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Precise calculation of the relic neutrino density
Sergio Pastor (IFIC)
ν
JIGSAW 2007TIFR Mumbai, February 2007
In collaboration with T. Pinto, G, Mangano, G. Miele, O. Pisanti and P.D. Serpico
NPB 729 (2005) 221 , NPB 756 (2006) 100
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Outline
Precise calculation of the relic neutrino density
New results in the SM and in presence of
electron-neutrino NSI
Introduction: the Cosmic Neutrino Background
Relic neutrino decoupling
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The CNB
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T~MeVt~sec
Neutrinos coupled by weak
interactions(in equilibrium)
1e1
T)(p,f p/Tν
Primordial
Nucleosynthesis
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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/Tν
Primordial
Nucleosynthesis
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• 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
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Relic neutrino decoupling
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-αα
-α
-α
βαβα
βαβα
ee
ee
νν
νν
νννν
νννν
Tν = Te = Tγ
1 MeV T mμ
Neutrinos in Equilibrium
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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 1T νdec
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
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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
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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
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Precise calculation of neutrino decoupling:
SM + flavour oscillations
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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)]
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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
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Momentum-dependent Boltzmann equation
9-dim Phase Space ProcessPi conservation
Statistical Factor
),(),( 111
tpItpfdp
dHp
dt
dcoll
+ evolution of total energy density:
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For T>2 MeV neutrinos are coupled
Between 2>T/MeV>0.1distortions grow
At lower temperaturesdistortions freeze out
f e f
Evolution of fν for a particular momentum p=10T
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Evolution of fν for a particular momentum p=10T
Final spectral distortion
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e
,
δf x10
1e
pp/T
2
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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
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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:
Bounds from BBN and from CMB+LSS
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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:
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e(%) (%) (%) Neff
Instantaneous decoupling
1.40102 0 0 0 3
SM 1.3978 0.94 0.43 0.43 3.046
0/TT fin
Dolgov, Hansen & Semikoz, NPB 503 (1997) 426Mangano et al, PLB 534 (2002) 8
Results
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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
GFE/MZ2[ρ(e-)+ρ(e+)]
Coupled neutrinos
Previous work by Hannestad,PRD 65 (2002) 083006
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Around T~1 MeV the oscillationsstart to modifythe distortion
The variationis larger for e
Effects of flavour neutrino oscillations on the spectral distortions
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Around T~1 MeV the oscillationsstart to modifythe distortion
The variationis larger for e
The differencebetween differentflavors is reduced
Effects of flavour neutrino oscillations on the spectral distortions
Oscillations smooth the flavour dependence of the distortion
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e(%) (%) (%) Neff
Instantaneous decoupling
1.40102 0 0 0 3
SM 1.3978 0.94 0.43 0.43 3.046
+3ν mixing(θ13=0) 1.3978 0.73 0.52 0.52 3.046
+3ν mixing(sin2θ13=0.047)
1.3978 0.70 0.56 0.52 3.046
0/TT fin
Mangano et al, NPB 729 (2005) 221
Results
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Changes in CNB quantities
• Contribution of neutrinos to total energy density today (3 degenerate masses)
• Present neutrino number density
c
3m0
94.12h2 eV2 2eV 20
14.93
3
h
m
n 335.7 cm-3
n 339.3 cm-3
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Precise calculation of neutrino decoupling:
Non-standard neutrino-electron interactions
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Electron-Neutrino NSI
New effective interactions between electron and neutrinos
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Electron-Neutrino NSI
Breaking of Lepton universality (=) Flavour-changing (≠ )
Limits on from scattering experiments, LEP data, solar vs Kamland data…
RL,
Berezhiani & Rossi, PLB 535 (2002) 207Davidson et al, JHEP 03 (2003) 011Barranco et al, PRD 73 (2006) 113001
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Analytical calculation of Tdec in presence of NSIAnalytical calculation of Tdec in presence of NSI
Contours of equal Tdec in MeV with diagonal NSI parameters
SM SM
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Neff varying the neutrino decoupling temperatureNeff varying the neutrino decoupling temperature
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Effects of NSI on the neutrino spectral distortions
Here largervariation for ,
Neutrinos keep thermal contact with e- until smaller temperatures
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e(%) (%) (%) Neff
Instantaneous decoupling
1.40102 0 0 0 3
+3ν mixing(θ13=0) 1.3978 0.73 0.52 0.52 3.046
Lee= 4.0 Ree= 4.0
1.3812 9.47 3.83 3.83 3.357
0/TT fin
Mangano et al, NPB 756 (2006) 100
Results
Very large NSI parameters, FAR from allowed regions
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e(%) (%) (%) Neff
Instantaneous decoupling
1.40102 0 0 0 3
+3ν mixing(θ13=0) 1.3978 0.73 0.52 0.52 3.046
Lee= 0.12 Ree= -1.58L= -0.5 R= 0.5
Le= -0.85 Re= 0.38
1.3937 2.21 1.66 0.52 3.120
0/TT fin
Mangano et al, NPB 756 (2006) 100
Results
Large NSI parameters, still allowed by present lab data
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Departure from Neff=3 not observable from present
cosmological data
Mangano et al, hep-ph/0612150
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…but maybe in the near future ?
Forecast analysis:CMB data
Bowen et al MNRAS 2002
ΔNeff ~ 3 (WMAP)
ΔNeff ~ 0.2 (Planck)
Bashinsky & Seljak PRD 69 (2004) 083002Example of futureCMB satellite
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The small spectral distortions from relic neutrino—electron processes can be
precisely calculated, leading to Neff=3.046 (or up to 3 times more including NSI)
Conclusions
ν
Cosmological observables can be used to bound (or measure) neutrino properties,
once the relic neutrino spectrum is known