04/22/23

MASSIVE NEUTRINOS AND COSMOLOGY

Sergio Pastor (IFIC)

ν

CuTAPP 2005,

Ringberg Castle

Current bounds and future sensitivities

Effect of neutrino mass on cosmological observables

Outline

Neutrinos as DM

The Cosmic Neutrino Background

• Number density

• Energy density

flavor per

cm )( 112

present at3- 3

23

3

11

3(6

11

3

2 CMBγννν Tπ

)ζn)(p,Tf

π)(

pdn

nm

T

)(p,Tfπ)(

pdmp

i

ii

CMB

νν

43/42

3

322

11

4

120

7

2

Massless

Massive mν>>T

Neutrinos decoupled at T~MeV, keeping a spectrum as that of a relativistic species 1e

1T)(p,f p/T

04/22/23

Relic neutrinos influence several cosmological epochs

T < eVT ~ MeV

Formation of Large Scale Structures

LSS

Cosmic Microwave Background

CMB

Primordial

Nucleosynthesis

BBN

No flavor sensitivity Neff & mννevs νμ,τ Neff

Non-instantaneous ν decoupling (including oscillations)

3.045N eff T.Pinto et al, in preparation

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

MpceV 30

m 41

-1

ν

Neutrino Free Streaming

b, cdm

eV 46 m 1 Ω eV 93.2

mhΩ

iiν

ii

2ν

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

eV 46 m 1 Ω eV 93.2

mhΩ

iiν

ii

2ν

MpceV 30

m 41

-1

ν

Neutrinos as Hot Dark Matter

• Effect of Massive Neutrinos: suppression of Power at small scales

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

CMB DATA: INCREASING PRECISION

Multipole Expansion

Angular Power SpectrumMap of CMBR temperature

Fluctuations

T

T-),T(),Δ(

Galaxy Redshift Surveys

SDSS

2dFGRS

~ 1300 M

pc

Power Spectrum of density fluctuations

Galaxy Surveys

CMB experiments

SDSS

Field of density Fluctuations

)(

)(x

x

Matter power spectrum is the Fourier transform of the

two-point correlation function

Power spectrum of density fluctuations

Bias b2(k)=Pg(k)/Pm(k)

Non-linearity

2dFGRS

kmax

SDSS

Neutrinos as Hot Dark Matter

W. Hu

• Effect of Massive Neutrinos: suppression of Power at small scales

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

Effect of massive neutrinos on the CMB and Matter Power

Spectra

Max Tegmark

www.hep.upenn.edu/~max/

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 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 (2dF,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), …

3 degenerate massive neutrinos Σmν = 3m0

Neutrino masses in 3-neutrino schemes

eV

From present evidences of atmospheric and solar neutrino oscillations

atmatm

solar

solar

eV 0.009 m

eV 0.05m

2sun

2atm

eV

m0

Absolute mass scale searches

Cosmology < 0.42-2.0 eV

Neutrinoless double beta decay

< 0.3-1.6 eVi

ieiee mUm 2

Tritium decay < 2.3 eV

i

im~

2/1

22

iiei mUm

e

Cosmological bounds on neutrino mass since 2003

390280640 . . .

Bound on Σmν (eV) at 95% CL

Data used

Ichikawa, Fukugita & KawasakiPRD 71 (2005) 043001

2.0 WMAP

SDSS Coll.PRD 69 (2004) 103501

1.7 WMAP, SDSS

HannestadJCAP 0305 (2003) 004

1.01 WMAP, other CMB, 2dF, HST

Crotty, Lesgourgues & SPPRD 69 (2004) 123007

1.0 [0.6] WMAP, other CMB, 2dF, SDSS [HST,SN]

Barger. Marfatia & TregrePLB 595 (2004) 55

0.75 WMAP, other CMB, 2dF, SDSS, HST

WMAP Coll.ApJ Suppl 148 (2003) 175

0.7

WMAP, other CMB,2dF (bias,galaxy clustering), Ly-α, HST

Fogli et al.PRD 70 (2004) 113003

0.47WMAP, other CMB, 2dF, SDSS (Ly-α),HST

Seljak et al.PRD (2005) [astro-ph/0407372]

0.42WMAP, SDSS (bias, galaxy clustering, Ly-α)

Neutrino masses in 3-neutrino schemes

Fig from Strumia & Vissani, hep-ph/0503246

CMB + galaxy clustering

+ HST, SNI-a [σ8]

+ Ly-α [bias]

Global analysis: oscillations + tritium decay + 02 + Cosmology

Fogli et al., PRD 70 (2004) 113003

CMB + 2dF

390280640 . . .

