Cosmological probes of neutrino masses (Neutrinos in Cosmology)
Lecture II
Sergio Pastor (IFIC Valencia)
INT. SCHOOL OF PHYSICSENRICO FERMI, CLXX COURSE
Varenna, June 2008
ν
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
Neutrinos in Cosmology2nd lecture
Degenerate relic neutrinos (Neutrino asymmetries)
Massive neutrinos as Dark Matter
Effects of neutrino masses on cosmological observables
Neutrino oscillations in the Early Universe
Neutrinos and Primordial Nucleosynthesis
( )
T~MeVt~sec
Primordial
Nucleosynthesis
Decoupled neutrinos(Cosmic Neutrino
Background or CNB)
Neutrinos coupled by weak
interactions
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: 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 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 2006
BBN: Predictions vs Observations
2B10
B10 h274Ω
10
/nnη ≅= −
γ
after WMAP5ΩBh2=0.02265±0.00059
Effect of neutrinos on BBN 1. Neff fixes the expansion rate during BBN
ρ(Neff)>ρ0 → ↑ 4He
Burles, Nollett & Turner 1999
2p3M
8π H
ρ= 3.4 3.23.0
2. Direct effect of electron neutrinos and antineutrinos on the n-p reactions
BBN: allowed ranges for Neff
Mangano et al, JCAP 0703 (2007) 006
Using 4He + D data (95% CL)
1.41.2 eff 3.1N +
−=
2B10
B10 h274Ω
10
/nnη ≅= −
γ
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. toGF(E/MZ
2 )[ρ(e-)
+ρ(e+)]
Coupled neutrinos
Flavour 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, light 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
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
Degenerate relic neutrinos (relic neutrino asymmetries)
T~MeVt~sec
Primordial
Nucleosynthesis
Decoupled neutrinos(Cosmic Neutrino
Background)
Neutrinos coupled by weak
interactions
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
1e1
T),(p,f )/T-(p +=
νµνν µ
ξν=µν /T
Relic neutrino asymmetries
νν nn ≠
[ ]32
3
)3(121
ννγ
ν
γ
ννν ξξπ
ζ+
=−=
TT
nnn
L
+
=∆
42
2715
πξ
πξ νν
νN
Raffelt
Fermi-Dirac spectrum with temperature T and
chemical potential µν
More radiation
Degenerate Big Bang Nucleosynthesis
If ξν≠ 0 , for any flavor
+
=∆
42
2715
πξ
πξ νν
νN ρ(ξν)> ρ(0) → ↑ 4He
Plus the direct effect on n↔p if ξ(νe) ≠ 0
−
−−=
e
pn
eq T
mm
pn ξexp ξ e>0 → ↓ 4He
Pairs of values (ξe,∆Nν) that produce the same observed abundances for larger ηBKang & Steigman 1992
Hansen et al 2001 Hannestad 2003
Combined bounds BBN & CMB-LSS
4.2 22.001.0 , ≤≤≤− τµξξe
In the presence of flavor oscillations ?
Degeneracy direction (arbitrary ξe)
Flavor neutrino oscillations in the Early Universe
• Density matrix
• Mixing matrix
• Expansion of the Universe• Charged lepton background (2nd order contribution)• Collisions (damping)• Neutrino background: diagonal and off-diagonal potentials
τττµτ
µτµµµ
τµ
ρρρρρρρρρ
e
e
eeee
−−−−−−
132313231223121323122312
132313231223121323122312
1313121312
ccscsscsccsscssssccssccs
scscc
Dominant term: Synchronized Neutrino Oscillations
BBN
Evolution of neutrino asymmetries
07.0 ≤νξEffective flavor equilibrium (almost) established →
Dolgov et al 2002Wong 2002Abazajian et al 2002
07.005.0 ≤≤− ξ Serpico & Raffelt 2005
End of 2nd lecture