Measuring neutrino masses with a photometric redshift survey Yvonne Y. Y. Wong RWTH Aachen [J. Hamann, S. Hannestad & Y3W, JCAP 1211 (2012) 052] Theory seminar, Université Libre de Bruxelles, February 1, 2013 The cosmic pie(s)... The ΛCDM model is the simplest model consistent with present observations. Cosmological constant Massless Neutrinos (3 families) Composition today 13.4 billion years ago (at photon decoupling) Plus flat spatial geometry+initial conditions from single-field inflation The cosmic neutrino background... Embedding the standard model in FLRW cosmology necessarily leads to a thermal neutrino background (decoupling at T ~ 1 MeV). Fixed by weak interactions Present temperature: 4 1/3 T = T =1.95K ν (11 ) γ Number density per flavour: 6 ζ(3) 3 −3 nν= T ν= 112 cm 4 π2 The cosmic neutrino background: energy density... The present-day neutrino energy density depends on whether the neutrinos are relativistic or nonrelativistic. ● Relativistic (m << T): Photon energy density 2 4/3 7 4 7 4 π 3ρν ρν= T ν= ργ ∼0.68 8 15 8 ( 11) ργ -4 ● Nonrelativistic (m >> T ~ 10 eV): 2 mν ρν=mν n ν Ω h = ν 93 eV Neutrino dark matter (not part of the vanilla ΛCDM) Flavour oscillations imply nonzero neutrino mass... Atmospheric & solar neutrino oscillations indicate that at least one neutrino mass eigenstate has a mass of > 0.05 eV. Cosmological implications: ● Relic neutrinos are nonrelativistic today. ● Present-day energy density: m Ω = ν >0.1 % ν 93 h2 eV Tritium β-decay limit on neutrino mass... Tritium β-decay end-point spectrum measurements impose an upper limit on the effective mass of the electron neutrino. Current upper limit: 2 2 1/2 me≡ ∑∣U ei∣ mi <2.2 eV i ( ) max∑ mν∼7 eV→ maxΩν∼15 % Lobashev [Troitsk] 2003; Krauss et al. [Mainz] 2005 Neutrino dark matter is hot... Neutrino dark matter come with large thermal motion. vthermal = 0 “Cold dark matter” ● Characteristic thermal speed: T ν eV −1 vthermal = ≃ 50.4(1+z) km s mν ( mν ) finite v Structures on scales below the (maximum) thermal free-streaming scale could not have been formed via gravitational instability: 1/2 −1/2 eV −1 λFS,max=31.8Ωm , 0 h Mpc (mν ) http://www.itp.uzh.ch/ cf galaxies (~100 kpc), galaxy clusters (~ 1 Mpc) Why bother with neutrino dark matter then? Because it's there. ● Neutrino dark matter = culmination of FLRW cosmology + SM + terrestrial experiment, a prediction as fundamental as the prediction of the cosmic microwave background. – Confirmation of FLRW cosmology – Determination of neutrino mass from cosmology ● You have to deal with it even if you don't care about it. – When performing parameter inference, the presence of neutrino dark matter may shift the values of those cosmological parameters you care about, e.g., inflation parameters, dark energy properties, etc. Plan... Looking for neutrino dark matter ● Direct detection ● Indirect detection Euclid sensitivity forecast ● Why Euclid is so good for the determination Cold dark matter of the neutrino mass from cosmology. Disclaimer: We are dealing with subdominant, sub-eV to eV-mass neutrino dark matter here! The bulk of the DM content is explained by something else. Neutrino DM 1. Looking for neutrino dark matter... Direct detection of neutrino dark matter... cf WIMP detection, … is a difficult business. ~ 10-46 cm2 G 2 m2 2 F ν −56 mν 2 ● Small interaction cross-section: σ ∼ ≃10 cm ν N π ( eV ) ● Neutrino energy too small to cross −3 most detection thresholds. p~m vearth ≃10 m – Conventional WIMP detection techniques don't work here. Speed of Earth with respect to the CMB, ~ 370 km s-1 A zero threshold process? ● One unique candidate here... Weinberg 1962 Cocco, Mangano & Messina 2007 Direct detection by neutrino capture... Lazauskas, Vogel & Volpe 2007 Blennow 2008 Lusignoli & Vignati 2010 β-decay end-point spectrum - 1. N → N '+e +̄νe Cν B - 2. νe +N → N ' +e Always allowed if mν+mN >mN ' +me m u r Local neutrino overdensity t c e nν p Monochromatic signal from Rate 7.5 year 100 g tritium s ∼ / / ( ) t relic neutrino capture (̄nν ) n i o p KATRIN - ∼0.1 mg tritium d n e y a c e d 2m - ν β Electron energy Qβ−mν Qβ≡mN −m N ' Qβ +mν Neutrino capture with KATRIN... Requires a 109 local overdensity of neutrinos in a 3-year run for a 90% C.L. detection. 