Neutrino oscillations in dense neutrino media

(1)

Cosmology and neutrino physics (now and) in the next 10 years

Sergio Pastor (IFIC)

Nufact 08

Valencia, July 2008

ν

Picture from Hubble ST

(2)

Outline

Effect of neutrino masses on cosmological observables Current cosmological bounds

on neutrino properties Future sensitivities

Introduction: the Cosmic

Neutrino Background

(3)

This is a neutrino!

(4)

T~MeV t~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 1

e T) 1

(p,

f_ν _p/T

 

Primord ial Nucleos

ynthesis

(5)

At least 2 species are

NR today

Relativistic neutrinos

T~m



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

(6)

The Cosmic Neutrino Background

• Number density

• Energy density

3 2

3 3

11 3 ( 6 11

3

2 ^ν ^ν ^γ ^CMB

ν T

π ) n ζ

) (p,T π) f

(

p

n 



d  











 



 



















n m

T )

(p,T π) f

(

p m d

p

i i

i

CMB ν

ν

4 3 / 2 4

3 2 3

2 11

4 120

7 2

Massless

Massive m_ν>>T Neutrinos decoupled at T~MeV, keeping a

spectrum as that of a relativistic species e 1 T) 1

(p,

f _p/T

 

 

At present 112 per flavour(   )cm^-3

Contribution to the energy density of the Universe

eV 93.2

m h

Ω ²



ⁱ ⁱ

ν 

5 2 1.7 10 h

Ω _ν   ^

(7)

01/28/24

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

(8)

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 are very large

• Ruled out by structure formation CDM

eV 15 m

0.3 Ω

Ω

eV 46

m

1 Ω

eV 93.2 h m

Ω

i i

m ν

i i

i i ν ν 2

















 

(9)

Neutrinos as Hot Dark Matter

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

(10)

Structure formation after equality

baryons and CDM (matter)

experience gravitational

clustering

(11)

clustering

(12)

Structure formation after equality

clustering

(13)

growth of 

(k,t)

 fixed by

gravity vs expansion balance 



 a

clustering

(14)

neutrinos experience free-streaming v = c or <p>/mwith

clustering

(15)

Structure formation after equality

baryon and CDM experience gravitational

clustering baryons and CDM (matter)

clustering

(16)

neutrinos cannot cluster below a diffusion length





= ∫ v dt < ∫ c dt

clustering

(17)

Structure formation after equality

clustering

(18)

Power Spectrum of density fluctuations

Matter power spectrum is the Fourier transform of the two-point correlation function

P(k) k e k( )

3 3 2

1 ² ¹

) 2 ) (

( )

( d ⁱ ^x ^x

x

x ^ ^



_ ^



Field of density Fluctuations



 ( x )   ( x )

(19)

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 m_ν from Structure Formation (combined with other cosmological data)

ff_ν

(20)

Effect of massive neutrinos on P(k)

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

P(k) massive P(k) massive P(k) massless

P(k) massless variousvarious

ff_ν

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

(21)

Cosmological observables: LSS

accélération

accélération décélération lente

décélération rqpide accélération

décélération rqpide

inflation radiation matière énergie noire

acceleration

acceleration slow deceleration

fast deceleration

inflation RD (radiation domination) MD (matter domination) dark energy domination

0<z<0.2 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

(22)

Cosmological observables : LSS

accélération

acceleration

fast deceleration

2<z<3 2<z<3

Lyman-α forests in quasar spectra

matter power spectrum P(k) various systematics

 Distribution of large-scale

structures at

medium z

(23)

Cosmological observables: CMB

accélération

acceleration

fast deceleration

z≈1100 z≈1100

 photon power spectra

CMB temperature/polarization anisotropies

Anisotropies of the Cosmic

Microwave

Background

(24)

Multipole Expansion

) , ( Y a )

,

Δ(  ^ _m __m  

 











m 0

Map of CMBR temperature Fluctuations

T T - ) , ) T(

,

Δ(  



 

Angular Power Spectrum

m m m m

m a a

1 2 a 1

a

C ^l _l

l l l

l

l l 







 



DATA on CMB temperature anisotropies

(25)

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

(26)

Effect of massive neutrinos on the CMB and Matter Power Spectra

Max Tegmark

www.hep.upenn.edu/~max/

(27)

How to get a bound (measurement) of neutrino masses from Cosmology

DATA

Fiducial cosmological model:

(Ω_bh², Ω_mh², h , n_s, τ, Σm_ν)

PARAMETER ESTIMATES

(28)

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 (Ω_m), HST (h), …

(29)

Cosmological Parameters: example

SDSS Coll, PRD 69 (2004) 103501

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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

(31)

Cosmological bounds on neutrino masses using WMAP

Fogli et al., PRD 75 (2007) 053001

Dependence on the data set used:

Fogli et al., arXiv:0805.2517

With WMAP3

With WMAP5

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Neutrino masses in 3-neutrino schemes

CMB + galaxy clustering + HST, SNI-a…

+ BAO and/or bias + including Ly-α CMB (+cluster mass

function)

Strumia & Vissani, hep-ph/0606054

(33)

Current cosmological bounds on neutrino masses

Goobar et al, JCAP 06 (2006) 019 [astro-ph/0602155]

Dependence on the data set AND the cosmological model used.

