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Strasbourg Strasbourg , 11 July , 11 July 200 200 6 6 Julien Lesgourgues (LAPTH Julien Lesgourgues (LAPTH , Annecy , Annecy ) )

Strasbourg , 11 July 200 6 Julien Lesgourgues (LAPTH , Annecy )

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neutrinos in cosmology. Strasbourg , 11 July 200 6 Julien Lesgourgues (LAPTH , Annecy ). acc élé ration. d écélé ration lente. d écélé ration rqpide. acc élé ration. inflation. radiation. mati è re. é nergie noire. The standard cosmological model. acc élé ration. acc ele ration. - PowerPoint PPT Presentation

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Page 1: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

StrasbourgStrasbourg, 11 July, 11 July 200 20066

Julien Lesgourgues (LAPTHJulien Lesgourgues (LAPTH, Annecy, Annecy))

Page 2: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

The standard cosmological The standard cosmological modelmodel

accélération

accélération

décélération lente

décélération rqpide

accélération

accélération

décélération lente

décélération rqpide

inflation radiation matière énergie noire

acceleration

acceleration

slow deceleration

fast deceleration

??

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

Page 3: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Neutrinos in the UniverseNeutrinos in the Universe

1)1) Early Universe: thermal plasmaEarly Universe: thermal plasma

left-handed neutrinos baryons, other leptons, …left-handed neutrinos baryons, other leptons, … weak interactionsweak interactions

• 3 species share Fermi-Dirac distribution:f= [eE/T+1]-1

• T>>m in early Universe, so neutrinos are ultra relativistic:

v ~ c , E p , p ~ T

• same density as for photons: = =

• effect of expansion on ulltrarelativistic neutrinos:

pp ~ T ~ T a a-1-1 , , = = a-4

Page 4: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Neutrinos in the UniverseNeutrinos in the Universe

2)2) T < MeV: neutrino decoupling:T < MeV: neutrino decoupling:

• weak interaction rate < expansion rate : freezing-outweak interaction rate < expansion rate : freezing-out

• neutrinos abandoned to themselves (gravitational coupling only)neutrinos abandoned to themselves (gravitational coupling only)

• keep Fermi-Dirac distributionkeep Fermi-Dirac distribution

• keep diluting like a a-4-4

3)3) soon after: positron annihilation:soon after: positron annihilation:

ee++ + e + e--

T , T unaffected, = 0.68 aa-4-4

4)4) T < T < ?? ?? eV: non-relativistic regimeeV: non-relativistic regime

• non relativistic regime: progressively p < mnon relativistic regime: progressively p < m

• so so E = mcE = mc22 , , a a-3-3

Page 5: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Neutrinos in the UniverseNeutrinos in the Universe

ln a

ln

CDM & b (H0,q,k)

(T)

total

eq

<p>=3kBT=m

0.1%0.1%to 1%to 1%

40%40%

today

Page 6: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

How can we prove How can we prove the existence of the existence of this cosmological this cosmological

neutrino neutrino background ?background ?

Page 7: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

How can we How can we measure neutrino measure neutrino

masses masses with cosmology with cosmology

??

Page 8: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

How can we prove the How can we prove the existence of a existence of a

cosmological neutrino cosmological neutrino background ?background ?

o direct detectiondirect detection very difficult: n = 340 cm very difficult: n = 340 cm-3-3, , EE < 1 eV < 1 eV

o indirect detection:indirect detection: effects in early Universe, when density = 40% effects in early Universe, when density = 40%

Big Bang Nucleosynthesis (BBN)Big Bang Nucleosynthesis (BBN)

Cosmological perturbations:Cosmological perturbations:

Cosmic Microwave Background (CMB)Cosmic Microwave Background (CMB)

Large Scale Structure (LSS)Large Scale Structure (LSS)

Page 9: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Big Bang NucleosynthesisBig Bang Nucleosynthesis

o ensemble of ensemble of nuclear reactionsnuclear reactions::

p, n, ep, n, e--, , H, D, He H, D, He33, He, He44, Li …, Li …

o freeze-out freeze-out caused by expansion:caused by expansion:

relative abundances constant until todayrelative abundances constant until today

o neutrinos contribute to neutrinos contribute to expansion rateexpansion rate: :

impact on relative abundancesimpact on relative abundances

o observationsobservations (mainly of deuterium/hydrogen): (mainly of deuterium/hydrogen):

//tottot = 0.4 ± 0.1 (68% confidence level) = 0.4 ± 0.1 (68% confidence level)

Page 10: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Cosmological perturbationsCosmological perturbations

accélération

accélération

décélération lente

décélération rqpide

accélération

accélération

décélération lente

décélération rqpide

inflation radiation matière énergie noire

acceleration

acceleration

slow deceleration

fast deceleration

??

