Neutrinos in Cosmology II Sergio Pastor IFIC Valencia

Neutrinos in Cosmology (II) ν Sergio Pastor (IFIC Valencia) Universidad de Buenos Aires Febrero 2009

Cosmology and neutrino masses ν Sergio Pastor (IFIC Valencia) Universidad de Buenos Aires Febrero 2009 Picture from Hubble ST

Neutrinos in Cosmology 2 nd lecture Massive neutrinos as Dark Matter Effects of neutrino masses on cosmological observables Bounds on mν from CMB, LSS and other data Bounds on the radiation content (Nν) Future sensitivities on mν and Nν from cosmology

T~m os Rel tic s i v ati rin t u ne t 2 s a le e At ies ar c y spe toda NR

Relic neutrinos influence several cosmological epochs Primordial Nucleosynthesis Cosmic Microwave Background Formation of Large Scale Structures BBN CMB LSS T ~ Me. V νevs νμ, τ Neff T < e. V No flavour sensitivity Neff & mν

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

Mixing Parameters. . . Maltoni , Schwetz , Tórtola, Valle, NJP 6 (2004) 122 [hep-ph/0405172 v 6]

Mixing Parameters. . . From present evidences of oscillations from experiments measuring atmospheric, solar, reactor and accelerator neutrinos Maltoni , Schwetz , Tórtola, Valle, (2004) 122 [hep-ph/0405172 v 6] NJP 6

. . . 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

Evolution of the background densities: 1 Me. V → now photons Ωi= ρi/ρcrit neutrinos Λ m =1 e. V cdm baryons m =0. 05 e. V m =0. 009 e. V m ≈ 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

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. Neutrino to be formed Universe became Free when Streaming matter -dominated ν Φ • Ruled out by structure b, formation 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 Effect of Massive Neutrinos: suppression of Power at small scales

Neutrinos as Hot Dark Matter Effect of Massive Neutrinos: suppression of Power at small scales

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

Cosmological observables n artaitoino r é é e l l é é e acaccc inflation ee anrtqriopqnipdid r n o o e i l i t t e a a c r r déleé dscétéclé faé d RD (radiation domination) nte note tile onle ra on ti etile cra era dlé é docéwéclé slé d MD matière (matter domination) elréartaitoinon ecléé acaccé énergie noiredomination dark energy

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

Galaxy Redshift Surveys 2 d. FGRS SDSS ~ 00 13 pc M

Cosmological observables: LSS n artaitoino r é é e l l é é e acaccc inflation nte note tile onle ra on ti etile cra era dlé é docéwéclé slé d ee anrtqriopqnipdid r n o o e i l i t t e a a c r r déleé dscétéclé faé d elréartaitoinon ecléé acaccé 0<z<0. 2 RD (radiation domination) MD matière (matter domination) énergie noiredomination dark energy bias uncertainty Distribution of large-scale structures at low z 60 Mpc linear non-linear δρ/ρ<1 δρ/ρ ~ 1 matter power spectrum P(k) galaxy redshift surveys

Power spectrum of density fluctuations Non-linearity Bias b 2(k)=Pg(k)/Pm(k) 2 d. FGRS SDSS kma x

Cosmological observables : LSS n artaitoino r é é e l l é é e acaccc ee anrtqriopqnipdid r n o o e i l i t t e a a c r r déleé dscétéclé faé d nte note tile onle ra on ti etile cra era dlé é docéwéclé slé d elréartaitoinon ecléé acaccé 2<z<3 inflation RD (radiation domination) Distribution of large-scale structures at medium z MD matière (matter domination) énergie noiredomination dark energy various systematics matter power spectrum P(k) Lyman-α forests in quasar spectra

Neutrinos as Hot Dark Matter 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 baryons and CDM experience gravitational clustering

Structure formation after equality baryons and CDM experience gravitational clustering

Structure formation after equality baryons and CDM experience gravitational clustering

Structure formation after equality baryons and CDM experience gravitational clustering growth of dr/r (k, t) fixed by « gravity vs. expansion » balance dr/r a

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

Structure formation after equality baryons andand CDM experience CDM gravitational experience gravitational clustering neutrinos experience free-streaming with v = c or <p>/m

Structure formation after equality baryons andand CDM experience CDM gravitational 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 baryons andand CDM experience CDM gravitational experience gravitational clustering neutrinos experience free-streaming with v = c or <p>/m

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

Structure formation after equality a dcdm db a 1 -3/5 fn dn 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.

Cosmological observables: CMB n artaitoino r é é e l l é é e acaccc ee anrtqriopqnipdid r n o o e i l i t t e a a c r r déleé dscétéclé faé d nte note tile onle ra on ti etile cra era dlé é docéwéclé slé d elréartaitoinon ecléé acaccé z≈1100 inflation RD (radiation domination) MD matière (matter domination) énergie noiredomination dark energy Anisotropies of the Cosmic Microwave Background CMB temperature/polarization anisotropies �photon power spectra

CMB TT DATA Map of CMBR temperature Fluctuations Multipole Expansion Angular Power Spectrum

CMB TT DATA Map of CMBR temperature Fluctuations Multipole Expansion Angular Power Spectrum

TT CMB Polarization DATA TE EE BB WMAP 3

CMB Polarization DATA

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

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 Dependence on the data set used. With WMAP 3 Fogli et al. , PRD 75 (2007) 053001 With WMAP 5 Fogli et al. , PRD 78 (2008) 033010

Neutrino masses in 3 -neutrino schemes CMB + galaxy clustering + HST, SNI-a… + BAO and/or bias + including Ly-α Strumia & Vissani, hep -ph/0606054

