NEUTRINO MASS BOUNDS FROM COSMOLOGICAL OBSERVABLES XIth International
NEUTRINO MASS BOUNDS FROM COSMOLOGICAL OBSERVABLES ν XIth International. Workshop on Neutrino Telescopes, Venice Feb 2005 Sergio Pastor (IFIC)
NEUTRINO MASS BOUNDS FROM COSMOLOGY Relic neutrinos Effect of neutrino mass on cosmological observables Current bounds and future sensitivities
NEUTRINO MASS BOUNDS FROM COSMOLOGY Relic neutrinos Effect of neutrino mass on cosmological observables Current bounds and future sensitivities
Standard Relic Neutrinos in equilibrium fν(p, T)=f. FD(p, T)
Neutrinos in Equilibrium 1 Me. V T mμ Tν = T e = Tγ
Neutrino decoupling
Neutrino decoupling Tdec (νe) ~ 2. 3 Me. V Tdec (νμ, τ) ~ 3. 5 Me. V Decoupled Neutrinos fν(p)=f. FD(p, Tν)
Neutrino and Photon temperatures At T~me, electron-positron pairs annihilate heating photons but not the decoupled neutrinos Decoupled neutrinos stream freely until non-relativistic
The Cosmic Neutrino Background • Number density • Energy density Massless Massive mν>>T
Neutrinos and Cosmology Neutrinos influence several cosmological epochs Primordial Nucleosynthesis Cosmic Microwave Background Formation of Large Scale Structures BBN CMB LSS T~Me. V νevs νμ, τ Nν T < e. V No flavor sensitivity Nν & m ν
Primordial Nucleosynthesis: allowed ranges for Neff Non-instantaneous decoupling + Flavor Oscillations Neff =3. 045(5) T. Pinto et al, in preparation Using 4 He + D data (2σ) Cuoco et al, IJMP A 19 (2004) 4431 Baryon abundance
NEUTRINO MASS BOUNDS FROM COSMOLOGY Relic neutrinos Effect of neutrino mass on cosmological observables Current bounds and future sensitivities
CMB DATA: FIRST YEAR WMAP vs COBE
CMB DATA: INCREASING PRECISION Map of CMBR temperature Fluctuations Multipole Expansion Angular Power Spectrum
Galaxy Surveys 2 d. FGRS SDSS
2 d. FGRS Galaxy Survey ~ 13 00 pc M
Power Spectrum of density fluctuations Field of density Fluctuations CMB experiments Matter power spectrum is the Fourier transform of the two-point correlation function SDSS Galaxy Surveys
Power spectrum of density fluctuations Bias b 2(k)=Pg(k)/Pm(k) Non-linearity 2 d. FGRS SDSS kmax
Neutrinos as Dark Matter • Neutrinos are natural DM candidates • They stream freely until non-relativistic (collisionless phase mixing) Neutrinos are HOT Dark Matter • First structures to be formed when Universe became Neutrino Free Streaming matter -dominated F • Ruled out by structure formation b, cdm CDM
Neutrinos as Dark Matter • Neutrinos are natural DM candidates • They stream freely until non-relativistic (collisionless phase mixing) Neutrinos are HOT Dark Matter • First structures to be formed when Universe became matter -dominated • HDM ruled out by structure formation CDM
Neutrinos as Hot Dark Matter Massive Neutrinos can still be subdominant DM: limits on mν from Structure Formation • Effect of Massive Neutrinos: suppression of Power at small scales W. Hu
Effect of massive neutrinos on the CMB and Matter Power Spectra Max Tegmark www. hep. upenn. edu/~max/
NEUTRINO MASS BOUNDS FROM COSMOLOGY Relic neutrinos Effect of neutrino mass on cosmological observables Current bounds and future sensitivities
Cosmological bounds on neutrino mass(es) A unique cosmological bound on mν DOES NOT exist ! Different analyses have found upper bounds on neutrino masses, but they depend on • The assumed cosmological model: number of parameters (problem of parameter degeneracies) • The combination of cosmological data used
Cosmological Parameters: example SDSS Coll, PRD 69 (2004) 103501
Cosmological Data • CMB Temperature: WMAP plus data from other experiments at large multipoles (CBI, ACBAR, VSA…) • CMB Polarization: WMAP • Large Scale Structure: * Galaxy Clustering (2 d. F, SDSS) * Bias (Galaxy, …): Amplitude of the Matter P(k) (SDSS, σ8) * Lyman-α forest: independent measurement of power on small scales • Priors on parameters from other data: SNIa (Ωm), HST (h), …
Absolute mass scale searches Tritium beta decay < 2. 3 e. V Cosmology < 0. 42 -2. 0 e. V Neutrinoless double beta decay < 0. 3 -1. 2 e. V
Neutrino masses in 3 -neutrino schemes From present evidences of atmospheric and solar neutrino oscillations e. V solar atm solar 3 degenerate massive neutrinos Σmν = 3 m 0
