Transcript Neutrino oscillations in dense neutrino media

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!
Decoupled neutrinos
(Cosmic Neutrino
Background or CNB)
Neutrinos coupled
by weak interactions
T~MeV
t~sec
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
Relic neutrinos influence several cosmological epochs
Primordial
Nucleosynthesis
Cosmic Microwave
Background
Formation of Large
Scale Structures
BBN
CMB
LSS
T ~ MeV
νevs νμ,τ
Neff
T < eV
No flavour sensitivity
Neff & mν
Cosmological Aspects of Neutrino Physics
1st lecture
Introduction: neutrinos and the History of the Universe
Basics of cosmology: background evolution
Relic neutrino production and decoupling
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
Books
Modern 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 reviews
Neutrino 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. Hannestad
hep-ph/0602058
BBN and Physics beyond the Standard Model, S. Sarkar
Rep. Prog. Phys. 59 (1996) 1493-1610 [hep-ph/9602260]
Eqs in the SM of Cosmology
The FLRW Model describes the evolution of the
isotropic and homogeneous expanding Universe
2

dr
2
μ
ν
2
2
2
2
2
2
2
ds  g μν dx dx  dt  a(t) 
 r dθ  r sin θdφ 
2
 1  kr

a(t) is the scale factor and k=-1,0,+1 the curvature
Einstein eqs
Energy-momentum
tensor of a
perfect fluid
G
1
 R  g  R  8GT  g 
2
T  ( p   )u u  pg
Eqs in the SM of Cosmology
00 component
(Friedmann eq)
ρ=ρM+ρR+ρΛ
d

 3H ( p  p)
dt
.
2
.
k
 a  8G
2
H (t )    
 2
3
a
a
 
H(t) is the Hubble parameter
k
  1
2 2
H (t ) a
ρcrit=3H2/8πG is the critical density
ρ = const a -3(1+α)
Eq of state p=αρ
Radiation α=1/3
ρR~1/a4
Ω= ρ/ρcrit
Matter α=0
ρM~1/a3
Cosmological constant α=-1
ρΛ~const
Evolution of the Universe
..
a
4G

(   3 p)
a
3
?
..
inflation
inflation
a(t)~eHt
a
4G

( 
3 p)
RD (radiation
domination)
radiation
a
3
a(t)~t1/2
MD matière
(matter domination)
a(t)~t2/3
énergie
noiredomination
dark energy
Evolution of the background densities: 1 MeV → now
3 neutrino
species
with
different
masses
Evolution of the background densities: 1 MeV → now
photons
Ωi= ρi/ρcrit
neutrinos
Λ
cdm
baryons
m3=0.05 eV
m2=0.009 eV
m1≈ 0 eV
Equilibrium
thermodynamics
Distribution function of particle momenta in
equilibrium
Thermodynamical variables
VARIABLE
Particles in equilibrium
when T are high and
interactions effective
T~1/a(t)
RELATIVISTIC
BOSE
FERMI
NON REL.
Neutrinos coupled
by weak interactions
(in equilibrium)
f (p, T) 
1
e p/T  1
T~MeV
t~sec
Neutrinos in Equilibrium
1 MeV  T  mμ
να νβ  να νβ
να νβ  να νβ
να e  να e
-
-
να να  e e

Tν = Te = Tγ
-
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
Rough, but quite accurate estimate of the decoupling temperature
Rate of weak processes ~ Hubble expansion rate
Γw  σw v n , H 2 
8πρ R
2 5

G
T 
F
2
3M p
8πρ R
3M p2
ν
 Tdec
 1 MeV
Since νe have both CC and NC interactions with e±
Tdec(νe) ~ 2 MeV
Tdec(νμ,τ) ~ 3 MeV
Free-streaming
neutrinos (decoupled)
Cosmic Neutrino
Background
Neutrinos coupled
by weak interactions
(in equilibrium)
f (p, T) 
1
e p/T  1
Neutrinos keep the energy
spectrum of a relativistic
fermion with eq form
T~MeV
t~sec
Neutrino and Photon (CMB) temperatures
At T~me,
electronpositron pairs
annihilate
e  e-  γγ
heating photons
but not the
decoupled
neutrinos
Tγ
 11 
 
Tν  4 
1/3
f (p, T) 
1
e p/T  1
Neutrino and Photon (CMB) temperatures
Photon temp falls
slower than 1/a(t)
At T~me,
electronpositron pairs
annihilate
e  e-  γγ
heating photons
but not the
decoupled
neutrinos
Tγ
 11 
 
Tν  4 
1/3
f (p, T) 
1
e p/T  1
The Cosmic Neutrino Background
1
Neutrinos decoupled at T~MeV, keeping a
f (p, T)  p/T
spectrum as that of a relativistic species 
e
1
• Number density
d3 p
3
6ζ (3 ) 3
nν  
f (p,Tν )  nγ 
TCMB
3 ν
2
( 2π)
11
11π
• Energy density
  
i
 7 2  4  4 / 3 4
  TCMB Massless

120  11
3

d
p

p 2  m2i
f (p,Tν )  
3 ν
( 2π)

m i n
Massive mν>>T


The Cosmic Neutrino Background
1
Neutrinos decoupled at T~MeV, keeping a
f (p, T)  p/T
spectrum as that of a relativistic species 
e
1
• Number density
d3 p
3
-36ζ (3 ) 3
(



