Neutrinos in Cosmology

1
Neutrinos in Cosmology
III International Pontecorvo Neutrino Physics
School

• Gianpiero Mangano
• INFN, Sezione di Napoli, Italy

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Neutrinos in Cosmology
1st lecture
Introduction neutrinos and the History of the
Universe
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Neutrinos coupled by weak interactions
Decoupled neutrinos (Cosmic Neutrino Background
or CNB)
Primordial Nucleosynthesis
TMeV tsec
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Relativistic neutrinos
At least 1 species is NR
TeV

• 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

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Relic neutrinos influence several cosmological
epochs
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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)
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Neutrinos in Cosmology
2nd lecture
Massive neutrinos as Dark Matter
Effects of neutrino masses on cosmological
observables
Bounds on m? from CMB, LSS and other data
Bounds on the radiation content (N?)
Bounds on non standard neutrino interactions
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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
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Basics of cosmology
The FLRW Model describes the evolution of the
isotropic and homogeneous expanding Universe
a(t) is the scale factor and k-1,0,1 the
curvature
Einstein eqs
Energy-momentum tensor of a perfect fluid
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Eqs in the SM of Cosmology
O ?/?crit
?crit3H2/8pG is the critical density
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Evolution of the Universe
a(t)t1/2
a(t)t2/3
a(t)eHt
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Evolution of the background densities 1 MeV ? now
3 neutrino species with different masses
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Evolution of the background densities
Oi ?i/?crit
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Equilibrium thermodynamics
Distribution function of particle momenta in
equilibrium Thermodynamical variables
VARIABLE RELATIVISTIC RELATIVISTIC NON REL.
VARIABLE BOSE FERMI NON REL.
Particles in equilibrium when T are high and
interactions effective
T1/a(t)
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Neutrinos coupled by weak interactions(in
equilibrium)
Primordial Nucleosynthesis
TMeV tsec
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Relic neutrino production and decoupling
1 MeV ? T ? mµ
T? Te T?
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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
Since ?e have both CC and NC interactions with
e Tdec(?e) 2 MeV Tdec(?µ,t) 3 MeV
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Neutrinos coupled by weak interactions(in
equilibrium)
Free-streaming neutrinos (decoupled) Cosmic
Neutrino Background
Neutrinos keep the energy spectrum of a
relativistic fermion with eq form
TMeV tsec
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Neutrino and Photon (CMB) temperatures
At Tme, electron-positron pairs
annihilate heating photons but not the
decoupled neutrinos
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Neutrino and Photon (CMB) temperatures
At Tme, electron-positron pairs
annihilate heating photons but not the
decoupled neutrinos
Photon temp falls slower than 1/a(t)
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The Cosmic Neutrino Background (CNB)

• Number density
• Energy density

Massless
Massive m?gtgtT
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The Cosmic Neutrino Background

• Number density
• Energy density

Massless
Massive m?gtgtT
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Relativistic particles in the Universe
At Tltme, the radiation content of the Universe
is
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Relativistic particles in the Universe
At Tltme, the radiation content of the Universe
is Effective number of relativistic neutrino
species Traditional parametrization of the energy
density stored in relativistic particles
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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 CMBLSS
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Relativistic particles in the Universe
At Tltme, the radiation content of the Universe
is Effective number of relativistic neutrino
species Traditional parametrization of the energy
density stored in relativistic particles
Neff is not exactly 3 for standard neutrinos
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Non-instantaneous neutrino decoupling
At Tme, ee- pairs annihilate heating photons
But, since Tdec(?) is close to me, neutrinos
share a small part of the entropy release
f?fFD(p,T?)1df(p)
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Momentum-dependent Boltzmann equation
Statistical Factor
9-dim Phase Space
Process
?Pi conservation
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Evolution of f? for a particular momentum p10T
At lower temperatures distortions freeze out
Between 2gtT/MeVgt0.1 distortions grow
For Tgt2 MeV neutrinos are coupled
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?e
??,?
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Effects of flavour neutrino oscillations on the
spectral distortions
The variation is larger for ?e
Around T1 MeV the oscillations start to
modify the distortion
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Effects of flavour neutrino oscillations on the
spectral distortions
The variation is larger for ?e
Around T1 MeV the oscillations start to
modify the distortion
The difference between different flavors is
reduced
Oscillations smooth the flavour dependence of
the distortion
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Results
???e() ???? () ????() Neff
Instantaneous decoupling 1.40102 0 0 0 3
SM 1.3978 0.94 0.43 0.43 3.046
3? mixing (?130) 1.3978 0.73 0.52 0.52 3.046
3? mixing (sin2?130.047) 1.3978 0.70 0.56 0.52 3.046
Dolgov, Hansen Semikoz, NPB 503 (1997) 426 G.M.
et al, PLB 534 (2002) 8
G.M. et al, NPB 729 (2005) 221
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Changes in CNB quantities