Neutrino masses in 3 -neutrino schemes
Bound on mν after first year WMAP data 3 degenerate massive neutrinos Hannestad JCAP 0305 (2003) 004 Elgarøy & Lahav JCAP 0305 (2003) 004 Σmν < 0. 7 e. V Ωνh 2 < 0. 0076 95% CL More conservative Σmν < 1. 01 e. V m 0 < 0. 23 e. V Barger et al, PLB 595 (2004) 55 Including also SDSS Σmν < 0. 75 e. V WMAP+CBI+ACBAR+2 d. FGRS+ σ8+Lyman α Spergel et al Ap. J. Suppl. 148 (2003) 175
Cosmological bounds on neutrino mass since 2003 WMAP Coll. Ap. J Suppl 148 (2003) 175 Hannestad JCAP 0305 (2003) 004 Bound on Σmν (e. V) at 95% CL Data used 0. 7 WMAP, other CMB, 2 d. F, σ8(a) , HST 1. 01 WMAP, other CMB, 2 d. F, HST WMAP, other CMB, 2 d. F, σ8(b) , X-ray galaxy cluster Allen, Smith & Bridle MNRAS 346 (2003) 593 SDSS Coll. PRD 69 (2004) 103501 Barger. Marfatia & Tregre PLB 595 (2004) 55 Crotty, Lesgourgues & SP PRD 69 (2004) 123007 Seljak et al. astro-ph/0407372 Fogli et al. PRD 70 (2004) 113003 Ichikawa, Fukugita & Kawasaki PRD 71 (2005) 043001 1. 7 WMAP, SDSS 0. 75 WMAP, other CMB, 2 d. F, SDSS, HST 1. 0 [0. 6] WMAP, other CMB, 2 d. F, SDSS [HST] 0. 42 WMAP, SDSS (bias, galaxy clustering, Ly-α) 0. 47 WMAP, other CMB, 2 d. F, SDSS (Ly-α), HST 2. 0 WMAP
Neutrino masses in 3 -neutrino schemes Currently disfavored
Global analysis: oscillations + tritium decay + 0 2 + Cosmology CMB + 2 d. F Fogli et al. , PRD 70 (2004) 113003
The bound depends on the number of neutrinos • Example: in the 3+1 scenario, there are 4 neutrinos (including thermalized sterile) Abazajian 2002, di Bari 2002 • Calculate the bounds with Nν > 3 WMAP + Other CMB + 2 d. F + HST + SN-Ia 3ν 4ν Hannestad JCAP 0305 (2003) 004 95% CL 5ν Hannestad (also Elgarøy & Lahav, JCAP 0304 (2003) 004)
Σmν and Neff degeneracy (0 e. V, 3) (0 e. V, 7) (2. 25 e. V, 7)
Analysis with Σmν and Neff free WMAP + ACBAR + SDSS + 2 d. F Hannestad & Raffelt, JCAP 0404 (2004) 008 Crotty, Lesgourgues & SP, PRD 69 (2004) 123007 Previous + priors (HST + SN-Ia) 2σ upper bound on Σmν (e. V)
Non-thermal relic neutrinos The spectrum could be distorted after neutrino decoupling Example: decay of a light scalar after BBN Thermal FD spectrum Distortion from decay CMB + LSS data still compatible with large deviations from a thermal neutrino spectrum (degeneracy NT distortion – Neff) * Better expectations for future CMB + LSS data, but model degeneracy NT- Neff remains Cuoco, Lesgourgues, Mangano & SP, astro-ph/0502465
Future sensitivities to Σmν • Next CMB data from WMAP and PLANCK (+other CMB experiments on large l’s) temperature and polarization spectra • SDSS galaxy survey: 106 galaxies (250, 000 for 2 d. F) • Forecast analysis in WMAP and ΩΛ=0 models Hu et al, PRL 80 (1998) 5255 Sensitivity to With current best-fit values
Analysis of future bounds on Σm ν • Forecast analysis calculating the Fisher matrix Fij + CMB part Galaxy Survey part Veff ~ effective volume of the galaxy survey Estimator of the error on parameter θi Fiducial cosmological model: (Ωbh 2 , Ωmh 2 , h , ns , τ, Σmν ) = (0. 0245 , 0. 148 , 0. 70 , 0. 98 , 0. 12, Σmν )
PLANCK+SDSS Ideal CMB+40 x. SDSS Lesgourgues, SP & Perotto, PRD 70 (2004) 045016
Analysis of future sensitivities on Σm ν: summary Σm detectable at 2σ if larger than 0. 21 e. V (PLANCK+SDSS) 0. 13 e. V (CMBpol+SDSS) measure absolute ν mass scale !!! 0. 07 e. V (ideal+40 x. SDSS)
Future sensitivities to Σm ν: new ideas galaxy weak lensing and no bias uncertainty small scales in linear regime CMB lensing makes CMB sensitive to much smaller masses
Future sensitivities to Σm ν: new ideas galaxy weak lensing and CMB lensing sensitivity of future weak lensing survey (4000º)2 to mν sensitivity of CMB (primary + lensing) to mν σ(mν) ~ 0. 1 e. V σ(mν) = 0. 15 e. V (Planck) σ(mν) = 0. 04 e. V (CMBpol) Abazajian & Dodelson Kaplinghat, Knox & Song PRL 91 (2003) 041301 PRL 91 (2003) 241301
Conclusions Cosmological observables efficiently constrain some properties of (relic) neutrinos ν Bounds on the sum of neutrino masses from CMB + 2 d. FGRS or SDSS, and other cosmological data (best Σmν<0. 42 e. V, conservative Σmν<1 e. V) Sub-e. V sensitivity in the next future (0. 1 -0. 2 e. V and better) Test degenerate mass region and eventually the IH case
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