Standard cosmological model+neutrino masses (8 par)

SCM+neutrino masses+N_eff+_s+w_DE (11 par)

(34)

Absolute mass scale searches

Neutrinoless double beta decay

Tritium β decay

2 / 1 2 2

 

 



  

i

ei

m

U m

e

Cosmology 

i

m

i

~





i

i ei

ee

U m

m

²

(35)

Tritium  decay, 0  2  and Cosmology

Fogli et al., PRD 75 (2007) 053001 [hep-

ph/0608060]

(36)

0  2  and Cosmology

Fogli et al.,

arXiv:0805.2517

(37)

0  2  and Cosmology

Fogli et al.,

arXiv:0805.2517

(38)

At T<m

_e

, the radiation content of the Universe is

Relativistic particles in the Universe









    



 









 



 



 











 3

11 4 8 1 7 15

8 3 7 15

3 / 4 2 4

2 4

r T T

(39)

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

data) (LEP

008 .

0 984

.

2 





# of flavour neutrinos:

N

Constraints on N

_eff

from BBN and from CMB+LSS

(40)

Allowed ranges for N

_eff

Mangano et al, JCAP 0703 (2007) 006 Using cosmological data (95% CL)

) - Ly and BAO

( 6.2 N

3.1

data) LSS

(CMB

7.9 N

3.0

eff eff











B 2 10

B

10 274Ω h

10 /n η n _ ^γ 

1.9 < N_eff < 7.8

(WMAP5+BAO+SN+HST)

WMAP Coll., arXiv:0803.0547

(41)

Analysis with Σm

_ν

and N

_eff

free

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

WMAP + ACBAR + SDSS + 2dF

Hannestad & Raffelt, JCAP 0611 (2006) 016

BBN allowed region

(42)

Future sensitivities to Σm

_ν

Future cosmological data will be available from

o CMB (Temperature & Polarization anis.) o High-z Galaxy redshift surveys

o Galaxy cluster surveys

o Weak lensing surveys (tomography) o CMB lensing

o Fluctuations in the 21 cm H line

Hannestad & Wong, JCAP 07 (2007) 004 Takada et al, PRD 73 (2006) 083520

Wang et al, PRL 95 (2005) 011302

Hannestad et al, JCAP 06 (2006) 025 Song & Knox, PRD 70 (2004) 063510

Perotto et al, JCAP 10 (2006) 013

Lesgourgues et al, PRD 73 (2006) 045021

Forecasts indicate

0.01-0.15 eV sensitivities to

Σm_νare possible

Loeb & Wyithe, PRL 100 (2008) 161301 Pritchard & Pierpaoli, arXiv:0805.1920

(43)

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:

(Ω_bh², Ω_mh², 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

(44)

Future sensitivities to Σm

_ν

: weak gravitational lensing

Frieman, Dodelson

Distant faint galaxies

(45)

Future sensitivities to Σm

_ν

No bias uncertainty Small scales much closer

to linear regime Tomography:

3D reconstruction

Foregroun d mass

Frieman, Dodelson

Measure a large number of elliptically shaped galaxies

Weak lensing of faint galaxies

(46)

_ν

No bias uncertainty Small scales much closer

to linear regime Tomography:

3D reconstruction

sensitivity of future weak lensing survey (4000º)

²

to m

_ν

σ(m_ν) ~ 0.1 eV

Abazajian & Dodelson

PRL 91 (2003) 041301

(47)

_ν

Makes CMB sensitive to smaller neutrino masses

lensing of the CMB signal

sensitivity of CMB (primary + lensing) to m

_ν

σ(m_ν) = 0.15 eV (Planck) σ(m_ν) = 0.044 eV (CMBpol)

Kaplinghat, Knox & Song

PRL 91 (2003) 241301

(48)

CMB lensing: recent forecast analysis

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

(49)

“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

(50)

“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

acceleration

fast deceleration

20>z>6 20>z>6

Redshifted line:

2.1 m at redshift 10

power spectrum of 21 cm brightness fluctuations P₂₁(k)

(51)

Future sensitivities on  m

_

from 21cm observ.

Pritchard & Pierpaoli, arXiv:0805.1920

Future Low-ν radio

telescopes

(also Loeb & Wyithe, PRL 100 (2008) 161301; Mao et al, arXiv:0802.1710)

(52)

Summary of future sensitivities

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

Future cosmic shear surveys

Future high-z 21cm observations

(53)

Future bounds on N

_eff

Forecast analysis:

Bowen et al,

MNRAS 334 (2002) 760

ΔN_eff~ 3 (WMAP)

ΔN_eff~ 0.2 (Planck)

Bashinsky & Seljak, PRD 69 (2004) 083002

(54)

Conclusions

Current bounds on the sum of neutrino masses from cosmological data

(best Σm_ν<0.2-0.4 eV, conservative Σm_ν<1 eV) Different cosmological observations in the next

future Sub-eV sensitivity (0.1-0.2 eV and better) Test degenerate mass region and eventually the mimimum total mass for IH case

Cosmological observables can be used to bound (or measure) neutrino properties, in particular the sum of neutrino masses (info

complementary to laboratory results)

ν

The radiation content of the Universe (N_eff) will be very constrained in the near future