)
cm
nAt
(p,Tν )  nγ  per
TCMB
ν present
2 flavour
 ( 2π)3 fν112
11
11π
• Energy density
 7 22  4  4 / 3 54
Ω
 ν h  1.710TCMB
120  11
3

d
p

Contribution
the energy
 i   p 2 to
m2i
f (p,Tν )  
mi

3 ν
density of the Universe
( 2π)
 h2 m ni
Ω
i 
ν
93.2
eV

Massless
Massive
mν>>T
Relativistic particles in the Universe
At T<me, the radiation content of the Universe is
4/3
2

7

7
4
  
4
4
 r      T  3   T  1    3 
15
8 15
 8  11 
2
Relativistic particles in the Universe
At T<me, the radiation content of the Universe is
Effective number of relativistic neutrino species
Traditional parametrization of the energy density
stored in relativistic particles
# of flavour neutrinos: N  2.984 0.008(LEP data)
Extra relativistic particles
• 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
Relativistic particles in the Universe
At T<me, the radiation content of the Universe is
Effective number of relativistic neutrino species
Traditional parametrization of the energy density
stored in relativistic particles
# of flavour neutrinos: N  2.984 0.008(LEP data)
Neff is not exactly 3 for standard neutrinos
Non-instantaneous neutrino decoupling
At T~me, e+e- pairs annihilate heating photons
e e  γγ

-
But, since Tdec(ν) is close to me, neutrinos
share a small part of the entropy release
f=fFD(p,T)[1+δf(p)]
Boltzmann Equation
Statistical Factor
9-dim Phase Space
Pi conservation
Process
e
,
δf x10
p2
e p/T  1
Non-instantaneous neutrino decoupling
 11
 
T  4 
T
fν=fFD(p,Tν)[1+δf(p)]
1/ 3
 1.40102
ρ(e) 0.73% larger
ρ(,) 0.52% larger
T a(t )  1.3978
Non-instantaneous decoupling + QED corrections to e.m. plasma
+ Flavor Oscillations
Neff=3.046
T.Pinto et al, NPB
Mangano
729 (2005)
et al 2002
221
BBN: Creation
of light
elements
Produced elements: D,
3He, 4He, 7Li and small
abundances of others
Theoretical inputs:
BBN: Creation of light elements
Range of temperatures: from 0.8 to 0.01 MeV
Phase I: 0.8-0.1 MeV
n-p reactions
n/p freezing and
neutron decay
BBN: Creation of light elements
Phase II: 0.1-0.01 MeV
Formation of light
nuclei starting from D
Photodesintegration
prevents earlier
formation for
temperatures closer
to nuclear binding
energies
0.07
MeV
0.03
MeV
BBN: Creation of light elements
Phase II: 0.1-0.01 MeV
Formation of light
nuclei starting from D
Photodesintegration
prevents earlier
formation for
temperatures closer
to nuclear binding
energies
0.07
MeV
0.03
MeV
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
BBN: Predictions vs Observations
after WMAP
ΩBh2=0.023±0.001
Fields & Sarkar PDG 2004
Effect of neutrinos on BBN
1. Neff fixes the expansion rate during BBN
8π
H 
3Mp2
3.4 3.2
(Neff)>0   4He
Burles, Nollett & Turner 1999
2. Direct effect of electron neutrinos and antineutrinos
on the n-p reactions
3.0
BBN: allowed ranges for Neff
Cuoco et al, IJMP A19 (2004)
4431 [astro-ph/0307203]
Using 4He + D data (2σ)
1.1
Neff  2.50.9
Neutrino oscillations in the Early Universe
Neutrino oscillations are effective when
medium effects get small enough
Coupled neutrinos
Compare oscillation term
with effective potentials
Oscillation term prop.
to Δm2/2E
Second order matter
effects prop. to
GF(E/MZ)2[n(e-)+n(e+)]
First order matter
effects prop. to
GF[n(e-)-n(e+)]
Strumia & Vissani,
hep-ph/0606054
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
Active-sterile neutrino oscillations
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)
Results depend on the sign of Δm2
(resonant vs non-resonant case)
Active-sterile neutrino oscillations
Additional
neutrino
fully in eq
Flavour
neutrino
spectrum
depleted
Dolgov & Villante,
NPB 679 (2004) 261
Active-sterile neutrino oscillations
Additional
neutrino
fully in eq
Kirilova, astro-ph/0312569
Flavour
neutrino
spectrum
depleted
Dolgov & Villante,
NPB 679 (2004) 261
Active-sterile neutrino oscillations
Additional
neutrino
fully in eq
Flavour
neutrino
spectrum
depleted
Dolgov & Villante,
NPB 679 (2004) 261
Active-sterile neutrino oscillations
Additional
neutrino
fully in eq
Dolgov & Villante,
NPB 679 (2004) 261
End of 1st lecture