Cosmological probes of neutrino masses (Neutrinos in Cosmology)
Lecture I
Sergio Pastor (IFIC Valencia)
INT. SCHOOL OF PHYSICSENRICO FERMI, CLXX COURSE
Varenna, June 2008
ν
Neutrinos in Cosmology
1st lecture
Introduction: neutrinos and the History of the Universe
This is a neutrino!
T~MeVt~sec
Primordial
Nucleosynthesis
Decoupled neutrinos(Cosmic Neutrino
Background or CNB)
Neutrinos coupled by weak
interactions
At
least 1
specie
s is NR
Relativistic neutrinos
T~
eVNeutrino 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
Relic neutrinos influence several cosmological epochs
T < eVT ~ MeV
Formation of Large Scale Structures
LSS
Cosmic Microwave Background
CMB
PrimordialNucleosynthe
sis
BBN
No flavour sensitivity Neff & mννevs ν , μ τ Neff
Basics of cosmology: background evolution
Introduction: neutrinos and the History of the Universe
Relic neutrino production and decoupling
Neutrinos in Cosmology
Neutrinos and Primordial Nucleosynthesis
Neutrino oscillations in the Early Universe
Neutrinos in Cosmology
Degenerate relic neutrinos (Neutrino asymmetries)
Massive neutrinos as Dark Matter
Effects of neutrino masses on cosmological observables
Bounds on mν from CMB, LSS and other data
Bounds on the radiation content (Nν)
Future sensitivities on mν and Nν from cosmology
Suggested References
BooksModern Cosmology, S. Dodelson (Academic Press, 2003)
The Early Universe, E. Kolb & M. Turner (Addison-Wesley, 1990)
Kinetic theory in the expanding Universe, Bernstein (Cambridge U., 1988)
Recent reviewsNeutrino Cosmology, A.D. Dolgov,
Phys. Rep. 370 (2002) 333-535 [hep-ph/0202122]
Massive neutrinos and cosmology, J. Lesgourgues & SP, Phys. Rep. 429 (2006) 307-379 [astro-ph/0603494]
Primordial Neutrinos, S. HannestadAnn. Rev. Nucl. Part. Sci. 56 (2006) 137-161 [hep-ph/0602058]
BBN and Physics beyond the Standard Model, S. SarkarRep. Prog. Phys. 59 (1996) 1493-1610 [hep-ph/9602260]
Eqs in the SM of Cosmology
++
−−== 22222
2
2222 sin
1dθ φrdθr
krdr
a(t)dtdxdxgds νμμν
µνµνµνµνµν π gGTRgRG Λ+=−= 821
The FLRW Model describes the evolution of the isotropic and homogeneous expanding
Universe
a(t) is the scale factor and k=-1,0,+1 the curvature
Einstein eqs
Energy-momentum tensor of a perfect fluid
µννµµν ρ pguupT −+= )(
Eqs in the SM of Cosmology
)(3.
ppHdtd +−== ρρ
Eq of state p=αρ ρ = const a
-3(1+α)
Radiation α=1/3 Matter α=0 Cosmological constant α=-1 ρR~1/a4 ρM~1/a3 ρΛ~const
2
2.
2
38
)(akG
aa
tH −=
= ρπ00 component
(Friedmann eq)
H(t) is the Hubble parameterρ=ρM+ρR+ρΛ
1)( 22 −= Ω
atHk
ρcrit=3H2/8πG is the critical density
Ω= ρ/ρcrit
Evolution of the Universe
)3(3
4..
pG
aa +−= ρπ
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
)3(3
4..
