III International Pontecorvo
Neutrino Physics School
Neutrinos in Cosmology
Gianpiero Mangano
INFN, Sezione di
Napoli, Italy
Neutrinos in Cosmology
1st lecture
Introduction: neutrinos and the History of the Universe
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
Neutrinos in Cosmology
1st lecture
Introduction: neutrinos and the History of the Universe
Basics of cosmology
Relic neutrino production and decoupling
Neutrinos and Primordial Nucleosynthesis
Neutrino oscillations in the Early Universe
Degenerate relic neutrinos (Neutrino asymmetries)
Neutrinos in Cosmology
2nd lecture
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)
Bounds on non standard neutrino interactions
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)
Reviews
Neutrino Cosmology, A.D. Dolgov,
Phys. Rep. 370 (2002) [hep-ph/0202122]
Massive neutrinos and cosmology, J. Lesgourgues & S. Pastor,
Phys. Rep. 429 (2006) [astro-ph/0603494]
Primordial Neutrinos, S. Hannestad
hep-ph/0602058
Nuclear reaction network for primordial nucleosynthesis:
A Detailed analysis of rates, uncertainties and light nuclei yields. ,
P.D. Serpico et al
JCAP 0412 (2004) [astro-ph/0408076]
Basics 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
4πG

(ρ  3 p)
a
3
?
..
inflation
inflation
a(t)~eHt
a
4G

(  domination)
3 p)
RD (radiation
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
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
Relic neutrino production and decoupling
1 MeV  T  mμ
να νβ  να νβ
Tν = Te = Tγ
να e -  να e -
να νβ  να νβ
να να  e e

-
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 
8πρR
2 5

G
T 
F
2
3M p
8πρR
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
1/3
 11 
 
Tν  4 
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
1/3
 11 
 
Tν  4 
f (p, T) 
1
e p/T  1
The Cosmic Neutrino Background (CNB)
1
Neutrinos decoupled at T~MeV, keeping a
f (p, T)  p/T
spectrum as that of a relativistic species 
e
1
• Number density
d3p
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
94.1
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)]
Momentum-dependent Boltzmann equation
d
d 
  Hp
 f ( p1 , t )  I coll ( p1 , t )
dp1 
 dt
Statistical Factor
9-dim Phase Space
Pi conservation
+ evolution of total energy density:
Process
Evolution of fν for a particular momentum p=10T
At lower
temperatures
distortions
freeze out
Between 2>T/MeV>0.1
distortions grow
f  f 
e

For T>2 MeV neutrinos are coupled
e
,
δf x10
p2
e p/T  1
Effects of flavour neutrino oscillations on the spectral distortions
The variation
is larger for e
Around
T~1 MeV
the oscillations
start to modify
the distortion
Effects of flavour neutrino oscillations on the spectral distortions
The variation
is larger for e
Around
T~1 MeV
the oscillations
start to modify
the distortion
Oscillations smooth the flavour
dependence of the distortion
The difference
between different
flavors is reduced
Results


e(%)  (%) (%)
T fin / T0
Neff
Instantaneous
decoupling
1.40102
0
0
0
3
SM
1.3978
0.94
0.43
0.43
3.046
1.3978
0.73
0.52
0.52
3.046
1.3978
0.70
0.56
0.52
3.046
+3ν mixing
(θ13=0)
+3ν mixing
(sin2θ13=0.047)
Dolgov, Hansen & Semikoz, NPB 503 (1997) 426
G.M. et al, PLB 534 (2002) 8
G.M. et al, NPB 729 (2005) 221
Changes in CNB quantities
• Contribution of neutrinos to total energy density
today (3 degenerate masses)

