Transcript Neutrino oscillations in dense neutrino media

Cosmological Aspects of
Neutrino Physics (II)
ν
Sergio Pastor (IFIC)
61st SUSSP
St Andrews, August 2006
Cosmological Aspects of Neutrino Physics
2nd lecture
Degenerate relic neutrinos (Neutrino asymmetries)
Massive neutrinos as Dark Matter
Effects of neutrino masses on cosmological observables
Decoupled neutrinos
(Cosmic Neutrino
Background)
Neutrinos coupled
by weak interactions
T~MeV
t~sec
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
f (p,  , T) 
1
e (p- )/T  1
   /T
T~MeV
t~sec
Relic neutrino asymmetries
Fermi-Dirac spectrum
with temperature T and
chemical potential 
n  n
Raffelt
n  n
1  T
L 

n
12 (3)  T
2
4

15       
N  2     
7        
3
 2
    3




More radiation
Degenerate Big Bang Nucleosynthesis
If 0 , for any flavor
2
4

15       
N  2     
7        
()>(0)   4He
Plus the direct effect on np if (e)0
 mn  m p

n
   exp 
  e 
T
 p  eq


e>0   4He
Pairs (e,N) that produce the same observed
abundances for larger B
Kang & Steigman 1992
Combined bounds BBN & CMB-LSS
Degeneracy direction
(arbitrary ξe)
Hansen et al 2001
 0.01   e  0.22
Hannestad 2003
  ,  2.4
In the presence of flavor oscillations ?
Flavor neutrino oscillations in the Early Universe
• Density matrix
• Mixing matrix
  ee

  e

 e
 e
 

c12 c13


  s12 c23  c12 s23 s13
 s s c c s
 12 23 12 23 13
 e 

  
 
s12 c13
c12 c23  s12 s23 s13
 c12 s23  s12 c23 s13
s13 

s23c13 
c23c13 
• Expansion of the Universe
• Charged lepton background (2nd order contribution)
• Collisions (damping)
• Neutrino background: diagonal and off-diagonal potentials
Dominant term: Synchronized Neutrino Oscillations
Evolution of neutrino asymmetries
BBN
Effective flavor equilibrium
(almost) established 
 0.05    0.07
  0.07
Serpico & Raffelt 2005
Dolgov et al 2002
Abazajian et al 2002
Wong 2002
Lunardini & Smirnov 2001
Massive Neutrinos and Cosmology
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
We know that flavour neutrino oscillations exist
From present evidences of oscillations from experiments measuring
atmospheric, solar, reactor and accelerator neutrinos
(e, μ, τ )  (ν1 , ν2, ν3 )
Evidence of Particle Physics
beyond the Standard Model !
Mixing Parameters...
From present evidences of oscillations from experiments measuring
atmospheric, solar, reactor and accelerator neutrinos
Mixing matrix U
Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122
Mixing Parameters...
From present evidences of oscillations from experiments measuring
atmospheric, solar, reactor and accelerator neutrinos
Mixing matrix U
Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122
Mixing Parameters...
From present evidences of oscillations from experiments measuring
atmospheric, solar, reactor and accelerator neutrinos
Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122
... and neutrino masses
Data on flavour oscillations do not fix the absolute scale of neutrino masses
eV
eV
2
Δmatm
 0.05 eV
Δm2sun  0.009 eV
solar
atm
INVERTED
NORMAL
atm
solar
What is the value of m0 ?
m0
Direct laboratory bounds on mν
Searching for non-zero neutrino mass in laboratory experiments
• Tritium beta decay: measurements of endpoint energy
H  3He  e-  e
3
m(νe) < 2.2 eV (95% CL) Mainz
Future experiments (KATRIN) m(νe) ~ 0.2-0.3 eV
• Neutrinoless double beta decay: if Majorana neutrinos
(A, Z)  (A, Z  2)  2eexperiments with 76Ge and other isotopes: ImeeI < 0.4hN eV
Absolute mass scale searches
Tritium β
decay
Neutrinoless
double beta
decay
Cosmology
1/ 2

2
2
m e    U ei mi 
 i

mee 
2
U
 ei mi
< 2.2 eV
< 0.4-1.6 eV
i
~  mi
i
< 0.3-2.0 eV
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
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
Neutrinos as Dark Matter
• Neutrinos are natural DM candidates
Ωνh 
2
m
i
i
93.2 eV
Ων  1   m i  46 eV
i
Ων  Ωm  0.3   m i  15 eV
i
• They stream freely until non-relativistic (collisionless
phase mixing)
Neutrinos are HOT Dark Matter
• First structuresNeutrino
to be formed
Universe became
Free when
Streaming
-1
matter -dominated
 mν 
ν
41 
 Mpc
 30 eV 
Φ
• Ruled out by structure
b, formation
cdm
CDM
Neutrinos as Dark Matter
• Neutrinos are natural DM candidates
Ωνh 
2
m
i
i
93.2 eV
Ων  1   m i  46 eV
i
Ων  Ωm  0.3   m i  15 eV
i
• They stream freely until non-relativistic (collisionless
phase mixing)
Neutrinos are HOT Dark Matter
• First structures to be formed when Universe became
matter -dominated
-1
 mν 
41 
 Mpc
 30 eV 
• Ruled out by structure formation
CDM
Neutrinos as Hot Dark Matter
Effect of Massive Neutrinos: suppression of Power at small scales
RAFFELT
Neutrinos as Hot Dark Matter
Effect of Massive Neutrinos: suppression of Power at small scales
RAFFELT
Neutrinos as Hot Dark Matter
Massive Neutrinos can still be subdominant DM: limits on mν
from Structure Formation (combined with other cosmological
data)
Cosmological observables
?
inflation
inflation
RD (radiation
radiation domination)
MD matière
(matter domination)
énergie
noiredomination
dark energy
Power Spectrum of density fluctuations
Field of density
Fluctuations
 ( x)
 ( x) 