pG
aa +−= ρπ
a(t)~t1/2 a(t)~t2/3 a(t)~eHt
Evolution of the background densities: 1 MeV → now
3 neutrino species
with different masses
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
Equilibrium thermodynami
cs
Particles in equilibriumwhen T are high and interactions effective
T~1/a(t)
Distribution function of particle momenta in equilibrium
Thermodynamical variables
VARIABLERELATIVISTIC
NON REL.BOSE FERMI
T~MeVt~sec
Primordial
Nucleosynthesis
Neutrinos coupled by weak
interactions(in equilibrium)
1e1
T)(p,f p/T +=ν
-αα
-α
-α
βαβα
βαβα
ee
ee+↔
↔
↔↔
νν
νν
νννν
νννν
Tν = Te = Tγ
1 MeV ≤ T ≤ mμ
Neutrinos in Equilibrium
Neutrino decoupling
As the Universe expands, particle densities are diluted and temperatures fall. Weak interactions become ineffective to keep neutrinos in good thermal contact with the e.m. plasma
Rate of weak processes ~ Hubble expansion rate
MeV T Mπρ
T GMπρ
n , HσΓ νdec
p
RF
p
Rww 1
38
38
v 252
22 ≈→≈→=≈
Rough, but quite accurate estimate of the decoupling temperature
Since νe have both CC and NC interactions with e±
Tdec(νe) ~ 2 MeVTdec(ν ,μ τ) ~ 3 MeV
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 +=ν
At T~me, electron-positron pairs annihilate
heating photons but not the decoupled neutrinos
γγ→+ -ee
Neutrino and Photon (CMB) temperatures
1e1
T)(p,f p/T +=
νν
1/3
411
T
T
=
ν
γ
At T~me, electron-positron pairs annihilate
heating photons but not the decoupled neutrinos
γγ→+ -ee
Neutrino and Photon (CMB) temperatures
1e1
T)(p,f p/T +=
νν
1/3
411
T
T
=
ν
γ
Photon temp falls
slower than 1/a(t)
• Number density
• Energy density
323
3
113(6
113
2 CMBγννν Tπ
)ζn)(p,Tf
π)(pd
n === ∫
→+= ∫νν
νν
π
ρnm
T
)(p,Tfπ)(pd
mp
i
ii
CMB
νν
43/42
3
322
114
1207
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 +
=νν
The Cosmic Neutrino Background
The Cosmic Neutrino Background
• Number density
• Energy density
323
3
113(6
113
2 CMBγννν Tπ
)ζn)(p,Tf
π)(pd
n === ∫
→+= ∫νν
νν
π
ρnm
T
)(p,Tfπ)(pd
mp
i
ii
CMB
νν
43/42
3
322
114
1207
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 +
=νν
At present 112 per flavour cm )( -3νν +
Contribution to the energy density of the Universe
eV 94.1
mh Ω i
i2
∑=ν
52 101.7h Ω −×=ν
At T<me, the radiation content of the Universe is
Relativistic particles in the Universe
γνγνγ ρππρρρ
+=××+=+= 3114
87
1158
73
15
3/44
24
2
r TT
At T<me, the radiation content of the Universe is
Effective number of relativistic neutrino speciesTraditional parametrization of the energy densitystored in relativistic particles
Relativistic particles in the Universe
data) (LEP 008.0984.2 ±=νN# of flavour neutrinos:
• Extra radiation can be:
scalars, pseudoscalars, sterile neutrinos (totally or partially thermalized, bulk), neutrinos in very low-energy reheating scenarios, relativistic decay products of heavy particles…
• Particular case: relic neutrino asymmetries
Constraints from BBN and from CMB+LSS
Extra relativistic particles
At T<me, the radiation content of the Universe is
Effective number of relativistic neutrino speciesTraditional parametrization of the energy densitystored in relativistic particles
Neff is not exactly 3 for standard neutrinos
Relativistic particles in the Universe
data) (LEP 008.0984.2 ±=νN# of flavour neutrinos:
But, since Tdec(ν) is close to me, neutrinos share a small part of the entropy release
At T~me, e+e- pairs annihilate heating photonsγγ→+ -ee
Non-instantaneous neutrino decoupling
fν=fFD(p,Tν)[1+ f(p)]δ
Momentum-dependent Boltzmann equation
9-dim Phase Space ProcessΣPi conservation
Statistical Factor
),(),( 111
tpItpfdpd
Hpdtd
coll=
− ν
+ evolution of total energy density:
ν e
ν µ ,τ
f x10δ
1e
pp/T
2
+
δ ρ ν e(
%)
δ ρ ν µ
(%)
δ ρ ν τ(
%)Neff
Instantaneous decoupling
1.40102
0 0 0 3
SM+3ν mixing(θ13=0)
1.3978 0.73 0.52 0.52 3.046
γγ0/TTfin
Mangano et al, NPB 729 (2005) 221
Non-instantaneous neutrino decoupling
Dolgov, Hansen & Semikoz, NPB 503 (1997) 426Mangano et al, PLB 534 (2002) 8
Changes in CNB quantities
• Contribution of neutrinos to total energy density today (3 degenerate masses)
• Present neutrino number density€
Ων=ρν
ρc
= 3m0
94.12h2 eV2 2eV 20
14.933hm=νΩ
€
nν=335.7 cm3
€
nν=339.3 cm3
Neff varying the neutrino decoupling temperature
End of 1st lecture
Exercises: try to calculate…
• The present number density of massive/massless neutrinos nν
0 in cm-3
• The present energy density of massive/massless neutrinos Ων
0 and find the limits on the total neutrino mass from Ων
0<1 and Ων0 <Ωm
0
• The final ratio Tγ /Tν using the conservation of entropy density before/after e± annihilations
• The decoupling temperature of relic neutrinos using Γ≈ Η
• The evolution of Ω(ν,γ ,b,cdm) with the expansion for (3,0,0), (1,1,1) and (0.05,0.009,0) [masses in eV]
• The value of Neff if neutrinos decouple at Tdec in [5,0.2] MeV