Transcript Neutrino oscillations in dense neutrino media

RELIC NEUTRINOS: NEUTRINO
PROPERTIES FROM COSMOLOGY
ν
Sergio Pastor (IFIC)
RELIC NEUTRINOS: OUTLINE
Standard neutrinos
Extra radiation and
Neutrino asymmetries
Massive neutrinos
RELIC NEUTRINOS
Standard neutrinos
Extra radiation and
Neutrino asymmetries
Massive neutrinos
Standard Relic Neutrinos
Neutrinos in equilibrium
fν(p,T)=fFD(p,T)
f (p, T) 
1
e p/T  1
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
-
Standard Relic Neutrinos
Neutrinos in equilibrium
fν(p,T)=fFD(p,T)
f (p, T) 
1
e p/T  1
Neutrino decoupling
rate of weak processes  Hubble expansionrate
Γν  H  GFT 5 
8π


T
dec  1 MeV
2
3Mp
Neutrino decoupling
Tdec(νe) ~ 2.3 MeV
Tdec(νμ,τ) ~ 3.5 MeV
Decoupled Neutrinos
fν(p)=fFD(p,Tν)
Neutrino and Photon temperatures
At T~me, electron-positron pairs annihilate
e e  γγ

-
heating photons but not the decoupled neutrinos
Tγ
 11 
 
Tν  4 
1/3
Decoupled neutrinos stream freely until non-relativistic
Neutrinos after decoupling
• Number density
nν   
i
at present
d p
9
6ζ (3 ) 3
-3
f
(p,T
)

n

T

112
(



)
cm
ν
ν
γ
CMB
( 2π)3
11
11π 2
3
per flavor
• Energy density
ν   
i
 21 4  4 / 3  2 4 Massless
TCMB
  
4 11
30
3

  
2
2 d p
p  m i
f (p,Tν )  
3 ν
( 2π)

m i n Massive mν>>T


i


Neutrinos and Cosmology
Neutrinos influence several cosmological scenarios
Primordial
Nucleosynthesis
Cosmic Microwave
Background
Formation of Large
Scale Structures
BBN
CMB
LSS
z~1010
z~1000
RELIC NEUTRINOS
Standard neutrinos
Extra radiation and
Neutrino asymmetries
Massive neutrinos
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
N  2.984 0.008(LEP data)
Neff is not exactly 3 for standard neutrinos (if mν<<T)
Non-instantaneous neutrino decoupling
At T~me, e+e- pairs annihilate heating photons
e e  γγ

