Neutrino properties constrained by WMAP Masahiro Kawasaki ICRR, University of Tokyo
Introduction WMAP (Wilkinson Microwave Anisotropy Probe) First detailed full-sky map of the oldest light in the universe http://map.gsfc.nasa.gov/
テキスト Angular Power spectrum ℓ n ) = ∑ ∑ Δ T ( � a ℓ m Y ℓ m ( � n ) m = − ℓ ℓ � a ℓ m a ∗ ℓ ′ m ′ � = δ ℓℓ ′ δ mm ′ C ℓ Bennett et al (2003) Cosmological Parameters are determined with accuracy <10%
Cosmological Parameters WMAP only, assuming a flat universe ω b ≡ Ω b h 2 = 0 . 024 ± 0 . 001 1. Baryon ω m ≡ Ω m h 2 = 0 . 14 ± 0 . 02 2. Matter 3. Hubble h = 0 . 72 ± 0 . 05 4. Spectral Index n s = 0 . 99 ± 0 . 04 τ = 0 . 166 +0 . 076 5. Optical Depth − 0 . 071 Spergel et al (2003)
WMAP and Neutrino CMB Fluctuation (Angular Power Spectrum ) is also sensitive to Cosmic Background Neutrinos WMAP provides useful constraints on properties of Cosmic Neutrinos Neutrino Mass Number of Neutrino Species . . . .
Plan of Talk 1. Introduction 2. WMAP Constraint on Neutrino Mass 3. Limit on Number of Neutrino Species 4. Conclusion
Masses of Neutrinos Oscillation Experiments (SK, K2K, SNO, Kamland) � � 7 × 10 − 5 eV 2 � m 2 � 2 − m 2 � δm 12 = 1 � � 3 × 10 − 3 eV 2 � m 2 � 3 − m 2 � δm 23 = 2 Tritium Beta Decay (PDG2005) m ν e < 3 eV Dobble Beta Decay � � � U 2 � < � m ν � = 1 j m ν j ∼ 1 eV � � � Cosmological Constraint
� � Effect of Neutrino Mass on CMB assuming m ν 1 = m ν 2 = m ν 3 Neutrino becomes non-relativistic at recombination 1 + z nr � 6 . 2 × 10 4 Ω ν h 2 z rec � 1088 Last Scattering Surface z nr > z rec ( m ν,tot > 1 . 6 eV , Ω ν h 2 > 0 . 017) I. Position of acoustic peaks are changed z nr < z rec d LS Ω ν � ⇒ Ω Λ � ⇒ d LS � ⇒ θ � compensated by decrease of Hubble
II. Acoustic peaks are enhanced z nr > z rec neutrino: relativistic non-relativistic ω ν ≡ Ω ν h 2 6000 ω = 0 ν l(l+1)C /2 ( K ) 2 ω = 0.01 5000 ν ω = 0.02 ν Faster Decay of π µ ω = 0.03 ν 4000 Gravitational Potential 3000 l 2000 1000 More forcing of acoustic oscillation 0 0 100 200 300 400 500 600 700 800 900 l
� � WMAP Constraint on Neutrino Mass 1448 WMAP only 1444 minimizing chi2 with 6 cosmological 1440 min parameters 1436 [ Ichikawa, Fukugita, MK (2004) ] 1432 ω ν ≡ Ω ν h 2 1428 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 � � (Ω ν h 2 < 0 . 021) � m ν < 2 . 0 eV ( In future ) m ν < 0 . 66 eV m ν < 0 . 5 eV z nr > z rec
III. Gravitational Lensing Gravitational field distorts the paths traveled by CMB photons overdense region High resolution maps of CMB temperature and Ψ polarization anisotropies CMB photon Deflection angle (d) power spectrum d = ∇ φ � φ = − 2 dr Ψ( r ˆ n, r )( r − r s ) / ( rr s ) Line-of-sight projection of the gravitational potential φ
