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

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

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

At least 2 species are NR today Relativistic neutrinos T~m

Relic neutrinos influence several cosmological epochs T < eVT ~ MeV Formation of Large Scale Structures LSS Cosmic Microwave Background CMB Primordial Nucleosynthesis BBN No flavour sensitivity N eff & m ν ν e vs ν μ,τ N eff

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/ v6]

Mixing Parameters... From present evidences of oscillations from experiments measuring atmospheric, solar, reactor and accelerator neutrinos Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122 [hep-ph/ v6]

... and neutrino masses Data on flavour oscillations do not fix the absolute scale of neutrino masses eV atm solar NORMAL INVERTED eV m0m0 What is the value of m 0 ?

Evolution of the background densities: 1 MeV → now photons neutrinos cdm baryons Λ m =0.05 eV m =0.009 eV m ≈ 0 eV Ω i = ρ i /ρ crit m =1 eV

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

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 Neutrino Free Streaming Φ b, cdm ν

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 m ν from Structure Formation (combined with other cosmological data)

Cosmological observables accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire acceleration slow deceleration fast deceleration inflation RD (radiation domination)MD (matter domination) dark energy domination

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

Galaxy Redshift Surveys SDSS 2dFGRS ~ 1300 Mpc

Cosmological observables: LSS accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire acceleration slow deceleration fast deceleration inflation RD (radiation domination)MD (matter domination) dark energy domination 0<z<0.2 matter power spectrum P(k) galaxy redshift surveys linear non-linear δρ/ρ<1 δρ/ρ ~ 1 60 Mpc bias uncertainty Distribution of large-scale structures at low z

Power spectrum of density fluctuations Bias b 2 (k)=P g (k)/P m (k) k ma x SDSS 2dFGRS Non-linearity

Cosmological observables : LSS accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire acceleration slow deceleration fast deceleration inflation RD (radiation domination)MD (matter domination) dark energy domination 2<z<3 Lyman- α forests in quasar spectra matter power spectrum P(k) various systematics Distribution of large-scale structures at medium z

Neutrinos as Hot Dark Matter Effect of Massive Neutrinos: suppression of Power at small scales Massive Neutrinos can still be subdominant DM: limits on m ν from Structure Formation (combined with other cosmological data) ffνffν

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  (k,t) fixed by « gravity vs. expansion » balance    a Structure formation after equality baryons and CDM experience gravitational clustering

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

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

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

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

J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/ ] Structure formation after equality d cdm dbdb dgdg dndn metric a Massless neutrinos

J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/ ] d cdm dbdb dgdg dndn metric a 1-3/5f n a Massive neutrinos f ν =0.1 Structure formation after equality

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

Cosmological observables: CMB accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire acceleration slow deceleration fast deceleration inflation RD (radiation domination)MD (matter domination) dark energy domination z≈1100  photon power spectra CMB temperature/polarization anisotropies Anisotropies of the Cosmic Microwave Background

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

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

CMB Polarization DATA TT TE EE BB WMAP 3

CMB Polarization DATA

Effect of massive neutrinos on the CMB spectra 1)Direct effect of sub-eV massive neutrinos on the evolution of the baryon-photon coupling is very small 2)Impact on CMB spectra is indirect: non-zero Ω ν today implies a change in the spatial curvature or other Ω i. The background evolution is modified Ex: in a flat universe, keep Ω Λ +Ω cdm +Ω b +Ω ν =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

How to get a bound (measurement) of neutrino masses from Cosmology DATA Fiducial cosmological model: (Ω b h 2, Ω m h 2, h, n s, τ, Σm ν ) 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 (2dF,SDSS) * Bias (Galaxy, …): Amplitude of the Matter P(k) (SDSS,σ 8 ) * Lyman-α forest: independent measurement of power on small scales * Baryon acoustic oscillations (SDSS) Bounds on parameters from other data: SNIa (Ω m ), HST (h), …

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

Cosmological bounds on neutrino mass(es) A unique cosmological bound on m ν DOES NOT exist ! ν

Cosmological bounds on neutrino mass(es) A unique cosmological bound on m ν 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 Fogli et al., PRD 75 (2007) Dependence on the data set used. Fogli et al., PRD 78 (2008) With WMAP3 With WMAP5

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

Direct laboratory bounds on m ν Searching for non-zero neutrino mass in laboratory experiments Tritium beta decay: measurements of endpoint energy m( ν e ) < 2.2 eV (95% CL) Mainz Future experiments (KATRIN) m( ν e ) ~ eV Neutrinoless double beta decay: if Majorana neutrinos experiments with 76 Ge, 130 Te and other isotopes: Im ee I < eV, depending on NME