• Contribution of neutrinos to total energy density
  today (3 degenerate masses)
• Present neutrino number density

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• Neff varying the neutrino decoupling temperature

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Neutrinos and Primordial Nucleosynthesis
Produced elements D, 3He, 4He, 7Li and small
abundances of others
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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
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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
0.03 MeV
0.07 MeV
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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
0.03 MeV
0.07 MeV
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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
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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

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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
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p n D ?
Pionless effective field theory at N2LO (M1V) and
N4LO (E1V) (Rupak)
error in 1-2 range
Serpico et al 04
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D p 3He ?
Impact of LUNA results error reduced from 13 to
3
Serpico et al 04
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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
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BBN theory vs data
OMeara et al 06
Bania et al 02
OliveSkillmann04
?bh20.0224
Izotov et al 07
Ryan et al 99
Bonifacio et al 06
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Effects of reaction rate uncertainties
D
3He
7Li
4He
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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
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BBN Predictions vs Observations
after WMAP OBh20.0240.001
Fields Sarkar PDG 2006
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Effect of neutrinos on BBN
1. Neff fixes the expansion rate during BBN
D
?(Neff)gt?0 ? ? 4He
3He
7Li
4He
2. Direct effect of electron neutrinos and
antineutrinos on the n-p reactions
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BBN allowed ranges for Neff
G.M. et al, astro-ph/0612150
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Neutrino oscillations in the Early Universe
Neutrino oscillations are effective when medium
effects get small enough
Compare oscillation term with effective potentials
Non-zero neutrino asymmetries flavour
oscillations lead to (almost) equilibrium for
all µ?
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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 Neff4
• If oscillations are effective after decoupling
  Neff3 but the spectrum of active neutrinos is
  distorted (direct effect of ?e and anti-?e on BBN)

Results depend on the sign of ?m2 (resonant vs
non-resonant case)
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Active-sterile neutrino oscillations
Additional neutrino fully in eq
Flavour neutrino spectrum depleted
Dolgov Villante, NPB 679 (2004) 261
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Additional neutrino fully in eq
Flavour neutrino spectrum depleted
Dolgov Villante, NPB 679 (2004) 261
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Additional neutrino fully in eq
Dolgov Villante, NPB 679 (2004) 261
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Degenerate relic neutrinos (Neutrino asymmetries)
Distribution function of particle momenta in
equilibrium
T1/a(t)
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Fermi-Dirac spectrum with temperature T and
chemical potential ??
Raffelt
More radiation
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Degenerate Big Bang Nucleosynthesis
If ?????0 , for any flavor
?(??)gt?(0) ? ? 4He
Plus the direct effect on n?p if ??(?e)?0
?egt0 ? ? 4He
Pairs ?(?e,?N?) that produce the same observed
abundances for larger ?B
Kang Steigman 1992
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Combined bounds BBN CMB-LSS
Degeneracy direction (arbitrary ?e)
Hannestad 2003
Hansen et al 2001
In the presence of flavor oscillations ?
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Flavor neutrino oscillations in the Early Universe

• Density matrix
• Mixing matrix
• Expansion of the Universe
• Charged lepton background (2nd order
  contribution)
• Collisions (damping)

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Evolution of neutrino asymmetries

BBN
Dolgov et al 2002 Wong 2002 Abazajian et al 2002
Effective flavor equilibrium (almost) established
?
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Massive neutrinos as Dark Matter
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Relic neutrinos influence several cosmological
epochs
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We know that flavour neutrino oscillations exist
From present evidences of oscillations from
experiments measuring atmospheric, solar, reactor
and accelerator neutrinos
Evidence of Particle Physics beyond the Standard
Model !
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Mixing Parameters...
From present evidences of oscillations from
experiments measuring atmospheric, solar, reactor
and accelerator neutrinos
Mixing matrix U
A.Marrone, IFAE 2007
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... and neutrino masses
Data on flavour oscillations do not fix the
absolute scale of neutrino masses
What is the value of m0 ?
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Direct laboratory bounds on m?
Searching for non-zero neutrino mass in
laboratory experiments

• Tritium beta decay measurements of endpoint
  energy
• m(?e) lt 2.2 eV (95 CL) Mainz
• Future experiments (KATRIN) m(?e) 0.2-0.3 eV
• Neutrinoless double beta decay if Majorana
  neutrinos
• experiments with 76Ge and other isotopes ImeeI
  lt 0.4hN eV

