Determining neutrino properties from precision cosmology Yvonne Y. Y. Wong RWTH Aachen International workshop on double beta decay and neutrinos, Osaka, November 14 – 17, 2011
Probe 1: Cosmic microwave background anisotropies... TT TE Many probes : EE > 0.5 deg: COBE, WMAP, ● Planck < 0.5 deg: DASI, CBI, ● ACBAR, Boomerang, VSA, QuaD, QUIET, BICEP, ACT, SPT, etc. NASA/WMAP science team
Probe 2: Large-scale structure (LSS) distribution... Galaxy clustering Cluster abundance Matter power spectrum Intergalactic Gravitational hydrogen clumps; lensing Lyman-α Tegmark et al., 2002
Probe 3: Standard candles (distance vs redshift)... Objects of known luminosity. ● Hubble diagram of SNIa measures ● luminosity distance vs redshift. Type Ia supernova (SNIa). Riess et al., 2007
Probe 4: Standard rulers (distance vs redshift)... Objects of known physical ● Large-scale correlation function size. BAO peak sourced by the ● same physics as CMB acoustic peaks → Position of peak in 2-point correlation of the matter distribution is known. Comoving separation (h -1 Mpc) Measures angular diameter ● distance vs redshift. Baryon acoustic oscillation (BAO) peak Measured by SDSS Eisenstein et al., 2005
The concordance flat Λ CDM model... The simplest model consistent with present observations . ● ν -to- γ energy density Cosmological ratio fixed by SM physics Massless constant Neutrinos (3 families) 13.4 billion years ago Composition today (at photon decoupling) Plus flat spatial geometry+initial conditions from single-field inflation
Neutrino energy density (standard picture)... Neutrino decoupling at T ~ O(1) MeV. Fixed by weak interactions ● Assuming instantaneous After e + e - annihilation (T ~ 0.2 MeV): decoupling ● T ν = ( 11 ) 1 / 3 4 – Temperature : T γ Photon temperature, number density, & ζ( 3 ) n ν = 6 3 = 3 energy density – Number density per flavour: 2 T ν 11 n γ 4 π 3 ρ ν 8 ( 11 ) 4 / 3 ρ γ ∼ 0.68 ρ ν = 7 4 = 7 4 π 2 ρ γ – Energy density per flavour: 15 T ν 8 2 = m ν ρ ν = m ν n ν If massive, then at T << m: Ω ν , 0 h ● 94 eV Hot dark matter (not within vanilla Λ CDM)
Plan... Constraining/measuring neutrino masses from cosmology. ● ● Hint of sterile neutrinos from the CMB?
Part 1: Neutrino masses from cosmology
Neutrino dark matter... m ν > T ν ~ 10 -4 eV If m ν > 1 meV, cosmological neutrinos are nonrelativistic today. ● m ν 2 = ∑ Total neutrino Ω ν , 0 h Neutrino dark matter energy density 94eV Predictions based on laboratory limits: ● min ∑ m ν ∼ 0.05 eV → min Ω ν ∼ 0.1 – Neutrino oscillations : – Tritium beta decay : max ∑ m ν ∼ 7 eV → max Ω ν ∼ 12 Neutrinos cannot make up all of the dark matter content in the universe
Neutrino hot dark matter... Neutrino dark matter comes with significant “thermal” motion. ● c ν ≃ 81 ( 1 + z ) ( m ν ) km s eV − 1 Hinders clustering Thermal speed on small scales ν z = redshift ν c c Gravitational potential wells FS ≡ 2 ≃ 4.2 Free-streaming m, 0 m h ≫ FS 2 c 2 ● 8 1 z eV − 1 Mpc Clustering length scale k ≪ k FS 3 m H & wavenumber: k FS ≡ 2 ≪ FS FS Non-clustering k ≫ k FS
In turn, free-streaming (non-clustering) neutrinos slow down the growth of ● gravitational potential wells on scales λ << λ FS or wavenumbers k >> k FS . Clustering → potential ν ν wells become deeper c c Some time later... ν Both CDM and neutrinos cluster Only CDM c clusters c ν c ν c ν c ν
|δ cdm | Initial time... |δ cdm | Some time later... Perturbation spectrum (depth of “potential wells”) CDM-only universe A Cold+Hot DM universe Large length scales Small length scales k k Perturbation wavenumber k FS (z=z nr ) Redshift at which neutrinos become nonrelativistic The presence of H ot D ark M atter slows down the growth of C old D ark ● M atter perturbations at large wavenumbers k.