3m0
 

 c 94.12h 2 eV 2
3m0
 
93.14h 2 eV 2
• Present neutrino number density
n  335.7 cm-3


n  339.3 cm-3
Neff varying the neutrino decoupling temperature
Neutrinos and Primordial Nucleosynthesis
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
Photodisintegration
prevents earlier
formation for
temperatures closer
to nuclear binding
energies
0.07
MeV
0.03
MeV
BBN: Creation of light elements
Phase III: 0.1-0.01 MeV
Formation of light
nuclei starting from D
Photodisintegration
prevents earlier
formation for
temperatures closer
to nuclear binding
energies
0.07
MeV
0.03
MeV
BBN accuracy
1.
Weak interactions
freeze out at T ~1 MeV
2. Deuterium forms via p n
D  at T ~ 0.1 MeV
3. Nuclear chain
4He
mass fraction:
weak rates and n/p freezing
neutrino decoupling
D,3He, 7Li:
nuclear rate network
no free parameters after WMAP for
standard scenario
BBN accuracy I
weak rates:
known at 0.1% level:
•Radiative corrections
•Finite nucleon mass
•Thermal effects
•Effects of non-thermal
features in neutrino
distribution
BBN accuracy III
Nuclear rate benchmarks:
Caughlan and Fowler ‘88
Smith, Kawano and Malaney ‘93
NACRE
Recent efforts: reanalysis of the whole
network including recent experimental results
(e.g. LUNA) and theoretical calculations (e.g.
pn D)
Cyburt 2004
Descouvement et al 2004
Serpico et al 2004
pn
D
Pionless effective
field theory at
N2LO (M1V) and
N4LO (E1V)
(Rupak)
error in 1-2% range
Serpico et al 04
Dp
3He

Impact of LUNA
results: error
reduced from 13 to
3%
Serpico et al 04
4He 3He
7Be

Dominant channel for
7Be production, and so
controls the final 7Li
yield
Also interesting for
solar neutrino flux
LUNA 06
Weizmann Inst. 04
C. Broggini,
Neutrino Telescope
Venice 2007
BBN theory vs data
bh2=0.0224
2.61
O’Meara et al 06
1.03
Bania et al 02
Olive&Skillmann04
0.2478
Izotov et al 07
1.14
Ryan et al 99
4.5
Bonifacio et al 06
Effects of reaction rate uncertainties
D
7Li
3He
4He
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=0.024±0.001
Fields & Sarkar PDG 2006
Effect of neutrinos on BBN
1. Neff fixes the expansion rate during BBN
H 
8ππ 
3
D
(Neff)>0   4He
7Li
 7  4  4 / 3 eff 
 R      v   x  1    N v   
 8  11 



4He
2. Direct effect of electron neutrinos and antineutrinos
on the n-p reactions
3He
BBN: allowed ranges for Neff
η10 
nB/nγ
10
10
 274ΩBh2
Using 4He + D data (95% CL)
Neff  3.1
1.4
1.2
G.M. et al, astro-ph/0612150
Neutrino oscillations in the Early Universe
Neutrino oscillations are effective when
medium effects get small enough
Compare oscillation term with
effective potentials
 M 2 8 2GF

i t  Hp p     2 E,    C (  )
mW
 p

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
Kirilova, astro-ph/0312569
Flavour
neutrino
spectrum
depleted
Dolgov & Villante,
NPB 679 (2004) 261
Additional
neutrino
fully in eq
Flavour
neutrino
spectrum
depleted
Dolgov & Villante,
NPB 679 (2004) 261
Additional
neutrino
fully in eq
Dolgov & Villante,
NPB 679 (2004) 261
Degenerate relic neutrinos (Neutrino asymmetries)
Distribution function of particle momenta in
equilibrium
T~1/a(t)
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
 

 e 

  
 
c12c13
s12c13
s13 



  s12c23  c12 s23s13 c12c23  s12 s23s13 s23c13 
 s s c c s


c
s

s
c
s
c
c
12 23
12 23 13
23 13 
 12 23 12 23 13
• Expansion of the Universe
• Charged lepton background (2nd order contribution)
• Collisions (damping)
Evolution of neutrino asymmetries
BBN
Effective flavor equilibrium
(almost) established 
 0.05    0.07
  0.07
Serpico & Raffelt 2005
Dolgov et al 2002
Wong 2002
Abazajian et al 2002
Massive neutrinos as Dark Matter
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
A.Marrone, IFAE 2007
... 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
m


