Neutrino masses from cosmological observables Sergio Pastor IFIC
Neutrino masses from cosmological observables ν 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 on cosmological observables Current bounds and future sensitivities
This is a neutrino!
Free-streaming neutrinos (decoupled) Cosmic Neutrino Background Neutrinos coupled by weak interactions (in equilibrium) Neutrinos keep the energy spectrum of a relativistic fermion with eq form al sis di e or nth im y Pr leos uc N T~Me. V t~sec
t 2 s a le e At ies ar c y spe toda NR os Rel T~e. V tic s i v ati rin t u ne 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
Evolution of the background densities: 1 Me. V → now photons Ωi= ρi/ρcrit neutrinos Λ cdm baryons m 3=0. 05 e. V m 2=0. 009 e. V m 1≈ 0 e. V
The Cosmic Neutrino Background Neutrinos decoupled at T~Me. V, keeping a spectrum as that of a relativistic species • Number density At present 112 per flavour • Energy density Massless Contribution to the energy density of the Universe Massive mν>>T
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 !
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
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
. . . and neutrino masses Data on flavour oscillations do not fix the absolute scale of neutrino masses e. V solar atm INVERTED NORMAL atm solar What is the value of m 0 ? m 0
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 e. V (95% CL) Mainz-Troitsk Future experiments (KATRIN) m(νe) ~ 0. 3 e. V • Neutrinoless double beta decay: if Majorana neutrinos 76 Ge experiments: Imee. I < 0. 4 h. N e. V
Absolute mass scale searches Tritium decay < 2. 2 e. V Neutrinoless double beta decay < 0. 4 -1. 6 e. V Cosmology < 0. 3 -2. 0 e. V
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 • Ruled out by structure formation CDM
Neutrinos as Hot Dark Matter Massive Neutrinos can still be subdominant DM: limits on mν from Structure Formation (combined with other cosmological data)
Power Spectrum of density fluctuations Field of density Fluctuations Matter power spectrum is the Fourier transform of the two-point correlation function
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
Structure formation after equality baryon and CDM experience gravitational clustering
Structure formation after equality baryon and CDM experience gravitational clustering
Structure formation after equality baryon and CDM experience gravitational clustering
Structure formation after equality baryon and CDM experience gravitational clustering growth of dr/r (k, t) fixed by « gravity vs. expansion » balance dr/r a
Structure formation after equality baryon and CDM experience gravitational clustering neutrinos experience free-streaming with v = c or <p>/m
Structure formation after equality baryon and CDM experience gravitational clustering neutrinos experience free-streaming with v = c or <p>/m
Structure formation after equality 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
Structure formation after equality baryon and CDM experience gravitational clustering neutrinos experience free-streaming with v = c or <p>/m for (2 p/k) < l , o neutrinos cannotsupresses cluster below diffusion length free-streaming growtha of structures during MD l = ∫ 1 -3/5 v dtf dr/r a < ∫ c dt with f = r /rm ≈ (Sm )/(15 e. V)
Structure formation after equality a dcdm Massless neutrinos db d dg metric J. Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/0603494]
Structure formation after equality a dcdm db a 1 -3/5 f d Massive neutrinos fν=0. 1 dg metric J. Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/0603494]
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, Rep. 429 (2006) 307 Phys.