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Absolute mass scale searches
Tritium ß decay lt 2.2 eV
Neutrinoless double beta decay lt 0.4-1.6 eV
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Evolution of the background densities 1 MeV ? now
Oi ?i/?crit
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The Cosmic Neutrino Background

• Number density
• Energy density

Massless
Massive m?gtgtT
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Neutrinos as Dark Matter

• Neutrinos are natural DM candidates
• They stream freely until non-relativistic
  (collisionless phase mixing)
  Neutrinos are HOT Dark Matter
• First structures to be formed when Universe
  became matter -dominated
• Ruled out by structure formation CDM

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Neutrinos as Dark Matter

• Neutrinos are natural DM candidates
• They stream freely until non-relativistic
  (collisionless phase mixing)
  Neutrinos are HOT Dark Matter
• First structures to be formed when Universe
  became matter -dominated
• HDM ruled out by structure formation
  CDM

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Neutrinos as Hot Dark Matter

• Effect of Massive Neutrinos suppression of Power
  at small scales

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Effects of neutrino masses on cosmological
observables
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Cosmological observables
accélération
acceleration
décélération lente
slow deceleration
décélération rqpide
fast deceleration
accélération
acceleration
?
inflation
RD (radiation domination)
MD (matter domination)
dark energy domination
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Power Spectrum of density fluctuations
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Galaxy Redshift Surveys
SDSS
1300 Mpc
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Cosmological observables LSS
accélération
acceleration
décélération lente
slow deceleration
décélération rqpide
fast deceleration
accélération
acceleration
0ltzlt0.2
?
inflation
RD (radiation domination)
MD (matter domination)
dark energy domination
Distribution of large-scale structures at low z
galaxy redshift surveys
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Power spectrum of density fluctuations
Bias b2(k)Pg(k)/Pm(k)
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Cosmological observables LSS
accélération
acceleration
décélération lente
slow deceleration
décélération rqpide
fast deceleration
accélération
acceleration
?
2ltzlt3
inflation
RD (radiation domination)
MD (matter domination)
dark energy domination
Distribution of large-scale structures at
medium z
Lyman-a forests in quasar spectra
84
Neutrinos as Hot Dark Matter
Massive Neutrinos can still be subdominant DM
limits on m? from Structure Formation (combined
with other cosmological data)

• Effect of Massive Neutrinos suppression of
  Power at small scales

85
Structure formation after equality
baryons and CDM experience gravitational clusterin
g
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Structure formation after equality
baryons and CDM experience gravitational clusterin
g
growth of dr/r (k,t) fixed by  gravity vs.
expansion  balance ? dr/r ? a
87
Structure formation after equality
baryons and CDM experience gravitational clusterin
g
neutrinos experience free-streaming with v c
or ltpgt/m
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Structure formation after equality
baryon and CDM experience gravitational clustering
baryons and CDM experience gravitational clusterin
g
neutrinos experience free-streaming with v c
or ltpgt/m

• neutrinos cannot cluster below a diffusion
  length
• l ? v dt lt ? c dt

89
Structure formation after equality
baryon and CDM experience gravitational clustering
baryons and CDM experience gravitational clusterin
g
neutrinos experience free-streaming with v c
or ltpgt/m

• neutrinos cannot cluster below a diffusion
  length
• l ? v dt lt ? c dt

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Structure formation after equality
J.Lesgourgues S. Pastor, Phys Rep 429 (2006)
307 astro-ph/0603494
91
Structure formation after equality
a
dcdm
db
1-3/5fn
a
Massive neutrinos f?0.1
dn
dg
metric
J.Lesgourgues S. Pastor, Phys Rep 429 (2006)
307 astro-ph/0603494
92
Cosmological observables CMB
accélération
acceleration
décélération lente
slow deceleration
décélération rqpide
fast deceleration
accélération
acceleration
?
z1100
inflation
RD (radiation domination)
MD (matter domination)
dark energy domination
Anisotropies of the Cosmic Microwave Background
? photon power spectra
CMB temperature/polarization anisotropies
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CMB TT DATA
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CMB TT DATA
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CMB Polarization DATA
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Effect of massive neutrinos on the CMB spectra

• Direct effect of sub-eV massive neutrinos on the
  evolution of the baryon-photon coupling is very
  small
• Impact on CMB spectra is indirect non-zero O?
  today implies a change in the spatial curvature
  or other Oi . The background evolution is
  modified
• Ex in a flat universe,
• keep O?OcdmObO?1
• constant