ν
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 
• HDM ruled out by structure formation
CDM
Neutrinos as Hot Dark Matter
Effect of Massive Neutrinos: suppression of Power at small scales
Effects of neutrino masses on cosmological observables
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
δρ/ρ<1
non-linear
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
of large-scale
structures at
medium z
MD matière
(matter domination)
énergie
noiredomination
dark energy
various systematics
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
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=1-3/5
∫ v f
dt
 /  a
< ∫ c dt
with f = /m ≈ (m)/(15 eV)
Structure formation after equality
a
cdm
Massless
neutrinos
b


J.Lesgourgues & S. Pastor, 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 & S. Pastor, Phys Rep 429 (2006) 307 [astro-ph/0603494]
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/
Bounds on mν from Cosmology
Neutrinos as Hot Dark Matter
Massive Neutrinos can still be subdominant DM: limits on mν
from Structure Formation (combined with other cosmological
data)
How to get a bound (measurement) of
neutrino masses from Cosmology
Fiducial cosmological model:
(Ωbh2 , Ωmh2 , h , ns , τ, Σmν )
DATA
PARAMETER
ESTIMATES
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
* Baryon acoustic oscillations (SDSS)
Bounds on parameters from other data: SNIa (Ωm), HST (h), …
Cosmological Parameters: example
SDSS Coll, PRD 69 (2004) 103501
Cosmological bounds on neutrino mass(es)
Different analyses have found upper bounds on neutrino
masses, since they depend on
• The combination of cosmological data used
• The assumed cosmological model: number of parameters
(problem of parameter degeneracies)
• The properties of relic neutrinos
Cosmological bounds on neutrino masses using WMAP3
Dependence on the data set used. An example:
Fogli et al., hep-ph/0608060
Neutrino masses in 3-neutrino schemes
CMB + galaxy clustering
+ HST, SNI-a…
+ BAO and/or bias
+ including Ly-α
J.Lesgourgues & S.Pastor, Phys. Rep. 429
(2006) 307
Tritium  decay, 02 and Cosmology
Fogli et al.,
hep-ph/0608060
02 and Cosmology
Fogli et al., hep-ph/0608060
Bounds on the radiation content (Nν)
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
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 on Neff from BBN and from CMB+LSS
Integrated Sachs-Wolfe effect
CMB anisotropies induced by passing through a time varying
gravitational potential:
T
T
  
  2  d 
  4 G a  
2
2
Poisson’s equation
• changes during radiation domination
• decays after curvature or dark energy come to dominate (z~1)
Effect of Neff at later epochs
• Neff modifies the radiation content:
• Changes the epoch of matter-radiation equivalence
CMB+LSS: allowed ranges for Neff
• Set of parameters: ( Ωbh2 , Ωcdmh2 , h , ns , A , b , Neff )
• DATA: WMAP + other CMB + LSS + HST (+ SN-Ia)
• Flat Models
Neff  3.5
3.3
2.1
95% CL
Crotty, Lesgourgues & Pastor, PRD 67 (2003)
Non-flat Models
2.0
Neff  4.11.9
3.0
Neff  4.02.1
Hannestad, JCAP 0305 (2003)
Pierpaoli, MNRAS 342 (2003)
95% CL
• Recent result
2.7  Neff  4.6
95% CL
Hannestad & Raffelt, astro-ph/0607101
Allowed ranges for Neff
η10 
nB/nγ
10
10
 274ΩBh2
Using cosmological data (95% CL)
3.0  Neff  7.9 (CMB  LSS data)
3.1  Neff  6.2 ( BAO and Ly -  )
G.M et al, JCAP 2006
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
PLANCK
WMAP
Lopez et al, PRL 82 (1999) 3952
Future bounds on Neff
Updated analysis:
Larger errors
Bowen et al 2002
ΔNeff ~ 3 (WMAP)
ΔNeff ~ 0.2 (Planck)
Bashinsky & Seljak 2003
Σmν and Neff degeneracy
(0 eV,3)
(0 eV,7)
(2.25 eV,7)
(0 eV,3)
(0 eV,7)
(2.25 eV,7)
Analysis with Σmν and Neff free
BBN allowed region
BBN allowed region
WMAP + ACBAR + SDSS + 2dF
Crotty, Lesgourgues & Pastor, PRD
69 (2004) 123007
Hannestad & Raffelt,
JCAP 0611 (2006) 016
Parameter degeneracy: Neutrino mass and w
In cosmological models with more parameters the neutrino mass
bounds can be relaxed.
Ex: quintessence-like dark energy with ρDE=w pDE
Λ
WMAP Coll, astro-ph/0603449
Non-standard relic neutrinos
The cosmological bounds on neutrino masses are
modified if relic neutrinos have non-standard
properties (or for non-standard models)
Two examples where the cosmological bounds do not apply
• Massive neutrinos strongly coupled to a light scalar field:
they could annihilate when becoming NR
• Neutrinos coupled to the dark energy: the DE density is a
function of the neutrino mass (mass-varying neutrinos)
Non-thermal relic neutrinos
The spectrum could be distorted after neutrino decoupling
Example: decay of a light scalar after BBN
  
