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Neutrino masses from cosmological observables

ν. Neutrino masses from cosmological observables. Sergio Pastor (IFIC) Benasque Cosmology workshop 15 / 08 / 2006. Outline. Introduction: the Cosmic Neutrino Background. Relic Neutrinos as DM. Neutrino masses from cosmological observables. Effect of neutrino masses

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Neutrino masses from cosmological observables

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  1. ν Neutrino masses from cosmological observables Sergio Pastor (IFIC) Benasque Cosmology workshop 15 / 08 / 2006

  2. Outline Introduction: the Cosmic Neutrino Background Relic Neutrinos as DM Neutrino masses from cosmological observables Effect of neutrino masses on cosmological observables Current bounds and future sensitivities

  3. This is a neutrino!

  4. Neutrinos coupled by weak interactions(in equilibrium) Free-streaming neutrinos (decoupled) Cosmic Neutrino Background Neutrinos keep the energy spectrum of a relativistic fermion with eq form Primordial Nucleosynthesis T~MeV t~sec

  5. Relativistic neutrinos At least 2 species are NR today T~eV • Neutrino cosmology is interesting because Relic neutrinos are very abundant: • The CNB contributes to radiation at early times and to matter at late times (info on the number of neutrinos and their masses) • Cosmological observables can be used to test non-standard neutrino properties

  6. photons neutrinos Λ cdm m3=0.05 eV baryons m2=0.009 eV m1≈ 0 eV Evolution of the background densities: 1 MeV → now Ωi= ρi/ρcrit

  7. Neutrinos decoupled at T~MeV, keeping a spectrum as that of a relativistic species Contribution to the energy density of the Universe At present 112 per flavour The Cosmic Neutrino Background • Number density • Energy density Massless Massive mν>>T

  8. We know that flavour neutrino oscillations exist From present evidences of oscillations from experiments measuring atmospheric, solar, reactor and accelerator neutrinos Evidence of Particle Physics beyond the Standard Model !

  9. Mixing Parameters... From present evidences of oscillations from experiments measuring atmospheric, solar, reactor and accelerator neutrinos Mixing matrix U Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122

  10. Mixing Parameters... From present evidences of oscillations from experiments measuring atmospheric, solar, reactor and accelerator neutrinos Mixing matrix U Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122

  11. eV solar m0 atm ... and neutrino masses Data on flavour oscillations do not fix the absolute scale of neutrino masses eV NORMAL INVERTED atm solar What is the value of m0 ?

  12. Direct laboratory bounds on mν Searching for non-zero neutrino mass in laboratory experiments • Tritium beta decay: measurements of endpoint energy • m(νe) < 2.2 eV (95% CL) Mainz-Troitsk • Future experiments (KATRIN) m(νe) ~ 0.3 eV • Neutrinoless double beta decay: if Majorana neutrinos • 76Ge experiments: ImeeI < 0.4hN eV

  13. Cosmology < 0.3-2.0 eV Absolute mass scale searches

  14. Neutrino Free Streaming n F b, 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 • Ruled out by structure formation CDM

  15. 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 • Ruled out by structure formation CDM

  16. Neutrinos as Hot Dark Matter Massive Neutrinos can still be subdominant DM: limits on mν from Structure Formation (combined with other cosmological data)

  17. Field of density Fluctuations Matter power spectrum is the Fourier transform of the two-point correlation function Power Spectrum of density fluctuations

  18. Neutrinos as Hot Dark Matter: effect on P(k) Massive Neutrinos can still be subdominant DM: limits on mν from Structure Formation (combined with other cosmological data) • Effect of Massive Neutrinos: suppression of Power at small scales fν

  19. Structure formation after equality baryon and CDM experience gravitational clustering

  20. Structure formation after equality baryon and CDM experience gravitational clustering

  21. Structure formation after equality baryon and CDM experience gravitational clustering

  22. Structure formation after equality baryon and CDM experience gravitational clustering • growth ofdr/r (k,t)fixed by • « gravity vs. expansion » balance •  dr/ra

  23. Structure formation after equality baryon and CDM experience gravitational clustering neutrinos experience free-streaming with v = c or <p>/m

  24. Structure formation after equality baryon and CDM experience gravitational clustering baryon and CDM experience gravitational clustering neutrinos experience free-streaming with v = c or <p>/m

  25. Structure formation after equality baryon and CDM experience gravitational clustering baryon and CDM experience gravitational clustering neutrinos experience free-streaming with v = c or <p>/m neutrinos cannot cluster below a diffusion length l = ∫ v dt < ∫ c dt

  26. for (2p/k) <l , • free-streaming supresses growth of structures during MD •  dr/r a1-3/5 fnwith fn = rn /rm ≈ (Smn)/(15 eV) Structure formation after equality baryon and CDM experience gravitational clustering baryon and CDM experience gravitational clustering neutrinos experience free-streaming with v = c or <p>/m • neutrinos cannot cluster below a diffusion length l = ∫ v dt < ∫ c dt

