04/21/23

Neutrino masses from cosmological observables

Sergio Pastor (IFIC)

Benasque Cosmology workshop

15 / 08 / 2006

ν

Outline

Relic Neutrinos as DM

Effect of neutrino masses on cosmological observables

Current bounds and future sensitivities

Neutrino masses from cosmological

observables

Introduction: the Cosmic Neutrino Background

This is a neutrino!

T~MeVt~sec

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

1e1

T)(p,f p/T

Primordial

Nucleosynthesis

At least 2

species are

NR today

Relativistic neutrinos

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

04/21/23

Evolution of the background densities: 1 MeV → now

photons

neutrinos

cdm

baryons

Λ

m3=0.05 eV

m2=0.009 eV

m1≈ 0 eV

Ωi= ρi/ρcrit

The Cosmic Neutrino Background

• Number density

• Energy density

323

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

At present 112 per flavour cm )( -3

Contribution to the energy density of the Universe

eV 93.2

mh Ω i

i2

ν

52 101.7h Ω ν

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 !

),,(),(e, 321 ννντμ

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

eV

Data on flavour oscillations do not fix the absolute scale of neutrino masses

atmatm

solar

solar

eV 0.009 Δm

eV 0.05Δm

2sun

2atm

NO

RM

AL

INV

ER

TE

D

eV

m0

What is the value of m0 ?

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

e -33 eHe H

-2e2)Z(A, Z)(A,

Absolute mass scale searches

Neutrinoless double beta decay

< 0.4-1.6 eV

Tritium decay < 2.2 eV

2/1

22

iiei mUm

e

< 0.3-2.0 eVCosmology i

im~

i

ieiee mUm 2

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 15 m 0.3Ω Ω

eV 46 m 1 Ω eV 93.2

mhΩ

iimν

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

• Ruled out by structure formation CDM

MpceV 30

m 41

-1

ν

eV 15 m 0.3Ω Ω

eV 46 m 1 Ω eV 93.2

mhΩ

iimν

iiν

ii

2ν

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

Matter power spectrum is the Fourier transform of the

two-point correlation function

Field of density Fluctuations

)(

)(x

x

Neutrinos as Hot Dark Matter: effect on P(k)

• 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)

ffν

Structure formation after equality

baryon and CDM

experiencegravitational

clustering

Structure formation after equality

baryon and CDM

experiencegravitational

clustering

Structure formation after equality

baryon and CDM

experiencegravitational

clustering

growth of /(k,t) fixed by

« gravity vs. expansion » balance

a

Structure formation after equality

baryon and CDM

experiencegravitational

clustering

neutrinosexperience

free-streamingwith

v = c or <p>/m

Structure formation after equality

baryon and CDM

experiencegravitational

clustering

Structure formation after equality

baryon and CDM

experiencegravitational

clustering

baryon and CDM

experiencegravitational

clustering

neutrinosexperience

free-streamingwith

v = c or <p>/m

neutrinos cannot cluster below a diffusion length

= ∫ v dt < ∫ c dt

Structure formation after equality

baryon and CDM

experiencegravitational

clustering

baryon and CDM

experiencegravitational

clustering

neutrinosexperience

free-streamingwith

v = c or <p>/m

o neutrinos cannot cluster below a diffusion length

= ∫ v dt < ∫ c dt

for (2/k) < ,free-streaming supresses growth of structures during MD

a1-3/5 f with f = /m ≈ (m)/(15 eV)

Structure formation after equality

baryon and CDM

experiencegravitational

clustering

baryon and CDM

experiencegravitational

clustering

neutrinosexperience

free-streamingwith

v = c or <p>/m

J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/0603494]

Structure formation after equality

cdm

b

metric

a

Massless neutrinos

J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/0603494]

Structure formation after equality

cdm

b

metric

a

1-3/5fa

Massive neutrinos

fν=0.1

Effect of massive neutrinos on P(k)

Observable signature of the total mass on Observable signature of the total mass on P(k) :P(k) :P(k) massiveP(k) massive

P(k) masslessP(k) massless

variousvariousffν

Lesgourgues & SP, Phys. Rep. 429 (2006) 307

DATA on CMB temperature /polarization anisotropies

Multipole Expansion

Map of CMBR temperature Fluctuations

T

T-),T(),Δ(

Angular Power Spectrum

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 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)

3.32.1eff 3.5N

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

DATA

Fiducial cosmological model:(Ωbh2 , Ωmh2 , h , ns , τ, Σmν )

PARAMETERESTIMATES

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), …

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 WMAP1

390280640 . . .