Large scale matter power spectrum, P(k) CMB Galaxy clustering surveys Lyman-α f ν = Neutrino fraction P ∝ 8 f ≡ 8 P m m 2 = ∑ h 93eV
Large scale matter power spectrum, P(k) CMB Galaxy clustering surveys Lyman-α f ν = Neutrino fraction P ∝ 8 f ≡ 8 P m m 2 = ∑ h 93eV
Large scale matter power spectrum, P(k) CMB Galaxy clustering surveys “Linear” 3 P k ≡ k Lyman-α ≪ 1 2 2 f ν = Neutrino fraction P ∝ 8 f ≡ 8 P m m 2 = ∑ h 93eV
Neutrino effects on the CMB anisotropies... Present constraints come ● ∑ m = 3 × 0.4eV = 1.2eV mainly via the early ISW ∑ m = 0 effect: – γ decoupling: T ~ 0.26 eV. – Equality at T ~ 1 eV. A O(0.1-1) eV neutrino ● becomes nonrelativistic in the same time frame. WMAP7 only ( Λ CDM+m ν ): ∑ m 1.3eV 95 % C.I. CMB = Minimal nonlinear physics Komatsu et al. 2010, Hannestad et al. 2010
Present constraints... CMB (WMAP7+ACBAR+BICEP+QuaD) + LSS (SDSS-HPS) + HST+SNIa ∑ m ν < 0.44 → 0.76 eV ( 95 CI ) depending on the model complexity Hannestad, Mirizzi, Raffelt & Y 3 W 2010 Gonzalez-Garcia et al. 2010, etc. Includes uncertainties in ● Number of neutrinos ● Dark energy equation of state ● Inflation physics (tensors, running spectral index) ● Spatial curvature
Present constraints and future sensitivities... CMB (WMAP7+ACBAR+BICEP+QuaD) + LSS (SDSS-HPS) + HST+SNIa Minimal nonlinear physics ∑ m ν < 0.44 → 0.76 eV ( 95 CI ) depending on the model complexity Hannestad, Mirizzi, Raffelt & Y 3 W 2010 Gonzalez-Garcia et al. 2010, etc. Planck alone (1 year) 2012–2013 ∑ m ν < 0.38 → 0.84eV ( 95 CI ) Perotto et al. 2006 Nonlinear physics Planck+Weak lensing (LSST) 2020+ involved ∑ m ν < 0.074 → 0.086eV ( 95 CI ) Hannestad, Tu & Y 3 W 2006
Part II: Hint of sterile neutrinos from the CMB?
Experimental anomalies & the sterile ν interpretation... Experiments at odds with the standard 3-neutrino interpretation of ● global neutrino oscillation data: – LSND ( ν e appearance) – MiniBooNE anti-neutrinos ( ν e appearance) – Short baseline reactor experiments (re-evaluation of neutrino fluxes) ( ν e disappearance) If interpreted as oscillation signals → a 4th (or more) sterile neutrino ● with Δ m 2 ~ O(1 eV 2 ). Sterile = does not violate LEP bound on Z decay width
Experimental anomalies & the sterile ν interpretation... Best-fits parameters: Kopp, Maltoni & Schwetz 2011 ● Global short baseline Reactor experiments only (including LSND+MiniBooNE) “3+1” “3+2” “1+3+1” ν s ν e ν μ ν τ
Impact of light (eV mass) sterile ν on cosmology... ν μ ↔ ν s Preferred Δ m 2 and mixing → ● thermalisation of sterile neutrino state prior to neutrino decoupling. → Excess relativistic energy 0.9 density. 0.7 Neutrino 0.5 ρ ν +ρ X = N eff ( 4 ) temperature 7 2 0.3 π per definition 15 T ν Δ N eff = 0.1 8 =( 3.046 +Δ N eff ) ( 4 ) 7 2 π 15 T ν m s < m μ 8 m s > m μ Observables Di Bari, Lipari & Lusignoli 2000 CMB, large-scale structure, BBN
Impact of light (eV mass) sterile ν on cosmology... Preferred Δ m 2 and mixing → ● thermalisation of sterile neutrino state prior to neutrino decoupling. → Excess relativistic energy If the sterile neutrino is ● density. sufficiently massive → Neutrino hot dark matter . ρ ν +ρ X = N eff ( 4 ) temperature 7 2 π per definition 15 T ν m s 8 2 = Ω s h 94eV =( 3.046 +Δ N eff ) ( 4 ) 7 2 π 15 T ν 8 Observables CMB, large-scale structure, BBN CMB, large-scale structure
2a. CMB+LSS
Evidence for N eff > 3 from CMB+LSS... Recent CMB+LSS data appear to prefer N eff > 3! ● Standard value Standard value WMAP WMAP+ACT WMAP+ACT+H 0 +BAO Dunkley et al. [Atacama Cosmology Telescope] 2010 Keisler et al. [South Pole Telescope] 2011
Evidence for N eff > 3 from CMB+LSS... Adapted from S. Hannestad Trend since WMAP-1. ● Exact numbers depend on the ● cosmological model and the combination of data used. Simplest model (vanilla ● Λ CDM+N eff ): – Evidence for N eff > 3 @ 98.4% (WMAP7+ACT+ACBAR+H 0 + BAO). Hou, Keisler, Knox, et al. 2011
How it works... CMB TT (Keeping other parameters fixed) Looks easy... but we also use the same data to measure at least 6 other ● 2 , Ω m h 2 ,h ,n s , A s , τ) cosmological parameters: (Ω b h
How it works: parameter degeneracies... N eff effects on the CMB... Matter-radiation equality (first ● peak height relative to plateau) Early ISW effect Sound horizon/angular positions ● of peaks Anisotropic stress ● Damping tail ● Redshift of equality Degeneracies... Matter density 2 1 + z eq =Ω m Ω r ≈ Ω m h ● 1 1 + 0.2271 N eff 2 Ω γ h
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