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 Future experiments (KATRIN) m(νe) ~ 0. 2 -0. 3 e. V • Neutrinoless double beta decay: if Majorana neutrinos experiments with 76 Ge, 130 Te and other isotopes: Imee. I < 0. 23 -0. 85 e. V , depending on NME

Absolute mass scale searches Tritium β decay 2. 2 e. V Neutrinoless double beta decay < 0. 2 -0. 8 e. V Cosmology < 0. 2 -2. 0 e. V

Tritium decay, 0 2 and Cosmology Fogli et al. , PRD 75 (2007) 053001

0 2 and Cosmology Fogli et al. , PRD 78 (2008) 033010

0 2 and Cosmology Fogli et al. , PRD 78 (2008) 033010

Relativistic particles in the Universe At T<me, the radiation content of the Universe is Effective number of relativistic neutrino species Traditional parametrization of the energy density stored in relativistic particles Constraints on Neff from BBN and from CMB+LSS

Effect of Neff at later epochs • Neff modifies the radiation content: • Changes the epoch of matter-radiation equivalence

CMB+LSS: allowed ranges for Neff • Set of parameters: ( Ωbh 2 , Ωcdmh 2 , h , ns , A , b , Neff ) • DATA: WMAP + other CMB + LSS + HST (+ SN-Ia) • Flat Models 95% CL Crotty, Lesgourgues & SP, PRD 67 (2003) 123005 Hannestad, JCAP 0305 (2003) 004 Non-flat Models Pierpaoli, MNRAS 342 (2003) L 63 95% CL • Recent result Hannestad & Raffelt, JCAP 0611 (2006) 016 95% CL

Allowed ranges for Neff Using cosmological data (95% CL) Mangano et al, JCAP 0703 (2007) 006 1. 9 < Neff < 7. 8 (WMAP 5+BAO+SN+HST) WMAP Coll. , ar. Xiv: 0803. 0547

Future bounds on Neff • Next CMB data from WMAP and PLANCK (other CMB experiments on large l’s) temperature and polarization spectra • Forecast analysis in ΩΛ=0 models PLANCK WMAP Lopez et al, PRL 82 (1999) 3952

Future bounds on Neff Updated analysis: Larger errors Bowen et al 2002 ΔNeff ~ 3 (WMAP) ΔNeff ~ 0. 2 (Planck) Bashinsky & Seljak 2003

The bound on Σmν 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 BBN allowed region 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)

Analysis with Σmν and Neff free BBN allowed region WMAP + ACBAR + SDSS + 2 d. F Crotty, Lesgourgues & SP, PRD 69 (2004) 123007 Hannestad & Raffelt, JCAP 0611 (2006) 016

Parameter degeneracy: Neutrino mass and w In cosmological models with more parameters the neutrino mass bounds can be relaxed. Ex: quintessence-like dark energy with ρDE=w p. DE Λ WMAP Coll, astro-ph/0603449

Non-standard relic neutrinos The cosmological bounds on neutrino masses are modified if relic neutrinos have non-standard properties (or for non-standard models) Two examples where the cosmological bounds do not apply • Massive neutrinos strongly coupled to a light scalar field: they could annihilate when becoming NR • Neutrinos coupled to the dark energy: the DE density is a function of the neutrino mass (mass-varying neutrinos)

Non-thermal relic neutrinos The spectrum could be distorted after neutrino decoupling Example: decay of a light scalar after BBN * CMB + LSS data still compatible Thermal FD spectrum Distortion from Φ decay 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, PRD 71 (2005) 123501

Future sensitivities to Σm ν Future cosmological data will be available from CMB (Temperature & Polarization anis. ) Galaxy redshift surveys Galaxy cluster surveys Weak lensing surveys CMB lensing WMAP, SPT, ACT, BICEP, QUa. D, BRAIN, Cl. OVER, PLANCK, SAMPAN, Inflation Probe, SDSS-II, ALHAMBRA, KAOS, DES, CFHTLS, SNAP, LSST, Pan-STARRS, DUO…

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 sensitivity of CMB (primary + lensing) to mν σ(mν) ~ 0. 1 e. V σ(mν) = 0. 15 e. V (Planck) σ(mν) = 0. 044 e. V (CMBpol) Abazajian & Dodelson Kaplinghat, Knox & Song PRL 91 (2003) 041301 PRL 91 (2003) 241301

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

“Measuring ” even mν=0. 05 e. V ? New cosmological observable as a potential probe of fluctuations at intermediate redshifts (6<z<20) study of fluctuations in the 21 cm line emitted by neutral H Karttunen et al. 2007

“Measuring ” even mν=0. 05 e. V ? New cosmological observable as a potential probe of fluctuations at intermediate redshifts (6<z<20) study of fluctuations in the 21 cm line emitted by neutral H taitoinon a r r é é e l l ecé acaccé inflation nte note tile onle ra on ti etile cra era dlé é docéwéclé slé d de qriopqnipdie t r a n r n o o e i l i t t e délerécara dscétéclé faé d elréartaitoinon ecléé acaccé 20>z>6 RD (radiation domination) Redshifted line: 2. 1 m at redshift 10 MD matière (matter domination) énergie noiredomination dark energy power spectrum of 21 cm brightness fluctuations P 21(k)

Future sensitivities on m from 21 cm exps. Future Low-ν radio telescopes Pritchard & Pierpaoli, ar. Xiv: 0805. 1920

Summary of future sensitivities Future cosmic shear surveys Lesgourgues & SP, Phys. Rep. 429 (2006) 307 Future high-z 21 cm observations