Transcript Neutrino oscillations in dense neutrino media

NEUTRINO MASS BOUNDS FROM
COSMOLOGICAL OBSERVABLES
ν
XIth International Workshop
on Neutrino Telescopes,
Venice Feb 2005
Sergio Pastor (IFIC)
NEUTRINO MASS BOUNDS FROM COSMOLOGY
Relic neutrinos
Effect of neutrino mass
on cosmological observables
Current bounds and
future sensitivities
NEUTRINO MASS BOUNDS FROM COSMOLOGY
Relic neutrinos
Effect of neutrino mass
on cosmological observables
Current bounds and
future sensitivities
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
-
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
The Cosmic Neutrino Background
• Number density
nν  
d p
3
6ζ (3 ) 3
f
(p,T
)

n

TCMB 
ν
γ
3 ν
2
( 2π)
11
11π
3
at present
112 (  ) cm-3
per flavor
• Energy density
  
i
 7 2  4  4 / 3 4
  TCMB Massless

3
 120  11
2
2 d p
p  m i
f (p,Tν )  
3 ν
( 2π)

m i n
Massive mν>>T


Neutrinos and Cosmology
Neutrinos influence several cosmological epochs
Primordial
Nucleosynthesis
Cosmic Microwave
Background
Formation of Large
Scale Structures
BBN
CMB
LSS
T~MeV
νevs νμ,τ
Nν
T < eV
No flavor sensitivity
Nν & mν
Primordial Nucleosynthesis:
allowed ranges for Neff
Non-instantaneous decoupling
+ Flavor Oscillations
Neff=3.045(5)
T.Pinto et al, in preparation
Using 4He + D data (2σ)
1.1
Neff  2.50.9
Cuoco et al, IJMP A 19 (2004) 4431
Baryon abundance
 bh2
NEUTRINO MASS BOUNDS FROM COSMOLOGY
Relic neutrinos
Effect of neutrino mass
on cosmological observables
Current bounds and
future sensitivities
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
Galaxy Surveys
2dFGRS
SDSS
2dFGRS Galaxy Survey
Power Spectrum of density fluctuations
Field of density
Fluctuations
 ( x)
 ( x) 

CMB experiments
Matter power spectrum is
the Fourier transform of the
two-point correlation function
SDSS
Galaxy Surveys
Power spectrum of density fluctuations
Bias b2(k)=Pg(k)/Pm(k)
Non-linearity
2dFGRS
SDSS
kmax
Neutrinos as Dark Matter
• Neutrinos are natural DM candidates
Ωνh 
2
m
i
i
Ων  1   mi  46 eV
93.2 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 

F
• Ruled out by structure formation
b, cdm
CDM
Neutrinos as Dark Matter
• Neutrinos are natural DM candidates
Ωνh 
2
m
i
i
Ων  1   mi  46 eV
93.2 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 
• HDM ruled out by structure formation
CDM
Neutrinos as Hot Dark Matter
Massive Neutrinos can still be subdominant DM: limits on mν
from Structure Formation
• 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
www.hep.upenn.edu/~max/
NEUTRINO MASS BOUNDS FROM COSMOLOGY
Relic neutrinos
Effect of neutrino mass
on cosmological observables
Current bounds and
future sensitivities
Cosmological bounds on neutrino mass(es)
A unique cosmological bound on mν DOES NOT exist !
Different analyses have found upper bounds on neutrino
masses, but they depend on
• The assumed cosmological model: number of parameters
(problem of parameter degeneracies)
• The combination of cosmological data used
Cosmological Parameters: example
SDSS Coll, PRD 69 (2004) 103501
Cosmological Data
• CMB Temperature: WMAP plus data from other
experiments at large multipoles (CBI,ACBAR,VSA…)
• CMB Polarization: WMAP
• Large Scale Structure:
* Galaxy Clustering (2dF,SDSS)
* Bias (Galaxy, …): Amplitude of the Matter P(k)
(SDSS,σ8)
* Lyman-α forest: independent measurement of
power on small scales
• Priors on parameters from other data: SNIa (Ωm),
HST (h), …
Absolute mass scale searches
Tritium beta 