-
But, since Tdec(νe) ~ me, neutrinos slightly share
a small part of the entropy release
Non-instantaneous neutrino decoupling
fν=fFD(p,Tν)[1+δf(p)]
ρ(νe) 1% larger
ρ(νμ,τ) 0.5% larger
Tν 0.15% larger
Non-instantaneous decoupling + QED corrections to e.m. plasma
But, since Tdec(νe) ~ me, neutrinos slightly share
a small part of the entropy release
Mangano et al 2002
Neff=3.0395
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
BBN: Creation of light elements
Produced elements: D,
3He, 4He, 7Li and small
abundances of others
Standard BBN: the baryon density is the sole parameter
BBN: Predictions vs Observations
After WMAP
ΩBh2=0.023±0.001
Fields & Sarkar PDG 2002
Effect of Neff on BBN
Neff fixes the expansion rate during BBN
H 
8π
3Mp2
(Neff)>0   4He
Burles, Nollett & Turner 1999
3.4 3.2
3.0
BBN: allowed ranges for Neff
0.4
Neff  2.60.3
Hannestad astro-ph/0303076
Hannestad astro-ph/0303076
Not significantly different
from previous analyses
Lisi et al 1999, Esposito et al 2000,
Burles et al 2001, Cyburt et al 2002…
Hannestad astro-ph/0303076
ΔNeff  0.4
Cyburt et al, astro-ph/0302431
CMB DATA: FIRST YEAR WMAP vs COBE
CMB DATA: INCREASING PRECISION
Map of CMBR temperature
Fluctuations
Δ( ,  ) 
T( ,  ) - T
T
Multipole Expansion
Angular Power Spectrum
CMB DATA: INCREASING PRECISION
Degrees (θ) 10
1
0.1
CMB DATA: FIRST YEAR OF WMAP
Degrees (θ) 10
1
0.1
Effect of Neff on CMB
• Neff modifies the radiation content:
• Changes the epoch of matter-radiation equivalence
CMB+LSS: allowed ranges for Neff
Problem: parameter degeneracies
• Set of parameters: ( Ωbh2 , Ωcdmh2 , h , ns , A , b , Neff )
• DATA: WMAP + other CMB + 2dF + HST (+ SN-Ia)
• Upper bound on h important to fix upper limit on Neff
• Flat Models
3.7
Neff  3.52.0
95% CL
• Non-flat Models
Crotty, Lesgourgues & SP, astro-ph/0302337
2.0
Neff  4.11.9
95% CL
Neff  0 at 3σ
Pierpaoli astro-ph/0302465
Future bounds on Neff
• Next CMB data from WMAP and PLANCK (other CMB
experiments on large l’s) temperature and polarization spectra
•Forecast analysis in ΩΛ=0 models
Lopez et al, PRL 82 (1999) 3952
PLANCK
Recent analysis:
Larger errors
WMAP
Bowen et al 2002
ΔNeff ~ 3 (WMAP)
ΔNeff ~ 0.2 (Planck)
Degenerate Relic Neutrinos
   /T
Neutrinos in equilibrium
fν(p,T)=fFD(p,T)
f (p,  , T) 
1
e (p- )/T  1
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 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 (finite T contribution)
• Collisions (damping)
• Neutrino background: diagonal and off-diagonal potentials
Dominant term: Synchronized Neutrino Oscillations
Evolution in ATM + solar LMA (13=0)
BBN
Effective flavor equilibrium
(almost) established 
  0.07
Dolgov et al 2002
Evolution in ATM + solar LOW (13=0)
BBN
Synchronized neutrino oscillations
Small conversion before the onset of BBN
RELIC NEUTRINOS
Standard neutrinos
Extra radiation and
Neutrino asymmetries
Massive neutrinos
Neutrinos as Dark Matter
• Neutrinos are natural DM candidates
Ωνh 
2
m
i
i
Ων  1   mi  46 eV
92.5 eV
i
• They stream freely until non-relativistic (collisionless
phase mixing)
Neutrinos are HOT Dark Matter
• First structures to be formed when Universe became
Neutrino Free Streaming
matter -dominated
-1
 mν 
41 
 Mpc
 30 eV 
• Ruled out by structure formation
CDM
Neutrinos as Dark Matter
• Neutrinos are natural DM candidates
Ωνh 
2
m
i
i
Ων  1   mi  46 eV
92.5 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
Power Spectrum of density fluctuations
Massive Neutrinos can still be subdominant DM:
limits on mν from Structure Formation
CMB experiments
Galaxy Surveys
Neutrinos as Hot Dark Matter
• Effect of Massive Neutrinos: suppression of Power at small scales
W. Hu
Effect of massive neutrinos on the
CMB and Matter Power Spectra
Max
Tegmark’s
homepage
www.hep.upenn.edu/~max/
2dFGRS Galaxy Survey
2dFGRS Galaxy Survey
Power spectrum of density fluctuations from 2dF
Non-linearity
Bias b2(k)=Pg(k)/Pm(k)
2dFGRS [Elgarøy et al] 2002
Neutrino mass in 3-neutrino schemes
From present evidences of atmospheric and solar neutrino oscillations
eV
m
2
atm
 0.06 eV
eV
2
msun
 0.008eV
solar
atm
atm
solar
3 degenerate massive neutrinos
Σmν = 3m0`
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-Troitsk
• Future experiments (KATRIN) m(νe) ~ 0.3 eV
• Neutrinoless double beta decay: if Majorana neutrinos
76Ge
experiments:
ImeeI < 0.35 eV
Bound on mν after first year WMAP data
3 degenerate
massive
neutrinos
Σmν < 0.71 eV
Ωνh2 < 0.0076
95% CL
m0 < 0.23 eV
WMAP+CBI+ACBAR+2dFGRS+Lyman α
Spergel et al astro-ph/0302209
Is the 3+1 LSND scenario ruled out ?
2
ΔmLSND
~ 1 eV2
Pierce & Murayama hep-ph/0302131
Strumia hep-ph/0201134 (v4)
3+1 solution
strongly disfavored
Σmν < 0.71 eV
2 < 0.0076
Ω
h
ν
Hannestad astro-ph/0303076
Elgarøy & Lahav astro-ph/0303089
More conservative
Σmν < 1.01 eV
Giunti hep-ph/0302173
Small marginally
allowed region
Real bound on the 3+1 LSND scenario
• Take into account the number of neutrino species
• 3+1 scenario: 4 neutrinos (including thermalized sterile)
Abazajian 2002, di Bari 2002
• Calculate the bounds with Nν > 3
WMAP + Other CMB + 2dF + HST + SN-Ia
3ν
4ν
Hannestad astro-ph/0303076
95% CL
(also Elgarøy & Lahav, astro-ph/0303089)
5ν
1 massive + 3 massless case
not yet considered
Crotty, Lesgourgues & SP, in preparation
Hannestad
Future bounds on Σmν
• Next CMB data from WMAP and PLANCK (other CMB
experiments on large l’s) temperature and polarization spectra
• SDSS galaxy survey: 106 galaxies (250,000 for 2dF)
• Forecast analysis in WMAP and ΩΛ=0 models
Hu et al, PRL 80 (1998) 5255
 Ωmh2 

Σmν  0.65 
 0.1Nν 
0.8
eV
With current best-fit values
Σm  0.37 eV
Future bounds on Σmν
• Updated analysis: Hannestad astro-ph/0211106
• Σm detectable at 2σ if larger than
0.45 eV
(WMAP+SDSS)
0.12 eV (PLANCK+SDSS)
• With a galaxy survey ~10 times SDSS
0.03-0.06 eV
• From weak gravitational lensing: sensitive to both dark
energy and neutrino mass. Future ~ 0.1 eV
Abazajian and Dodelson astro-ph/0212216
Conclusions
Cosmological observables efficiently constrain
some properties of (relic) neutrinos
Bounds on the radiation content of the
Universe (Neff) from BBN (with ηB input from
CMB) and CMB+LSS (Neff<7 at 95%CL)
Stringent limits on potential relic neutrino
asymmetries from flavor equilibrium before BBN
(lξνl<0.07), fixing the cosmic neutrino density to 1%
Bounds on the sum of neutrino masses from
CMB + 2dFGRS (conservative Σmν<1 eV), with
sub-eV sensitivity in the next future