Cosmological Aspects of Neutrino Physics (II)

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Cosmological Aspects of Neutrino Physics (II)
?

• Sergio Pastor (IFIC)
• 61st SUSSP
• St Andrews, August 2006

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Cosmological Aspects of Neutrino Physics
2nd lecture
Degenerate relic neutrinos (Neutrino asymmetries)
Massive neutrinos as Dark Matter
Effects of neutrino masses on cosmological
observables
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Neutrinos coupled by weak interactions
Decoupled neutrinos (Cosmic Neutrino Background)
Primordial Nucleosynthesis
TMeV tsec
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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
Primordial Nucleosynthesis
TMeV tsec
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Relic neutrino asymmetries
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)
Hansen et al 2001
Hannestad 2003
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)
• Neutrino background diagonal and off-diagonal
  potentials

Dominant term Synchronized Neutrino Oscillations
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Evolution of neutrino asymmetries

BBN
Dolgov et al 2002 Abazajian et al 2002 Wong
2002 Lunardini Smirnov 2001
Effective flavor equilibrium (almost) established
?
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Massive Neutrinos and Cosmology
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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
Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122
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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
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Mixing Parameters...
From present evidences of oscillations from
experiments measuring atmospheric, solar, reactor
and accelerator neutrinos
Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122
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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
• 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

RAFFELT
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Neutrinos as Hot Dark Matter

• Effect of Massive Neutrinos suppression of Power
  at small scales

RAFFELT
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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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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
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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)

• Effect of Massive Neutrinos suppression of
  Power at small scales

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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
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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
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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

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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

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Structure formation after equality
J.Lesgourgues SP, Phys Rep 429 (2006) 307
astro-ph/0603494
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Structure formation after equality
a
dcdm
db
1-3/5fn
a
Massive neutrinos f?0.1
dn
dg
metric
J.Lesgourgues SP, Phys Rep 429 (2006) 307
astro-ph/0603494
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Effect of massive neutrinos on P(k)
Observable signature of the total mass on P(k)
P(k) massive P(k) massless
various f?
Lesgourgues SP, Phys. Rep. 429 (2006)
307
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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/
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End of 2nd lecture