decay
U


Cosmology
Neutrinoless
double beta
decay
1/ 2
2
ei
i

m 

2
i
~  mi
i
U
i
2
ei
mi
< 2.3 eV
< 0.42-2.0 eV
< 0.3-1.2 eV
Neutrino masses in 3-neutrino schemes
From present evidences of atmospheric and solar neutrino oscillations
eV
m
2
atm
 0.05 eV
eV
2
msun
 0.009eV
solar
atm
atm
solar
3 degenerate massive neutrinos
Σmν = 3m0
m0
Neutrino masses in 3-neutrino schemes
Bound on mν after first year WMAP data
3 degenerate
massive
neutrinos
Hannestad JCAP 0305 (2003) 004
Σmν < 0.7 eV
Ωνh2 < 0.0076
95% CL
Elgarøy & Lahav JCAP 0305 (2003) 004
More conservative
Σmν < 1.01 eV
m0 < 0.23 eV
Barger et al, PLB 595 (2004) 55
Including also SDSS
Σmν < 0.75 eV
WMAP+CBI+ACBAR+2dFGRS+σ8+Lyman α
Spergel et al ApJ. Suppl.148 (2003) 175
Cosmological bounds on neutrino mass since 2003
WMAP Coll.
ApJ Suppl 148 (2003) 175
Hannestad
JCAP 0305 (2003) 004
Allen, Smith & Bridle
MNRAS 346 (2003) 593
SDSS Coll.
PRD 69 (2004) 103501
Barger. Marfatia & Tregre
PLB 595 (2004) 55
Crotty, Lesgourgues & SP
PRD 69 (2004) 123007
Seljak et al.
astro-ph/0407372
Fogli et al.
PRD 70 (2004) 113003
Ichikawa, Fukugita & Kawasaki
PRD 71 (2005) 043001
Bound on Σmν (eV) at 95% CL
Data used
0.7
WMAP, other CMB, 2dF,
σ8(a) , HST
1.01
WMAP, other CMB, 2dF,
HST
0.64
 0 .39
 0 .28
1.7
WMAP, other CMB, 2dF,
σ8(b) , X-ray galaxy
cluster
WMAP, SDSS
0.75
WMAP, other CMB, 2dF,
SDSS, HST
1.0 [0.6]
WMAP, other CMB, 2dF,
SDSS [HST]
0.42
WMAP, SDSS (bias,
galaxy clustering, Ly-α)
0.47
WMAP, other CMB, 2dF,
SDSS (Ly-α), HST
2.0
WMAP
Neutrino masses in 3-neutrino schemes
Currently
disfavored
Global analysis:  oscillations +
tritium  decay + 02 + Cosmology
CMB + 2dF
Fogli et al., PRD 70 (2004) 113003
The bound depends on the number
of neutrinos
• Example: in the 3+1 scenario, there are 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 JCAP 0305 (2003) 004
95% CL
5ν
Hannestad
(also Elgarøy & Lahav, JCAP 0304 (2003)
004)
Σmν and Neff degeneracy
(0 eV,3)
(0 eV,7)
(2.25 eV,7)
Analysis with Σmν and Neff free
WMAP + ACBAR + SDSS + 2dF
Hannestad & Raffelt,
JCAP 0404 (2004) 008
Crotty, Lesgourgues & SP,
PRD 69 (2004) 123007
Previous + priors (HST + SN-Ia)
2σ upper
bound on
Σmν (eV)
Non-thermal relic neutrinos
 The spectrum could be distorted after neutrino decoupling
Example: decay of a
light scalar after BBN
F  
Thermal FD spectrum
Distortion from F decay
 CMB + LSS data still compatible
with large deviations from a
thermal neutrino spectrum
(degeneracy NT distortion – Neff)
* Better expectations for future
CMB + LSS data, but model
degeneracy NT- Neff remains
p  /T
Cuoco, Lesgourgues, Mangano & SP, astro-ph/0502465
Future sensitivities to 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
Sensitivity to
 Ωmh2 

Σmν  0.65 
 0.1Nν 
0.8
eV
With current best-fit values
Σm  0.37 eV
Analysis of future bounds on Σmν
• Forecast analysis calculating the Fisher matrix Fij
+
CMB part
Galaxy Survey part
Veff ~ effective volume of the galaxy survey
Estimator of the error
on parameter θi
σ(i )  (F-1 )ii
Fiducial cosmological model:
(Ωbh2 , Ωmh2 , h , ns , τ, Σmν ) = (0.0245 , 0.148 , 0.70 , 0.98 , 0.12, Σmν )
PLANCK+SDSS
Ideal CMB+40xSDSS
Lesgourgues, SP & Perotto, PRD 70 (2004) 045016
Analysis of future sensitivities on Σmν: summary
Σm detectable at 2σ if larger than
0.21 eV (PLANCK+SDSS)
0.13 eV (CMBpol+SDSS)
measure
absolute ν mass scale !!!
0.07 eV (ideal+40xSDSS)
Future sensitivities to Σmν: new ideas
galaxy weak lensing and
no bias uncertainty
small scales in linear regime
CMB lensing
makes CMB sensitive to
much smaller masses
Future sensitivities to Σmν: new ideas
galaxy weak lensing and
CMB lensing
sensitivity of future
weak lensing survey
(4000º)2 to mν
sensitivity of CMB
(primary + lensing) to
mν
σ(mν) ~ 0.1 eV
σ(mν) = 0.15 eV (Planck)
σ(mν) = 0.04 eV (CMBpol)
Abazajian & Dodelson
Kaplinghat, Knox & Song
PRL 91 (2003) 041301
PRL 91 (2003) 241301
Conclusions
Cosmological observables efficiently constrain
some properties of (relic) neutrinos
ν
Bounds on the sum of neutrino masses from CMB
+ 2dFGRS or SDSS, and other cosmological data
(best Σmν<0.42 eV, conservative Σmν<1 eV)
Sub-eV sensitivity in the next future (0.1-0.2 eV
and better)  Test degenerate mass region and
eventually the IH case
FINE