strasbourg , 11 july 200 6 julien lesgourgues (lapth , annecy )
DESCRIPTION
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 PresentationTRANSCRIPT
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StrasbourgStrasbourg, 11 July, 11 July 200 20066
Julien Lesgourgues (LAPTHJulien Lesgourgues (LAPTH, Annecy, Annecy))
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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
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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
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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
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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
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How can we prove How can we prove the existence of the existence of this cosmological this cosmological
neutrino neutrino background ?background ?
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How can we How can we measure neutrino measure neutrino
masses masses with cosmology with cosmology
??
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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)
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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)
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Cosmological perturbationsCosmological perturbations
accélération
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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
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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
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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
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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!
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How can we How can we measure neutrino measure neutrino
masses masses with cosmology with cosmology
??
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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
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Structure formation after Structure formation after equalityequality
baryon and CDM
experiencegravitational
clustering
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Structure formation after Structure formation after equalityequality
baryon and CDM
experiencegravitational
clustering
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Structure formation after Structure formation after equalityequality
baryon and CDM
experiencegravitational
clustering
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growth of /(k,t) fixed by
« gravity vs. expansion » balance
a
Structure formation after Structure formation after equalityequality
baryon and CDM
experiencegravitational
clustering
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neutrinosexperience
free-streamingat
v = c or <p>/m
Structure formation after Structure formation after equalityequality
baryon and CDM
experiencegravitational
clustering
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Structure formation after Structure formation after equalityequality
baryon and CDM
experiencegravitational
clustering
neutrinosexperience
free-streamingat
v = c or <p>/m
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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
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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
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cdm
b
metric
a
J.L.
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cdm
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a
1-3/5fa
J.L.
& S
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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
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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
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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
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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
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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
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ProspectsProspects
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Prospects onProspects on neutrino neutrino mass mass boundsbounds
1) future CMB + galaxy redshift surveys
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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
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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
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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
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summary of 2 expected errors on Smn (eV) :
CMBpol lensing
PLANCK + gal. lensing
Prospects onProspects on neutrino neutrino mass mass boundsbounds
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