* CMB + LSS data still compatible
Thermal FD spectrum
Distortion from Φ decay
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
A. Cuoco, J. Lesgourgues, G.M. & S.Pastor, PRD 71 (2005)
123501
Bounds on non standard neutrino interactions
New effective interactions between electron and neutrinos
Electron-Neutrino NSI
Breaking of Lepton universality (=)

Flavour-changing (≠ )
L, R
Limits on
 from scattering experiments,
LEP data, solar vs Kamland data…
Berezhiani & Rossi, PLB 535 (2002) 207
Davidson et al, JHEP 03 (2003) 011
Barranco et al, PRD 73 (2006) 113001
Analytical calculation of Tdec in presence of NSI
SM
SM
Contours of equal Tdec in MeV with diagonal NSI parameters
Neff varying the neutrino decoupling temperature
Effects of NSI on the neutrino spectral distortions
Here larger
variation for ,
Neutrinos keep thermal contact
with e- until smaller temperatures
Results

T fin
/ T0
e(%)  (%) (%)
Neff
Instantaneous
decoupling
1.40102
0
0
0
3
+3ν mixing
(θ13=0)
1.3978
0.73
0.52
0.52
3.046
Lee= 4.0
Ree= 4.0
1.3812
9.47
3.83
3.83
3.357
Very large NSI parameters,
FAR from allowed regions
G.M. et al, NPB 756 (2006) 100
Results

T fin
/ T0
e(%)  (%) (%)
Neff
Instantaneous
decoupling
1.40102
0
0
0
3
+3ν mixing
(θ13=0)
1.3978
0.73
0.52
0.52
3.046
Lee= 0.12
Ree= -1.58
L= -0.5
R= 0.5
Le= -0.85
Re= 0.38
1.3937
2.21
1.66
0.52
3.120
Large NSI parameters, still
allowed by present lab data
G.M. et al, NPB 756 (2006) 100
Departure from Neff=3 not observable
from present cosmological data
G.M. et al, hep-ph/0612150
…but maybe in the near future ?
Forecast analysis:
CMB data
Bowen et al MNRAS 2002
Example of future
CMB satellite
ΔNeff ~ 3 (WMAP)
ΔNeff ~ 0.2 (Planck)
Bashinsky & Seljak PRD 69 (2004) 083002
III International Pontecorvo
Neutrino Physics School
Neutrinos in Cosmology
DIRECT OBSERVATION?
Pauli to his friend Baade:
Several indirect effects of the neutrino background
on cosmological observables
“Today I did something a physicist should
Informations
on neutrino properties:
mass
never
do.
I
predicted
something
which
oscillations, extra relativistic species, lifetime,
willmagnetic
nevermoments,……
be observed experimentally…”