Bound on Σmν (eV) [95% CL]

Data used

Ichikawa et al, PRD 71 (2005) 043001Sánchez et al, MNRAS 366 (2006) 189MacTavish et al, astro-ph/0507503

1.6 - 3.1 CMB only

Hannestad, JCAP 0305 (2003) 004 SDSS Coll., PRD 69 (2004) 103501Barger et al, PLB 595 (2004) 55Crotty et al, PRD 69 (2004) 123007Rebolo et al, MNRAS 353 (2004) 747Fogli et al. PRD 70 (2004) 113003Seljak et al, PRD 71 (2005) 103515Sánchez et al, MNRAS 366 (2006) 189MacTavish et al, astro-ph/0507503

1.0 - 1.7 [0.6-1.2]

WMAP1, other CMB, 2dF/SDSS-gal [HST,SNIa]

WMAP Coll., ApJ Suppl 148 (2003) 175Fogli et al. PRD 70 (2004) 113003 Seljak et al, PRD 71 (2005) 103515MacTavish et al, astro-ph/0507503Hannestad, hep-ph/0409108

0.42-0.68

WMAP1, other CMB, 2dF/SDSS-gal, 2dF/SDSS-bias and/or Ly-α

Cosmological bounds on neutrino masses using WMAP3

390280640 . . .

Bound on Σmν (eV) [95% CL] Data used

WMAP Coll., astro-ph/0603449Fukugita et al, astro-ph/0605362Kristiansen et al, astro-ph/0608017

1.7 – 2.3 CMB only

WMAP Coll., astro-ph/0603449Goobar et al, astro-ph/0602155

0.68 – 0.91WMAP3, other CMB, 2dF/SDSS-gal, SNIa

Goobar et al, astro-ph/0602155Seljak et al, astro-ph/0604335Kristiansen et al, astro-ph/0608017

0.17-0.48

WMAP3, other CMB, 2dF/SDSS-gal, SDSS-BAO and/or Ly-α

Fogli et al., hep-ph/0608060

Neutrino masses in 3-neutrino schemes

Fig from Strumia & Vissani, NPB726(2005)294

CMB + galaxy clustering

+ HST, SNI-a…

+ BAO and/or bias

+ including Ly-α

02 and Cosmology

Fogli et al., hep-ph/0608060

Future sensitivities to Σmν

1. CMB (T+P) + galaxy redshift surveys

2. CMB (T+P) and CMB lensing

3. Weak lensing surveys

4. Weak lensing surveys + CMB lensing

When future cosmological data will be available

PLANCK+SDSS

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

Σm detectable at 2σ if larger than

0.21 eV (PLANCK+SDSS)

0.13 eV (CMBpol+SDSS)

Fiducial cosmological model:(Ωbh2 , Ωmh2 , h , ns , τ, Σmν ) =

(0.0245 , 0.148 , 0.70 , 0.98 , 0.12, Σmν )

• Fisher matrix analysis: expected sensitivities assuming a fiducial cosmological model, for future experiments with known specifications

Future sensitivities to Σmν: new ideas

weak gravitational and CMB lensing

lensing

No bias uncertaintySmall scales much closer

to linear regimeTomography:

3D reconstruction

Makes CMB sensitive to smaller neutrino masses

Future sensitivities to Σmν: new ideas

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

Lesgourgues, Perotto, SP & PiatPRD 73 (2006) 045021

weak gravitational and CMB lensing

lensing

CMB lensing: recent analysis

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

Perotto et al, astro-ph/06062271

CMB lensing: recent analysis

Summary of future sensitivities

Lesgourgues & SP, Phys. Rep. 429 (2006) 307

Future cosmic shear surveys

Physics Reports 429 (2006) 307-379 [astro-ph/0603494]

For more details see

Current bounds on the sum of neutrino masses from cosmological data

(best Σmν<0.2-0.4 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 can be used to bound (or measure) the absolute scale of

neutrino masses. Information complementary

to laboratory results