Cosmological%20aspects%20of%20neutrinos%20(I)

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Cosmological aspects of neutrinos (I)
?

• Sergio Pastor (IFIC Valencia)
• JIGSAW 2007
• TIFR Mumbai, February 2007

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Cosmological aspects of neutrinos
1st lecture
Introduction neutrinos and the History of the
Universe
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This is a neutrino!
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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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Cosmological aspects of neutrinos
1st lecture
Introduction neutrinos and the History of the
Universe
Basics of cosmology background evolution
Relic neutrino production and decoupling
Neutrinos and Primordial Nucleosynthesis
Neutrino oscillations in the Early Universe
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Cosmological aspects of neutrinos
2nd 3rd lectures
Degenerate relic neutrinos (Neutrino asymmetries)
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?)
Future sensitivities on m? and N? from cosmology
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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) Recent reviews Neutrino Cosmology, A.D.
Dolgov, Phys. Rep. 370 (2002) 333-535
hep-ph/0202122 Massive neutrinos and
cosmology, J. Lesgourgues SP, Phys. Rep. 429
(2006) 307-379 astro-ph/0603494 Primordial
Neutrinos, S. Hannestad hep-ph/0602058 BBN and
Physics beyond the Standard Model, S. Sarkar Rep.
Prog. Phys. 59 (1996) 1493-1610 hep-ph/9602260
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Eqs in the SM 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 1 MeV ? now
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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Neutrinos in Equilibrium
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

• 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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?e
??,?
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Non-instantaneous neutrino decoupling
???e() ???? () ????() Neff
Instantaneous decoupling 1.40102 0 0 0 3
SM3? mixing (?130) 1.3978 0.73 0.52 0.52 3.046
Dolgov, Hansen Semikoz, NPB 503 (1997)
426 Mangano et al, PLB 534 (2002) 8
Mangano 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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BBN Creation of light elements
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
Photodesintegration 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 II 0.1-0.01 MeV Formation of light nuclei
starting from D
Photodesintegration prevents earlier formation
for temperatures closer to nuclear binding
energies
0.03 MeV
0.07 MeV
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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
2. Direct effect of electron neutrinos and
antineutrinos on the n-p reactions
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BBN allowed ranges for Neff
Mangano 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
Coupled neutrinos
Oscillation term prop. to ?m2/2E
Second order matter effects prop.
to GF(E/MZ)2n(e-)n(e)
First order matter effects prop.
to GFn(e-)-n(e)
Strumia Vissani, hep-ph/0606054
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Flavor neutrino oscillations in the Early Universe
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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Active-sterile neutrino oscillations
Additional neutrino fully in eq
Flavour neutrino spectrum depleted
Dolgov Villante, NPB 679 (2004) 261
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Active-sterile neutrino oscillations
Additional neutrino fully in eq
Dolgov Villante, NPB 679 (2004) 261
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End of 1st lecture