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Effect of massive neutrinos on the CMB spectra
Problem with parameter degeneracies change
in other cosmological parameters can mimic the
effect of nu masses
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Effect of massive neutrinos on the CMB and Matter
Power Spectra
Max Tegmark www.hep.upenn.edu/max/
99
Bounds on m? from Cosmology
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Neutrinos as Hot Dark Matter
Massive Neutrinos can still be subdominant DM
limits on m? from Structure Formation (combined
with other cosmological data)
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How to get a bound (measurement) of neutrino
masses from Cosmology
Fiducial cosmological model (Obh2 , Omh2 , h ,
ns , t, Sm? )
PARAMETER ESTIMATES
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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,s8)
• Lyman-a forest independent measurement of
  power on small scales
• Baryon acoustic oscillations (SDSS)
• Bounds on parameters from other data SNIa (Om),
  HST (h),

103
Cosmological Parameters example
SDSS Coll, PRD 69 (2004) 103501
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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

105
Cosmological bounds on neutrino masses using WMAP3
Dependence on the data set used. An example
Fogli et al., hep-ph/0608060
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Neutrino masses in 3-neutrino schemes
CMB galaxy clustering
J.Lesgourgues S.Pastor, Phys. Rep. 429 (2006)
307
107
Tritium ? decay, 0?2? and Cosmology
Fogli et al., hep-ph/0608060
108
0?2? and Cosmology
Fogli et al., hep-ph/0608060
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Bounds on the radiation content (N?)
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Relativistic particles in the Universe
At Tltme, the radiation content of the Universe
is Effective number of relativistic neutrino
species Traditional parametrization of the energy
density stored in relativistic particles
111
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 CMBLSS
112
Integrated Sachs-Wolfe effect
CMB anisotropies induced by passing through a
time varying gravitational potential
Poissons equation

• changes during radiation domination
• decays after curvature or dark energy come to
  dominate (z1)

113
Effect of Neff at later epochs

• Neff modifies the radiation content
• Changes the epoch of matter-radiation equivalence

114
CMBLSS allowed ranges for Neff

• Set of parameters ( Obh2 , Ocdmh2 , h , ns , A
  , b , Neff )
• DATA WMAP other CMB LSS HST ( SN-Ia)
• Flat Models
• Non-flat Models
• Recent result

Hannestad Raffelt, astro-ph/0607101
95 CL
115
Allowed ranges for Neff
Using cosmological data (95 CL)
G.M et al, JCAP 2006
116
Future bounds on Neff

• Next CMB data from WMAP and PLANCK (other CMB
  experiments on large ls) temperature and
  polarization spectra
• Forecast analysis in O?0 models

Lopez et al, PRL 82 (1999) 3952
PLANCK
WMAP
117
Future bounds on Neff
Updated analysis Larger errors
?Neff 3 (WMAP) ?Neff 0.2 (Planck)
Bowen et al 2002
Bashinsky Seljak 2003
118
Sm? and Neff degeneracy
119
Analysis with Sm? and Neff free
WMAP ACBAR SDSS 2dF
Hannestad Raffelt, JCAP 0611 (2006) 016
Crotty, Lesgourgues Pastor, PRD 69 (2004) 123007
120
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 ?DEw pDE
121
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)

122
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 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

123
Bounds on non standard neutrino interactions
124
Electron-Neutrino NSI
Breaking of Lepton universality (??)
Flavour-changing (?? ?)
Berezhiani Rossi, PLB 535 (2002) 207 Davidson
et al, JHEP 03 (2003) 011 Barranco et al, PRD 73
(2006) 113001
125

• Analytical calculation of Tdec in presence of NSI

Contours of equal Tdec in MeV with diagonal NSI
parameters
126

• Neff varying the neutrino decoupling temperature

127
Effects of NSI on the neutrino spectral
distortions
Here larger variation for ??,?
Neutrinos keep thermal contact with e-? until
smaller temperatures
128
Results
???e() ???? () ????() Neff
Instantaneous decoupling 1.40102 0 0 0 3
3? mixing (?130) 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
129
Results
???e() ???? () ????() Neff
Instantaneous decoupling 1.40102 0 0 0 3
3? mixing (?130) 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
130
Departure from Neff3 not observable from present
cosmological data
G.M. et al, hep-ph/0612150
131
but maybe in the near future ?
Forecast analysis CMB data
?Neff 3 (WMAP) ?Neff 0.2 (Planck)
Bowen et al MNRAS 2002
Bashinsky Seljak PRD 69 (2004) 083002
Example of future CMB satellite
132
Neutrinos in Cosmology
III International Pontecorvo Neutrino Physics
School
DIRECT OBSERVATION?
Pauli to his friend Baade Today I did something
a physicist should never do. I predicted
something which will never be observed
experimentally
Several indirect effects of the neutrino
background on cosmological observables Information
s on neutrino properties mass oscillations,
extra relativistic species, lifetime, magnetic
moments,