106 CνB events/yr 0 CνB events/yr Neutrino clustering onto the Galactic halo Expected background ~ 10 mHz Kaboth, Formaggio & Monreal (2010) Indirect detection... Exploit the effects of (subdominant) neutrino dark matter on precision cosmological observables: ● Cosmic microwave background anisotropies – Effects on the evolution of the homogeneous background ● Large-scale matter distribution – Effects on the level of the inhomegeneities Neutrino dark matter and the CMB anisotropies... Background effect 1 eV mass neutrino Relativistic Nonrelativistic ● eV-mass neutrinos become nonrelativistic close to equality and photon decoupling. ● A non-trivial transition from radiation to matter domination. → Affects sound horizon. → A nonstandard early Integrated Sachs-Wolfe effect. Sachs-Wolfe effect: Gravitational potential Redshift Blueshift Observer Ψ=0 Ψ CMB photon Δ T Δ T Observed CMB = +Ψ temperature fluctuation T observed T intrinsic Integrated Sachs-Wolfe (ISW) effect: Gravitational potential Redshift Observer Ψ=0 CMB photon ● Except during matter domination, gravitational potentials decay with time. Observer – CMB photons suffer less redshift than in the case of a constant Ψ. – Larger observed temperature fluctuations: time τ T 0 Δ −κ( τ) ˙ ˙ (n̂ )=∫ d τ e [ Ψ(τ ,n̂ (τ 0−τ))+Φ(τ ,n̂ ( τ0−τ))] T ISW 0 Optical depth Early ISW effect m =1×1.2 eV ∑ ν Current constraints from m 3 0.4 eV ∑ ν= × CMB alone: ∑ mν=0 eV ∑ mν<1.2 eV (95 %C.L.) ΛCDM + neutrino mass (7 parameters) Komatsu et al. [WMAP7] 2010 Fixed total matter density ∑ mν<1.3 eV (95 %C.L.) Hinshaw et al. [WMAP9] 2012 Sound horizon shift Indirect detection... Exploit the effects of (subdominant) neutrino dark matter on precision cosmological observables: ● Cosmic microwave background anisotropies – Effects on the evolution of the homogeneous background ● Large-scale matter distribution – Effects on the level of the inhomegeneities Subdominant neutrino DM and large-scale structure... The presence of CDM acts as a source of density perturbations. ● No complete erasure of perturbations on small scales. ● But thermal motion of the relic neutrinos still makes neutrino clustering difficult. ν ν c c Gravitational potential wells Free-streaming scale: ≫ FS Clustering 2 2 k ≪k FS 8 π vthermal 1+z eV −1 2 π λFS≡ 2 ≃4.2 h Mpc ; k FS≡ Ω ≪ FS 3Ω H m ,0 ( mν ) λFS m √ Non-clustering √ k ≫k FS Consider a neutrino and a cold dark matter particle encountering two gravitational potential wells of different sizes: ν Clustering → potential ν wells become deeper c c Some time later... λ≫λ FS λ≪λ FS ν Both CDM and neutrinos cluster Only CDM c clusters c ν c ν c ν c ν → Free-streaming (non-clustering) neutrinos slows down the growth of density perturbations on scales λ<< λFS. δρ δρ ∣δ∣≡ ∣ ̄ρ ∣ Initial time... ∣ ρ̄ ∣ Some time later... Perturbation spectrum (depth of “potential wells”) CDM-only universe A cold+neutrino DM Large length scales Small length scales universe k k Perturbation wavenumber kFS(znr) znr = Redshift at which neutrinos become nonrelativistic The presence of neutrino dark matter induces a step-like feature in the spectrum of density perturbations. ) 2 k P (k)=〈∣δ(k)∣ 〉 ( P , m CMB Galaxy u r redshift t c surveys e p s r e w o Replace some CDM p with neutrinos r Lyman-α e t f = Neutrino t ν a fraction m e l a Δ P Ω ν c ∝8 f ν≡8 s P Ω m e g r 2 mν a Ων h = L ∑ 93eV ) 2 k P (k)=〈∣δ(k)∣ 〉 ( P , m CMB Galaxy u r redshift t c surveys e p s r e w o p r Lyman-α e t f = Neutrino t ν a fraction m e l a Δ P Ων c ∝8 f ν≡8 s P Ωm e g r 2 mν a Ων h = L ∑ 93eV ) 2 k P (k)=〈∣δ(k)∣ 〉 ( P , m CMB Galaxy u r redshift t c surveys e p s r e w o “Linear” 3 p k Pk r ≡ 2 ≪1 Lyman-α e 2 t f = Neutrino t ν a fraction m e l a Δ P Ων c ∝8 f ν≡8 s P Ωm e g r 2 mν a Ων h = L ∑ 93eV Change in the total matter power P P f 0k−P f 0k m ≡ ≠ = spectrum relative to the massless case: P P k m f =0 0.15 eV Linear perturbation theory: 0.3 eV P m ~8 P 0.45 eV m m Linear 0.6 eV With nonlinear corrections: Simulations (particle representation for P m both CDM and neutrinos) ~9.8 P m m Brandbyge, Hannestad, Haugbolle & Thomsen 2008; Viel, Haehnelt & Springel 2010; Bird, Viel & Haehnelt 2012 Approximation scheme Brandbyge & Hannestad 2009, 2010; (linear neutrino evolution) Ali-Haimoud & Bird 2012 3 Semi-analytical: Loops and beyond... Saito et al. 2008; Y W 2008; Shoji & Komatsu 2009 Lesgourgues, Matarrese, Pietroni & Riotto 2009 0.9 0.9 ∑ mν=0.3 eV 0.8 0.8 ∑ mν=0.6 eV 0.7 0.7 ) z = 4 z= 2.33 0 0.6 0.6 = ν m ( 0.5 0.5 P 0.0 1.0 0.0 1.0 / 0.0 ) ν 0.9 0.9 m ( P 0.8 0.8 0.7 0.7 0.6 z = 1 0.6 z = 0 = One-loop 0.5 0.5 = RG Power = + + 2 + ..