Sterile neutrinos and precision cosmology Yvonne Y. Y. Wong RWTH - PowerPoint PPT Presentation

Sterile neutrinos and precision cosmology Yvonne Y. Y. Wong RWTH Aachen SNAC2011, Blacksburg VA, September 25 – 28, 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 ratio fixed by SM physics Massless 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)

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 ) and sin 2 2 θ > 10 -3 .

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

1. 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

How it works: parameter degeneracies... N eff effects on the CMB... Matter-radiation equality (first ● peak height relative to plateau) Sound horizon/angular positions ● of peaks Anisotropic stress ● Damping tail ● Degeneracies... z eq affects the sound horizon: degenerate with baryon and DM densities. ● Angular positions depend on distance to LSS and hence on DE density. ●

How it works: parameter degeneracies... N eff effects on the CMB... Matter-radiation equality (first ● peak height relative to plateau) Sound horizon/angular positions ● of peaks Anisotropic stress ● Free-streaming Damping tail ● particles Degeneracies... Anisotropic stress; damps oscillations at l > 200. ● Partially degenerate with primordial fluctuation amplitude. ●

Measurement of the anisotropic stress (since WMAP-5) gives lower limit ● on N eff from CMB alone (without supplementary large-scale structure data). Komatsu et al. [WMAP5] 2008 Upper limit (pre 2010) requires combination with other observations ● (LSS, HST, SN) sensitive to the matter density and the expansion rate... OR...

How it works: parameter degeneracies... N eff effects on the CMB... Matter-radiation equality (first ● peak height relative to plateau) Sound horizon/angular positions ● of peaks Anisotropic stress ● Damping tail ● Degeneracies... N eff → higher expansion rate → more Silk damping. ● Some degeneracy with the Helium fraction. ●

N eff and the CMB damping tail: ● Different N eff visible - Matter-radiation equality in the damping tail - Baryon density (probed by ACT & SPT - Sound horizon and Planck) fixed to agree with WMAP Degeneracy with the helium fraction is not exact → Can be resolved with Planck Hou, Keisler, Knox et al. 2011

2. BBN

Evidence for N eff > 3 from BBN... Light element abundances are sensitive to excess relativistic energy ● density. Using CMB prior on ω b Baryon Helium-4 density + 0.0033 Y p = 0.2573 − 0.0088 90% Aver, Olive & Skillman 2011 99% Deuterium τ n = 878.5s log [ D / H ] p =− 4.55 ± 0.03 τ n = 885.7s Pettini et al. 2008 Effective number of sterile neutrinos N eff = 3.046 + N s Hamann, Hannestad, Raffelt & Y 3 W 2011

Evidence for N eff > 3 from BBN... Mild preference for N eff > 3 (or N s > 0) from Deuterium+Helium-4. ● But N s = 2 is strongly disfavoured. ● τ n = 878.5s τ n = 885.7s + CMB prior on baryon density Hamann, Hannestad, Raffelt & Y 3 W 2011

Quick fix: degenerate BBN... Introduce a neutrino chemical potential (= O(0.1) lepton asymmetry). ● Then even N s = 3 is allowed by BBN. ● Lepton asymmetry L ≡ n ν α − n ̄ ν α n γ 90% 12 ζ( 3 ) ( T γ ) 3 1 T ν 2 ξ+ξ 3 ) = (π 99% Neutrino chemical potential Question : How to simultaneously get L = O(0.1) and B = O(10 -10 )? Hamann, Hannestad, Raffelt & Y 3 W 2011

3. Implications for the LSND/MiniBooNE/reactor ν s

Can the reactor/MiniBooNE sterile ν explain N eff > 3? Short answer : Not so easy. ● Reason : eV mass sterile neutrinos violate CMB+LSS ν mass bounds. ● Mass of each sterile neutrino [eV] 3+1 thermalised sterile : ● CMB+SDSS7+HST m s  0.48 eV  95 % C.I.  Λ CDM+N eff +m s 99% 95% m s ~ 1 eV Lab best-fit: 3+2 thermalised sterile : 68% ● m s1  m s2  0.9 eV  95 % C.I.  m s1 ∼ 0.7 eV , m s2 ∼ 0.9 eV Number of sterile neutrinos Lab best-fit: Hamann, Hannestad, Raffelt, Tamborra & Y 3 W 2010

Is there a way out? Plan A : Suppress sterile neutrino thermalisation (e.g., using a large lepton ● asymmetry). – N eff > 3 explained by some other physics (sub-eV thermal axions, hidden photons, etc.?)

Is there a way out? Plan A : Suppress sterile neutrino thermalisation (e.g., using a large lepton ● asymmetry). – N eff > 3 explained by some other physics (sub-eV thermal axions, hidden photons, etc.?) Plan B : Failing to suppress ν s thermalisation, exploit parameter ● degeneracies in the CMB+LSS to engineer a good fit. – Some known degeneracies: ● Neutrino mass ↑ – Extra massless degrees of freedom ↑ ● Neutrino mass ↑ – Dark energy EoS parameter w ↓ Either way new physics is required...

Even more thermalised Non-standard dark energy massless species equation of state Best-fit CMB+LSS can reasonably accommodate 1 x 1 eV sterile neutrinos if we ● modify the dark energy sector and put in extra massless d.o.f. 1 x 2 eV is still problematic... ● Hamann, Hannestad, Raffelt & Y 3 W 2011 also Elgarøy & Kristiansen 2011