Matter power spectrum is
the Fourier transform of the
two-point correlation function
Galaxy Redshift
Surveys
2dFGRS
SDSS
Cosmological observables: LSS
0<z<0.2
?
inflation
inflation
RD (radiation
radiation domination)
Distribution
of large-scale
structures at low z
MD matière
(matter domination)
énergie
noiredomination
dark energy
bias uncertainty
60 Mpc
linear non-linear
δρ/ρ<1 δρ/ρ ~ 1
matter power spectrum P(k)  galaxy redshift surveys
Power spectrum of density fluctuations
Non-linearity
Bias b2(k)=Pg(k)/Pm(k)
2dFGRS
SDSS
kma
x
Cosmological observables : LSS
?
2<z<3
inflation
inflation
RD (radiation
radiation domination)
Distribution
MD matière
(matter domination)
énergie
noiredomination
dark energy
various systematics
of large-scale
structures at
medium z
matter power spectrum P(k)  Lyman-α forests in quasar spectra
Neutrinos as Hot Dark Matter
Massive Neutrinos can still be subdominant DM: limits
on mν from Structure Formation (combined with other
cosmological data)
• Effect of Massive Neutrinos:
suppression of Power at small scales
fν
Structure formation after equality
baryons and
CDM
experience
gravitational
clustering
Structure formation after equality
baryons and
CDM
experience
gravitational
clustering
Structure formation after equality
baryons and
CDM
experience
gravitational
clustering
growth of /(k,t) fixed by
« gravity vs. expansion » balance
 /  a
Structure formation after equality
baryons and
CDM
experience
gravitational
clustering
neutrinos
experience
free-streaming
with
v = c or <p>/m
Structure formation after equality
baryon
baryons
andand
CDM
experience
CDM
gravitational
experience
gravitational
clustering
clustering
neutrinos
experience
free-streaming
with
v = c or <p>/m
neutrinos cannot cluster below a diffusion length
l= ∫ v dt < ∫ c dt
Structure formation after equality
baryon
baryons
andand
CDM
experience
CDM
gravitational
experience
gravitational
clustering
clustering
neutrinos
experience
free-streaming
with
v = c or <p>/m
for (2/k) < l ,
o neutrinos
cannot cluster below a diffusion length
free-streaming supresses growth of structures during MD
l=
∫ v dtf < ∫ c dt
1-3/5
 /  a
with f = /m ≈ (Sm)/(15 eV)
Structure formation after equality
a
cdm
Massless
neutrinos
b


J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/0603494]
Structure formation after equality
a
cdm
b
a 1-3/5f

Massive
neutrinos
fν=0.1

J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/0603494]
Effect of massive neutrinos on P(k)
Observable signature of the total mass on P(k) :
P(k) massive
P(k) massless
various
fν
Lesgourgues & SP,
Phys. Rep. 429 (2006) 307
Cosmological observables: CMB
?
z≈1100
inflation
inflation
RD (radiation
radiation domination)
MD matière
(matter domination)
énergie
noiredomination
dark energy
Anisotropies
of the Cosmic
Microwave
Background
CMB temperature/polarization anisotropies  photon power spectra
CMB TT DATA
Map of CMBR temperature
Fluctuations
Δ( ,  ) 
T( ,  ) - T
T
Multipole Expansion
Angular Power Spectrum
CMB TT DATA
Map of CMBR temperature
Fluctuations
Δ( ,  ) 
T( ,  ) - T
T
Multipole Expansion
Angular Power Spectrum
TT
CMB
Polarization
DATA
TE
EE
BB
WMAP 3
Effect of massive neutrinos on the CMB spectra
1) Direct effect of sub-eV massive neutrinos on the evolution
of the baryon-photon coupling is very small
2) Impact on CMB spectra is indirect: non-zero Ων today
implies a change in the spatial curvature or other Ωi . The
background evolution is modified
Ex: in a flat universe,
keep ΩΛ+Ωcdm+Ωb+Ων=1
constant
Effect of massive neutrinos on the CMB spectra
Problem with parameter degeneracies: change in other
cosmological parameters can mimic the effect of nu masses
Effect of massive neutrinos on the
CMB and Matter Power Spectra
Max Tegmark
www.hep.upenn.edu/~max/
End of 2nd lecture