Massive Neutrino z nr < z rec Changes gravitational potential after recombination Changes deflection angle power spectrum Planck has a sensitivity down to 0.15 eV [ Kaplinghat (2003) ] m ν = 0 . 1 eV
Other Cosmological Effects of m ν Neutrino Free Streaming Erases density perturbations on small scales Changes Spectrum of Matter Fluctuations 10 5 ω = 0 ν ω = 0.01 ν ω = 0.02 ν ω = 0.03 P(k) [( h Mpc) ] ν 3 ω ν ≡ Ω ν h 2 10 4 data: SDSS -1 10 3 0.01 0.1 1 -1 k ( h Mpc )
Constraints from CMB and LSS CMB LSS Other data Limit (eV) Ref. Spergel et al 2dFGRS Ly α 0.71 WMAP+CBI+ACBAR (2003) Hannestad 2dFGRS HST,SNIa 1.01 WMAP+CBI+ACBAR (2003) 0.56+0.30 Allen et al 2dFGRS X-ray WMAP+Wang comp. (2003) -0.26 - Tegmark et al WMAP SDSS 1.7 (2003) 2dFGRS - Barger et al WMAP 0.75 +SDSS (2003) - 2dFGRS Crotty et al WMAP+ACBAR 1.0 +SDSS (2004) Sejlak et al WMAP SDSS Bias 0.54 (2004) - - Ichikawa et al WMAP 2.0 (2004)
Problem in using LSS data Spectrum of Matter Fluctuations Galaxy Survey (2dFGRS, SDSS) uncertain However, δ m � = δ galaxy b: bias P ( k ) galaxy = b 2 P ( k ) m Without information on bias stringent constraint cannot be derived For example [ only use shape of P(k) ] Tegmark et al m ν,tot < 1 . 7 eV [ shape & amplitude of P(k) ] Spergel et al m ν,tot < 0 . 71 eV
ν ν Number of Neutrino Species N Why is N important? ρ ν N ν = ρ ν,eq Sterile Neutrino or New Particles may exist N ν � Hot Universe may begin at MeV scale N ν � Dark Radiation from Extra-Dimension H 2 = 8 πG N ν � or � ρ + ρ dark 3 e.g. Rundall & Sundrum Model (1999), Shiromizu, Maeda, Sasaki (1999)
ν CBR Constraint on N -10 � ( � + 1) C � X 10 7 N = 3 6 N = 2 N = 0.5 5 4 3 2 1 0 0 200 400 600 800 1000 1200 1400 1600 � Hannestad (2003) Hannestad (2003) N ν = 2 . 1 +6 . 7 (95%CL) WMAP only − 2 . 2 N ν = 3 . 1 +3 . 9 WMAP + 2dF − 2 . 8
WMAP+CBI+2dF Crotty, Lesgourgues, Pierpaoli(2003) Pastor (2003) WMAP + CBI.+2dF WMAP + Wang comp.+2dF N ν = 4 . 3 +2 . 8 N ν = 3 . 5 +3 . 3 − 1 . 7 − 2 . 1
CBR+BBN BBN can impose a stringent limit on N ν N ν � ⇒ Y p � Fields, Olive (1998) Y p = 0 . 238 ± 0 . 005 More systematic errors? Olive, Skillman (2004) Y p = 0 . 249 ± 0 . 009 Hannestad (2003) N ν = 3 . 1 ± 0 . 7 N ν = 2 . 6 +0 . 4 Cyburt et al (2005) − 0 . 3
Summary WMAP provides a more stringent limit on neutrino mass than laboratory experiments Together with large scale structure data improve the limit WMAP also give a constraint on the number of neutrino specie
ν � H 2 h and ω degeneracy H 1 � 1 ω ν ≡ Ω ν h 2 17 ∆ ω b ω b − 26 ∆ ω m h + 36 ∆ n s ω m − 44 ∆ h ∆ � 1 = n s − 532∆ ω ν 3 . 3 ∆ ω b ω b − 3 . 1 ∆ ω m ω m − 2 . 5 ∆ h h + 18 ∆ n s n s − 1 . 6 ∆ τ ∆ H 1 = τ + 9 . 8∆ ω ν − 0 . 31 ∆ ω b ω b − 0 . 0093 ∆ ω m ω m + 0 . 42 ∆ n s ∆ H 2 = n s − 0 . 19∆ ω ν Ichikawa, Fukugita, MK (2004)
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