Absolute mass scale searches Neutrinoless double beta decay < eV Tritium β decay  2.2 eV < eV Cosmology

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

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

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

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

Effect of N eff at later epochs N eff modifies the radiation content: Changes the epoch of matter-radiation equivalence

CMB+LSS: allowed ranges for N eff Set of parameters: ( Ω b h 2, Ω cdm h 2, h, n s, A, b, N eff ) DATA: WMAP + other CMB + LSS + HST (+ SN-Ia) Flat Models Non-flat Models Recent result Pierpaoli, MNRAS 342 (2003) L63 95% CL Crotty, Lesgourgues & SP, PRD 67 (2003) % CL Hannestad, JCAP 0305 (2003) 004 Hannestad & Raffelt, JCAP 0611 (2006) % CL

Allowed ranges for N eff Mangano et al, JCAP 0703 (2007) 006 Using cosmological data (95% CL) 1.9 < N eff < 7.8 (WMAP5+BAO+SN+HST) WMAP Coll., arXiv:

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

Future bounds on N eff Updated analysis: Larger errors Bowen et al 2002 ΔN eff ~ 3 (WMAP) ΔN eff ~ 0.2 (Planck) Bashinsky & Seljak 2003

The bound on Σm ν depends on the number of neutrinos Example: in the 3+1 scenario, there are 4 neutrinos (including thermalized sterile) Calculate the bounds with N ν > 3 Abazajian 2002, di Bari 2002 Hannestad JCAP 0305 (2003) 004 (also Elgarøy & Lahav, JCAP 0304 (2003) 004) 3 ν 4 ν 5 ν Hannestad 95% CL WMAP + Other CMB + 2dF + HST + SN-Ia

Σm ν and N eff degeneracy (0 eV,3) (0 eV,7) (2.25 eV,7) (0 eV,3) (0 eV,7) (2.25 eV,7)

Analysis with Σm ν and N eff free Hannestad & Raffelt, JCAP 0404 (2004) 008 Crotty, Lesgourgues & SP, PRD 69 (2004) σ upper bound on Σm ν ( eV) WMAP + ACBAR + SDSS + 2dF Previous + priors (HST + SN-Ia) BBN allowed region

Analysis with Σm ν and N eff free Crotty, Lesgourgues & SP, PRD 69 (2004) WMAP + ACBAR + SDSS + 2dF Hannestad & Raffelt, JCAP 0611 (2006) 016 BBN allowed region

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 ρ DE =w p DE WMAP Coll, astro-ph/ Λ

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 Cuoco, Lesgourgues, Mangano & SP, PRD 71 (2005) Thermal FD spectrum Distortion from Φ decay * CMB + LSS data still compatible with large deviations from a thermal neutrino spectrum (degeneracy NT distortion – N eff ) * Better expectations for future CMB + LSS data, but model degeneracy NT- N eff remains

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

PLANCK+SDSS Lesgourgues, SP & Perotto, PRD 70 (2004) Σm detectable at 2σ if larger than 0.21 eV (PLANCK+SDSS) 0.13 eV (CMBpol+SDSS) Fiducial cosmological model: (Ω b h 2, Ω m h 2, h, n s, τ, Σm ν ) = (0.0245, 0.148, 0.70, 0.98, 0.12, Σm ν ) Fisher matrix analysis: expected sensitivities assuming a fiducial cosmological model, for future experiments with known specifications

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

Future sensitivities to Σm ν : new ideas sensitivity of future weak lensing survey (4000º) 2 to m ν σ(m ν ) ~ 0.1 eV Abazajian & Dodelson PRL 91 (2003) sensitivity of CMB (primary + lensing) to m ν σ(m ν ) = 0.15 eV (Planck) σ(m ν ) = eV (CMBpol) Kaplinghat, Knox & Song PRL 91 (2003) weak gravitational and CMB lensing lensing

CMB lensing: recent analysis σ(M ν ) in eV for future CMB experiments alone : Lesgourgues et al, PRD 73 (2006)

“Measuring” even m ν =0.05 eV ? New cosmological observable as a potential probe of fluctuations at intermediate redshifts (6<z<20)  study of fluctuations in the 21cm line emitted by neutral H Karttunen et al. 2007

“Measuring” even m ν =0.05 eV ? New cosmological observable as a potential probe of fluctuations at intermediate redshifts (6<z<20)  study of fluctuations in the 21cm line emitted by neutral H accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire acceleration slow deceleration fast deceleration inflation RD (radiation domination)MD (matter domination) dark energy domination 20>z>6 Redshifted line: 2.1 m at redshift 10 power spectrum of 21 cm brightness fluctuations P 21 (k)

Future sensitivities on  m from 21cm exps. Pritchard & Pierpaoli, arXiv: Future Low- ν radio telescopes

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