Theory :Theory :

• inhomogeneities decomposed in comobile Fourier space

• physical wavelengths grow with scale factor : (t) = (2/k) a(t)

• causal horizon during RD/MD grows with Hubble radius : d(t1,t2) c/H t

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

gravity / photon pressure

acoustic oscillations of , binside horizon

gravity only

gravitational clustering of b, CDMinside horizon

quantumquantumfluctuationsfluctuations

Page 11: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

accélération

accélération

décélération lente

décélération rqpide

accélération

accélération

décélération lente

décélération rqpide

inflation radiation matière énergie noire

acceleration

acceleration

slow deceleration

fast deceleration

??

CMB temperature/polarization anisotropies

z ≈ 1100z ≈ 1100

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

Cosmological observationsCosmological observations

Best data available:Best data available: WMAP (3yrs)WMAP (3yrs)

photon power spectra

Page 12: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Cosmological observationsCosmological observations

accélération

accélération

décélération lente

décélération rqpide

accélération

accélération

décélération lente

décélération rqpide

inflation radiation matière énergie noire

acceleration

acceleration

slow deceleration

fast deceleration

??

galaxy redshift surveys matter power spectrum P(k)

linear non-linear/<1 /~1

60 Mpc

bias uncertainty …

0<z<0.20<z<0.2

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

Best data available:Best data available: 2dF GRS2dF GRS SDSSSDSS

Page 13: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Cosmological perturbationsCosmological perturbationsand neutrinosand neutrinos

o physics of acoustic oscillations and structure formationphysics of acoustic oscillations and structure formation

sensitive to sensitive to relative abundance of matter/radiationrelative abundance of matter/radiation

o combined analysis of CMB+LSS gives result consitent BBN with combined analysis of CMB+LSS gives result consitent BBN with

similar errorbar (30% at the 68% confidence level)similar errorbar (30% at the 68% confidence level)

o error bar could shrink by factor ~10 in the futureerror bar could shrink by factor ~10 in the future

Existence of cosmic neutrino background proved Existence of cosmic neutrino background proved

indirectly by two independent methods!indirectly by two independent methods!

Page 14: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

How can we How can we measure neutrino measure neutrino

masses masses with cosmology with cosmology

??

Page 15: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

How can we measure neutrino How can we measure neutrino masses with cosmology?masses with cosmology?

accélération

accélération

décélération lente

décélération rqpide

accélération

accélération

décélération lente

décélération rqpide

inflation radiation matière énergie noire

acceleration

acceleration

slow deceleration

fast deceleration

??

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

gravity only

gravitational clustering of b, CDMinside horizon

structure formation after equalitystructure formation after equality

Page 16: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Structure formation after Structure formation after equalityequality

baryon and CDM

experiencegravitational

clustering

Page 17: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Structure formation after Structure formation after equalityequality

baryon and CDM

experiencegravitational

clustering

Page 18: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Structure formation after Structure formation after equalityequality

baryon and CDM

experiencegravitational

clustering

Page 19: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

growth of /(k,t) fixed by

« gravity vs. expansion » balance

a

Structure formation after Structure formation after equalityequality

baryon and CDM

experiencegravitational

clustering

Page 20: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

neutrinosexperience

free-streamingat

v = c or <p>/m

Structure formation after Structure formation after equalityequality

baryon and CDM

experiencegravitational

clustering

Page 21: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Structure formation after Structure formation after equalityequality

baryon and CDM

experiencegravitational

clustering

neutrinosexperience

free-streamingat

v = c or <p>/m

Page 22: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

o neutrinos cannot cluster below a diffusion length

= ∫ v dt < ∫ c dt

Structure formation after Structure formation after equalityequality

baryon and CDM

experiencegravitational

clustering

neutrinosexperience

free-streamingat

v = c or <p>/m

Page 23: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

o neutrinos cannot cluster below a diffusion length

= ∫ v dt < ∫ c dt

for (2/k) < ,free-streaming prevents growth of structure during

MD :

a1-3/5 f with f = /m ≈ (m)/(15 eV)

Structure formation after Structure formation after equalityequality

baryon and CDM

experiencegravitational

clustering

neutrinosexperience

free-streamingat

v = c or <p>/m

Page 24: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

cdm

b

metric

a

J.L.

