on P(k) : P(k) massive P(k) massless various fn

m 0.05 eV 2 D » atm m 0.009 eV 2 D » sun Bounds on neutrino mass • situation taking neutrino oscillationdata into account: at least 3% effect in P(k)

Bounds on neutrino mass • mass bounds for 3-n scenarios : THERE IS NOT A UNIQUE « COSMOLOGICAL BOUND » !!! • depends on the exact data set • depends on the underlying cosmological model

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 Lighest neutrino mass (eV)

Bounds on neutrino mass • experiments sensitive to absolute neutrino mass scale : KATRIN: 0.2 eV ?? (2s) dep. on CP phases, Dirac/Majorana

Prospects

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

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

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

Strasbourg , 11 July 200 6 Julien Lesgourgues (LAPTH , Annecy )