DATA on CMB temperature /polarization anisotropies Map of CMBR temperature Fluctuations Multipole Expansion Angular Power Spectrum
Effect of massive neutrinos on the CMB spectra 1) Direct effect of sub-e. V massive neutrinos on the evolution of the baryon-photon coupling is very small 2) Impact on CMB spectra is indirect: non-zero Ων today 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 Crotty, Lesgourgues & SP, PRD 67 (2003)
Effect of massive neutrinos on the CMB spectra Problem with parameter degeneracies: change in other cosmological parameters can mimic the effect of nu masses
Effect of massive neutrinos on the CMB and Matter Power Spectra Max Tegmark www. hep. upenn. edu/~max/
How to get a bound (measurement) of neutrino masses from Cosmology Fiducial cosmological model: (Ωbh 2 , Ωmh 2 , h , ns , τ, Σmν ) DATA PARAMETER ESTIMATES
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 * Baryon acoustic oscillations (SDSS) Bounds on parameters from other data: SNIa (Ωm), HST (h), …
Cosmological Parameters: example SDSS Coll, PRD 69 (2004) 103501
Cosmological bounds on neutrino mass(es) A unique cosmological bound on mν DOES NOT exist ! ν
Cosmological bounds on neutrino mass(es) A unique cosmological bound on mν DOES 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
Cosmological bounds on neutrino masses using WMAP 1 Bound on Σmν (e. V) [95% CL] Data used Ichikawa et al, PRD 71 (2005) 043001 Sánchez et al, MNRAS 366 (2006) 189 Mac. Tavish et al, astro-ph/0507503 1. 6 - 3. 1 CMB only Hannestad, JCAP 0305 (2003) 004 SDSS Coll. , PRD 69 (2004) 103501 Barger et al, PLB 595 (2004) 55 Crotty et al, PRD 69 (2004) 123007 Rebolo et al, MNRAS 353 (2004) 747 Fogli et al. PRD 70 (2004) 113003 Seljak et al, PRD 71 (2005) 103515 Sánchez et al, MNRAS 366 (2006) 189 Mac. Tavish et al, astro-ph/0507503 1. 0 - 1. 7 [0. 6 -1. 2] WMAP 1, other CMB, 2 d. F/SDSS-gal [HST, SNIa] 0. 42 -0. 68 WMAP 1, other CMB, 2 d. F/SDSS-gal, 2 d. F/SDSS-bias and/or Ly-α WMAP Coll. , Ap. J Suppl 148 (2003) 175 Fogli et al. PRD 70 (2004) 113003 Seljak et al, PRD 71 (2005) 103515 Mac. Tavish et al, astro-ph/0507503 Hannestad, hep-ph/0409108
Cosmological bounds on neutrino masses using WMAP 3 Data used Bound on Σmν (e. V) [95% CL] WMAP Coll. , astro-ph/0603449 Fukugita et al, astro-ph/0605362 Kristiansen et al, astro-ph/0608017 WMAP Coll. , astro-ph/0603449 Goobar et al, astro-ph/0602155 Seljak et al, astro-ph/0604335 Kristiansen et al, astro-ph/0608017 1. 7 – 2. 3 CMB only 0. 68 – 0. 91 WMAP 3, other CMB, 2 d. F/SDSSgal, SNIa 0. 17 -0. 48 WMAP 3, other CMB, 2 d. F/SDSSgal, SDSS-BAO and/or Ly-α Fogli et al. , hep-ph/0608060
Neutrino masses in 3 -neutrino schemes CMB + galaxy clustering + HST, SNI-a… + BAO and/or bias + including Ly-α Fig from Strumia & Vissani, NPB 726(2005)294
0 2 and Cosmology Fogli et al. , hep-ph/0608060
Future sensitivities to Σm ν When future cosmological data will be available 1. CMB (T+P) + galaxy redshift surveys 2. CMB (T+P) and CMB lensing 3. Weak lensing surveys 4. Weak lensing surveys + CMB lensing
PLANCK+SDSS • Fisher matrix analysis: expected sensitivities assuming a fiducial cosmological model, for future experiments with known specifications Fiducial cosmological model: (Ωbh 2 , Ωmh 2 , h , ns , τ, Σmν ) = (0. 0245 , 0. 148 , 0. 70 , 0. 98 , 0. 12, Σmν ) Σm detectable at 2σ if larger than 0. 21 e. V (PLANCK+SDSS) 0. 13 e. V (CMBpol+SDSS) Lesgourgues, SP & Perotto, PRD 70 (2004) 045016
Future sensitivities to Σm ν: new ideas weak gravitational and CMB lensing No bias uncertainty Small scales much closer to linear regime Tomography: 3 D reconstruction Makes CMB sensitive to smaller neutrino masses
Future sensitivities to Σm ν: new ideas weak gravitational and CMB lensing sensitivity of future weak lensing survey (4000º)2 to mν σ(mν) ~ 0. 1 e. V sensitivity of CMB (primary + lensing) to mν σ(mν) = 0. 15 e. V (Planck) σ(mν) = 0. 044 e. V (CMBpol) Kaplinghat, Knox & Song PRL 91 (2003) 241301 Abazajian & Dodelson PRL 91 (2003) 041301 Lesgourgues, Perotto, SP & Piat PRD 73 (2006) 045021
CMB lensing : recent analysis σ(Mν) in e. V for future CMB experiments alone : Lesgourgues et al, PRD 73 (2006) 045021
CMB lensing : recent analysis Perotto et al, astro-ph/06062271
Summary of future sensitivities Lesgourgues & SP, Phys. Rep. 429 (2006) 307 Future cosmic shear surveys
For more details see Physics Reports 429 (2006) 307 -379 [astro-ph/0603494]
Conclusions Cosmological observables can be used to bound (or measure) the absolute scale of neutrino masses. Information complementary to laboratory results ν Current bounds on the sum of neutrino masses from cosmological data (best Σmν<0. 2 -0. 4 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
- Slides: 51