& S

. Past

or,

Physi

cs R

eport

s, in p

ress

[ast

ro-p

h/0

60

34

94

]J.L.

& S

. Past

or,

Physi

cs R

eport

s, in p

ress

[ast

ro-p

h/0

60

34

94

] Structure formation after Structure formation after equalityequality

Page 25: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

cdm

b

metric

a

1-3/5fa

J.L.

& S

. Past

or,

Physi

cs R

eport

s, in p

ress

[ast

ro-p

h/0

60

34

94

]J.L.

& S

. Past

or,

Physi

cs R

eport

s, in p

ress

[ast

ro-p

h/0

60

34

94

] Structure formation after Structure formation after equalityequality

Page 26: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Effect of neutrinoEffect of neutrino mass mass

o observable signature of the total mass on observable signature of the total mass on P(k) :P(k) :P(k) massiveP(k) massiveP(k) masslessP(k) massless

variousvariousff

Page 27: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

BoundsBounds o onn neutrino neutrino mass mass

o situation taking neutrino oscillation data into account:

at least 3%effect in P(k)eV 0.009 m

eV 0.05m

2sun

2atm

Page 28: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

mass bounds for 3- scenarios :

THERE IS NOT A UNIQUE « COSMOLOGICAL BOUND » !!!

depends on the exact data set

depends on the underlying cosmological model

BoundsBounds o onn neutrino neutrino mass mass

Page 29: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Lighest neutrino mass (eV)Lighest neutrino mass (eV)

mass bounds for 3-n scenarios : 7-parameter fits

extra parameters

degeneracies

bounds grow by factor < 2

(e.g. extra rel. d.o.f., tilt running, w …)

BoundsBounds o onn neutrino neutrino mass mass

Page 30: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

experiments sensitive to absolute neutrino mass scale :

Cosmology < 1 eV

Tritium beta decay

< 2.3 eV

Neutrinoless double beta

decay< 0.3-1.2 eV

i

im~

2/1

22

i

iei mU

i

ieimU 2

dep. on CP phases, Dirac/Majorana

KATRIN:0.2 eV ??(2)

BoundsBounds o onn neutrino neutrino mass mass

Page 31: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

ProspectsProspects

Page 32: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Prospects onProspects on neutrino neutrino mass mass boundsbounds

1) future CMB + galaxy redshift surveys

Page 33: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Prospects onProspects on neutrino neutrino mass mass boundsbounds

2) CMB weak lensing

dT/Tobs(n)=dT/T(n+)

gravitational potential

integrated along line-of-sight with window function probing up to

z~3

deflection field measurable statistically !! no bias uncertainty small scales much closer to linear regime makes CMB alone more sensitive to masses < 0.3eV

Page 34: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

Prospects onProspects on neutrino neutrino mass mass boundsbounds

3) galaxy weak lensing

deflection sensitive to gravitational potential

integrated along line-of-sight with window function centered on

d ~ dS/2

deflection field measurable statistically !! no bias uncertainty small scales close to linear regime tomography: 3D reconstruction

Page 35: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

expected power spectrum of deflection field

from sources at z ~ 0.2, 0.6, … 3.0(error for LSST)

from sources at z ~ 1100 (CMB)(error for CMBpol)

linea

r

Prospects onProspects on neutrino neutrino mass mass boundsbounds

Page 36: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

summary of 2 expected errors on Smn (eV) :

CMBpol lensing

PLANCK + gal. lensing

Prospects onProspects on neutrino neutrino mass mass boundsbounds

Page 37: Strasbourg , 11 July  200 6 Julien Lesgourgues (LAPTH , Annecy )

EndEnd