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Cosmological Aspects of Neutrino Physics (I). ν. Sergio Pastor (IFIC) 61st SUSSP St Andrews, August 2006. Cosmological Aspects of Neutrino Physics. 1st lecture. Introduction: neutrinos and the History of the Universe. This is a neutrino!. Neutrinos coupled by weak interactions. - PowerPoint PPT Presentation
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04/22/23
Cosmological Aspects of Neutrino Physics (I)
Sergio Pastor (IFIC)61st SUSSP
St Andrews, August 2006
ν
Cosmological Aspects of Neutrino Physics1st 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~
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
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Relic neutrinos influence several cosmological epochs
T < eVT ~ MeV
Formation of Large Scale Structures
LSS
Cosmic Microwave Background
CMB
Primordial
Nucleosynthesis
BBN
No flavour sensitivity Neff & mννevs νμ,τ Neff
Basics of cosmology: background evolution
1st lecture
Introduction: neutrinos and the History of the Universe
Relic neutrino production and decoupling
Cosmological Aspects of Neutrino Physics
Neutrinos and Primordial Nucleosynthesis
Neutrino oscillations in the Early Universe*
* Advanced topic
Cosmological Aspects of Neutrino Physics
2nd & 3rd lectures
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
* Advanced topic
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. Hannestadhep-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
1θdφrdθr
kr
dra(t)dtdxdxgds νμ
μν
gGTRgRG 82
1
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
pguupT )(
Eqs in the SM of Cosmology
)(3.
ppHdt
d
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
3
8)(
a
kG
a
atH
00 component
(Friedmann eq)
H(t) is the Hubble parameterρ=ρM+ρR+ρΛ
1)( 22
atH
k
ρcrit=3H2/8πG is the critical density
Ω= ρ/ρcrit
Evolution of the Universe
)3(3
4..
pG
a
a
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
a
a
a(t)~t1/2 a(t)~t2/3 a(t)~eHt
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Evolution of the background densities: 1 MeV → now
3 neutrino species
with different masses
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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
-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 M
πρT G
M
πρ n , HσΓ ν
decp
RF
p
Rww 1
3
8
3
8v
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(νμ,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,fp/T
At T~me, electron-positron pairs annihilate
heating photons but not the decoupled neutrinos
γγ -ee
Neutrino and Photon (CMB) temperatures
1e1
T)(p,fp/T
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,fp/T
1/3
411
T
T
ν
γ
Photon temp falls
slower than 1/a(t)
• 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
The Cosmic Neutrino Background
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
At T<me, the radiation content of the Universe is
Relativistic particles in the Universe
311
4
8
71
158
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 N# 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 N# 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
f=fFD(p,T)[1+δf(p)]
Boltzmann Equation
9-dim Phase Space ProcessPi conservation
Statistical Factor
e
,
δf x10
1e
pp/T
2
ρ(e) 0.73% largerρ() 0.52% larger
fν=fFD(p,Tν)[1+δf(p)]
Mangano et al 2002
Non-instantaneous neutrino decoupling
Non-instantaneous decoupling + QED corrections to e.m. plasma+ Flavor Oscillations
Neff=3.046 T.Pinto et al, NPB 729 (2005) 221
40102.14
113/1
T
T
3978.1)( taT
Produced elements: D, 3He, 4He, 7Li and
small abundances of others
BBN: Creation of light
elements
Theoretical inputs:
Range of temperatures: from 0.8 to 0.01 MeV
BBN: Creation of light elements
n/p freezing and neutron decay
Phase I: 0.8-0.1 MeVn-p reactions
BBN: Creation of light elements
0.03 MeV
0.07 MeV
Phase II: 0.1-0.01 MeVFormation of light nuclei starting from D
Photodesintegrationprevents earlier formation for temperatures closer to nuclear binding energies
BBN: Creation of light elements
0.03 MeV
0.07 MeV
Phase II: 0.1-0.01 MeVFormation of light nuclei starting from D
Photodesintegrationprevents earlier formation for temperatures closer to nuclear binding energies
BBN: Measurement of Primordial abundances
Difficult task: search in astrophysical systems with chemical evolution as small as possible
Deuterium: destroyed in stars. Any observed abundance of D is a lower limit to the primordial abundance. Data from high-z, low metallicity QSO absorption line systems
Helium-3: produced and destroyed in stars (complicated evolution)Data from solar system and galaxies but not used in BBN analysis
Helium-4: primordial abundance increased by H burning in stars. Data from low metallicity, extragalatic HII regions
Lithium-7: destroyed in stars, produced in cosmic ray reactions.Data from oldest, most metal-poor stars in the Galaxy
Fields & Sarkar PDG 2004
BBN: Predictions vs Observations
after WMAPΩBh2=0.023±0.001
Effect of neutrinos on BBN 1. Neff fixes the expansion rate during BBN
(Neff)>0 4He
Burles, Nollett & Turner 1999
2p3M
8π H
3.4 3.2
3.0
2. Direct effect of electron neutrinos and antineutrinos on the n-p reactions
BBN: allowed ranges for Neff
Cuoco et al, IJMP A19 (2004) 4431 [astro-ph/0307203]
Using 4He + D data (2σ)
1.10.9eff 2.5N
Neutrino oscillations in the Early Universe
Neutrino oscillations are effective when medium effects get small enough
Compare oscillation term with effective potentials
Strumia & Vissani, hep-ph/0606054
Oscillation term prop. to Δm2/2E
First order matter effects prop. toGF[n(e-)-n(e+)]
Second order matter effects prop. to
GF(E/MZ)2[n(e-)+n(e+)]
Coupled neutrinos
Flavor neutrino oscillations in the Early Universe
Standard case: all neutrino flavours equally populated oscillations are effective below a few MeV, but have
no effect (except for mixing the small distortions δfν)Cosmology is insensitive to neutrino flavour after decoupling!
Non-zero neutrino asymmetries: flavour oscillations lead
to (almost) equilibrium for all μν
What if additional, sterile neutrino species are mixed with the flavour neutrinos?
If oscillations are effective before decoupling: the additional species can be brought into equilibrium: Neff=4
If oscillations are effective after decoupling: Neff=3 but the spectrum of active neutrinos is distorted (direct effect of νe and anti-νe on BBN)
Active-sterile neutrino oscillations
Results depend on the sign of Δm2
(resonant vs non-resonant case)
Active-sterile neutrino oscillations
Dolgov & Villante, NPB 679 (2004) 261
Additional neutrino
fully in eq
Flavour neutrino spectrum depleted
Active-sterile neutrino oscillations
Dolgov & Villante, NPB 679 (2004) 261
Additional neutrino
fully in eq
Flavour neutrino spectrum depleted
Kirilova, astro-ph/0312569
Active-sterile neutrino oscillations
Dolgov & Villante, NPB 679 (2004) 261
Additional neutrino
fully in eq
Flavour neutrino spectrum depleted
Active-sterile neutrino oscillations
Dolgov & Villante, NPB 679 (2004) 261
Additional neutrino
fully in eq
End of 1st lecture