  27. a dcdm Massless neutrinos db dn dg metric Structure formation after equality J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/0603494]

  28. Structure formation after equality a dcdm db 1-3/5fn a Massive neutrinos fν=0.1 dn dg metric J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/0603494]

  29. Effect of massive neutrinos on P(k) Observable signature of the total mass on P(k) : P(k) massive P(k) massless various fν Lesgourgues & SP, Phys. Rep. 429 (2006) 307

  30. Map of CMBR temperature Fluctuations Multipole Expansion Angular Power Spectrum DATA on CMB temperature /polarization anisotropies

  31. Effect of massive neutrinos on the CMB spectra Crotty, Lesgourgues & SP, PRD 67 (2003) • Direct effect of sub-eV massive neutrinos on the evolution of the baryon-photon coupling is very small • Impact on CMB spectra is indirect: non-zero Ωνtoday implies a change in the spatial curvature or other Ωi . The background evolution is modified • Ex: in a flat universe, • keep ΩΛ+Ωcdm+Ωb+Ων=1 • constant

  32. Effect of massive neutrinos on the CMB spectra Problem with parameter degeneracies: change in other cosmological parameters can mimic the effect of nu masses

  33. Effect of massive neutrinos on the CMB and Matter Power Spectra Max Tegmark www.hep.upenn.edu/~max/

  34. DATA How to get a bound (measurement) of neutrino masses from Cosmology Fiducial cosmological model: (Ωbh2 , Ωmh2 , h , ns , τ, Σmν) PARAMETER ESTIMATES

  35. Cosmological Data • CMB Temperature: WMAP plus data from other experiments at large multipoles (CBI, ACBAR, VSA…) • CMB Polarization: WMAP,… • Large Scale Structure: • * Galaxy Clustering (2dF,SDSS) • * Bias (Galaxy, …): Amplitude of the Matter P(k) (SDSS,σ8) • *Lyman-α forest: independent measurement of power on small scales • * Baryon acoustic oscillations (SDSS) • Bounds on parameters from other data: SNIa (Ωm), HST (h), …

  36. Cosmological Parameters: example SDSS Coll, PRD 69 (2004) 103501

  37. ν Cosmological bounds on neutrino mass(es) A unique cosmological bound on mνDOES NOT exist !

  38. Cosmological bounds on neutrino mass(es) A unique cosmological bound on mνDOES NOT exist ! • Different analyses have found upper bounds on neutrino masses, since they depend on • The combination of cosmological data used • The assumed cosmological model: number of parameters (problem of parameter degeneracies) • The properties of relic neutrinos

  39. Cosmological bounds on neutrino masses using WMAP1

  40. Cosmological bounds on neutrino masses using WMAP3 Fogli et al., hep-ph/0608060

  41. + HST, SNI-a… + BAO and/or bias + including Ly-α Neutrino masses in 3-neutrino schemes CMB + galaxy clustering Fig from Strumia & Vissani, NPB726(2005)294

  42. 02 and Cosmology Fogli et al., hep-ph/0608060

  43. Future sensitivities to Σmν When future cosmological data will be available • CMB (T+P) + galaxy redshift surveys • CMB (T+P) and CMB lensing • Weak lensing surveys • Weak lensing surveys + CMB lensing

  44. Σm detectable at 2σ if larger than • 0.21 eV (PLANCK+SDSS) • 0.13 eV (CMBpol+SDSS) Lesgourgues, SP & Perotto, PRD 70 (2004) 045016 PLANCK+SDSS • Fisher matrix analysis: expected sensitivities assuming a fiducial cosmological model, for future experiments with known specifications Fiducial cosmological model: (Ωbh2 , Ωmh2 , h , ns , τ, Σmν) = (0.0245, 0.148, 0.70 , 0.98, 0.12,Σmν)

  45. weak gravitational and CMB lensing lensing Future sensitivities to Σmν: new ideas No bias uncertainty Small scales much closer to linear regime Tomography: 3D reconstruction Makes CMB sensitive to smaller neutrino masses

  46. weak gravitational and CMB lensing lensing Future sensitivities to Σmν: new ideas sensitivity of future weak lensing survey (4000º)2 to mν σ(mν) ~ 0.1 eV Abazajian & Dodelson PRL 91 (2003) 041301 sensitivity of CMB (primary + lensing) to mν σ(mν) = 0.15 eV (Planck) σ(mν) = 0.044 eV (CMBpol) Kaplinghat, Knox & Song PRL 91 (2003) 241301 Lesgourgues, Perotto, SP & Piat PRD 73 (2006) 045021

  47. CMB lensing: recent analysis σ(Mν) in eV for future CMB experiments alone : Lesgourgues et al, PRD 73 (2006) 045021

  48. CMB lensing: recent analysis Perotto et al, astro-ph/06062271

  49. Summary of future sensitivities Future cosmic shear surveys Lesgourgues & SP, Phys. Rep. 429 (2006) 307

  50. For more details see Physics Reports 429 (2006) 307-379 [astro-ph/0603494]

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