Bound on Σmν (eV) at 95% CL

Data used

Ichikawa, Fukugita & KawasakiPRD 71 (2005) 043001

2.0 WMAP

SDSS Coll.PRD 69 (2004) 103501

1.7 WMAP, SDSS

HannestadJCAP 0305 (2003) 004

1.01 WMAP, other CMB, 2dF, HST

Crotty, Lesgourgues & SPPRD 69 (2004) 123007

1.0 [0.6] WMAP, other CMB, 2dF, SDSS [HST,SN]

Barger. Marfatia & TregrePLB 595 (2004) 55

0.75 WMAP, other CMB, 2dF, SDSS, HST

WMAP Coll.ApJ Suppl 148 (2003) 175

0.7

WMAP, other CMB,2dF (bias,galaxy clustering), Ly-α, HST

Fogli et al.PRD 70 (2004) 113003

0.47WMAP, other CMB, 2dF, SDSS (Ly-α),HST

Seljak et al.PRD (2005) [astro-ph/0407372]

0.42WMAP, SDSS (bias, galaxy clustering, Ly-α)

Allen, Smith & BridleMNRAS 346 (2003) 593

WMAP, other CMB, 2dF, X-ray galaxy cluster

390280640 . . .

The bound depends on the number of neutrinos

• Example: in the 3+1 scenario, there are 4 neutrinos (including thermalized sterile)

• Calculate the bounds with Nν > 3

Abazajian 2002, di Bari 2002

Hannestad JCAP 0305 (2003) 004

(also Elgarøy & Lahav, JCAP 0304 (2003) 004)

3 ν4 ν

5 ν

Hannestad

95% CL

WMAP + Other CMB + 2dF + HST + SN-Ia

Σmν and Neff degeneracy

(0 eV,3)

(0 eV,7)

(2.25 eV,7)(0 eV,3)

(0 eV,7)

(2.25 eV,7)

Analysis with Σmν and Neff free

Hannestad & Raffelt, JCAP 0404 (2004) 008

Crotty, Lesgourgues & SP, PRD 69 (2004) 123007

2σ upper bound on Σmν (eV)

WMAP + ACBAR + SDSS + 2dF Previous + priors (HST + SN-Ia)

Non-thermal relic neutrinos

The spectrum could be distorted after neutrino decoupling

Example: decay of a

light scalar after BBN

Cuoco, Lesgourgues, Mangano & SP, astro-ph/0502465

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

/T p

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 2dF)

• Fisher matrix analysis: expected sensitivities assuming a fiducial cosmological model

• Forecast analysis for

WMAP and ΩΛ=0 models Hu et al, PRL 80 (1998) 5255

Sensitivity to

With current best-fit values

eV 0.1N

hΩ 0.65 Σm

0.82m

νν

eV0.37 Σm

Recent update: Lesgourgues, SP & Perotto, PRD 70 (2004) 045016

Fiducial cosmological model:(Ωbh2 , Ωmh2 , h , ns , τ, Σmν ) = (0.0245 , 0.148 , 0.70 , 0.98 , 0.12, Σmν )

PLANCK+SDSS

Lesgourgues, SP & Perotto, PRD 70 (2004) 045016

Ideal CMB+40xSDSS

Σm detectable at 2σ if larger than

0.21 eV (PLANCK+SDSS)

0.13 eV (CMBpol+SDSS)

Σm Σm

Fiducial value

2 sensitivity

Future sensitivities to Σmν: new ideas

galaxy weak lensing and CMB lensing

no bias uncertaintysmall scales in linear regime

makes CMB sensitive to much smaller masses

Future sensitivities to Σmν: new ideas

galaxy weak lensing and CMB lensing

sensitivity of future weak lensing survey(4000º)2 to mν

σ(mν) ~ 0.1 eV

Abazajian & DodelsonPRL 91 (2003) 041301

sensitivity of CMB(primary + lensing) to mν

σ(mν) = 0.15 eV (Planck)

σ(mν) = 0.044 eV (CMBpol)

Kaplinghat, Knox & SongPRL 91 (2003) 241301

Neutrino masses in 3-neutrino schemes

Fig from Strumia & Vissani, hep-ph/0503246

CMB + galaxy clustering

+ HST, SNI-a [σ8]

+ Ly-α [bias]

PLANCK + SDSS

CMBpol + SDSS

CMBpol (including CMB lensing)

KATRIN

Bounds on the sum of neutrino masses from CMB + 2dFGRS or SDSS, and other

cosmological data (best Σmν<0.42 eV, conservative Σmν<1 eV)

Conclusions

Sub-eV sensitivity in the next future (0.1-0.2 eV and better) Test degenerate

mass region and eventually the IH case

ν

Cosmological observables efficiently constrain some properties of (relic) neutrinos