Program
1. The standard cosmological model
2. The observed universe
3. Inflation. Neutrinos in cosmology
The flatness problem (I)
Rewrite Friedmann eq. as
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Spatial flatness
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The flatness problem (II)
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unstable
How our universe can be so flat today ?
The horizon problem
t_0
t_LS
Acausal volumes in our
present Hubble volume
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How can be the CMB so uniform with no previous contact ?
Inflation
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Period with
Simplest example:
(cosm. ct.)
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Solves flatness problem
Inflation
horizon
physical scale
expansion scale
Solves homogeneity problem
Inflation models
Inflaton field evolving slowly in potential
INFLATION
Inflaton fluctuations produce perturbations
Adiabatic
(equal entropy per particle)
Almost scale invariant
(equal amplitude for all wavelengths)
cosmology
and neutrinos
Impact of cosmology
on neutrino properties
- Complementary to
properties obtained
in solar/atmospheric/laboratory exps
-
is a “Cicerone” of the universe;
it plays or may play a role in almost all
epochs of the universe
Big Bang Nucleosynthesis
Cosmic Microwave Background
Large Scale Structure
…
in the early universe
Cicerone
Expanding universe
Luminosity
distances
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Rate of expansion
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Neutrinos in thermal equilibrium
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Weak interactions
Interaction rate
Equilibrium when
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Number density
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Equilibrium distribution
(No chemical potential)
Neutrino decoupling
rates
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after decoupling density dilutes
and keep form
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because both
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(provided m<<T)
(Exactly the reason why we observe photon black body today)
Neutrino “temperature”
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From entropy cons.
relic neutrino background (CNB)
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Properties of CNB
can be obtained
from CMB
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Big Bang Nucleosynthesis (BBN)
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Production of primordial nuclei
- Helium mass-fraction
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- Deuterium and other light
elements number-fraction
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…
From PDG 2006
BBN
Light element production depends on number neutrinos
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Does not depend on mass provided
(what it is important is the expansion rate)
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Parameterize deviations from
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(neutrino decoupling
near e+e- annih.)
N_eff takes into account other possible light fermions
or bosons, even if not fully in thermal equilibrium with the rest
BBN limits on neutrinos
Attitude has changed since baryon density
is deduced from CMB observations
Tension between D and 4He,
with 4He less in agreement with CMB
Probably 4He systematics
Limits on Neff are “author dependent”
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Evidence of
cosmol. nus
BBN may also probe non-standard interactions of neutrinos
Review:Sarkar, hep-ph/9602260
BBN NOT in crisis
BBN and asymmetries
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Possibility not as constrained as for charged particles
Introduce general distribution with chemical potentials
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1.
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BBN and asymmetries
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2.
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In principle, good bounds for nu_e
and not as good for nu_mu and nu_tau
BUT, take into account mixing/oscillations
(Use density matrices to describe evolution)
Tendency to flavor equilibrium
Flavor evolution in BBN epoch
Preferred
solution
Dolgov et al
hep-ph/0201287
Updated bound
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Serpico & Raffelt
astro-ph/0506162
Consequence: standard expectations on neutrino density OK
in the late universe
Cicerone
Standard Cosmological Model
Cosmological Observations
CMB,LSS,SNIa
Ly-alpha, lensing,…
Standard Cosmological Model
DM neutrinos
The bulk of the cosmological dark matter
has to be cold.
Neutrinos have to be subdominant.
OK with masses we have measured
(excluding highly degenerate masses)
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cf.
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Structure formation lead by NR matter,
impact of nus on structure formation?
1.
2.
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move at v=c
Structure formation
Graph from Raffelt
Small scales affected
Neutrino free-streaming suppreses growth
of (small scale) structures
Evolution equation at small scales
(& other assumptions)
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(Notice
Solution
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Small f_nu, MD univ.
Expect change at scales smaller than horizon
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Power spectrum
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Lesgourgues, Pastor
hep-astro/0603494
Power spectrum
From Strumia & Vissani hep-ph/0606054
Neutrino mass and
Cosmic Microwave Background
Mass effect in CMB
Massive nu goes from R to NR :
*** R-M equality
Change in expansion rate history
Time variation of potentials in RD vs MD
No big effects (not as large as LLS)
but CMB important
when doing a complete fit to all data
Neutrino-mass limits
Many authors using
different inputs
and different priors
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Fogli et al
hep-ph/0608060
Absolute mass scale
N_effective of neutrinos (radiation)
Neff limited by CMB+LSS+…
Change in expansion history
Radiation smoothes small scale structure
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Hannestad astro-ph/0510582
CNB “detected”
Generalization to thermal relics
Hannestad & Raffelt astro-ph/0312154
Caveats
Most bounds in standard minimal
in fact
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M=Mixed
Care with degeneracies
degeneracy m_nu and w broken by BAO
Hannestad astro-ph/0505551
Minimal standard model (standard neutrinos)
Experimental systematics
(Remember 4He)
Bias luminous/dark
Bias-free limit
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Kristiansen et al astro-ph/0611761
Future
Lesgourgues, Pastor hep-astro/0603494
Early universe, Late universe
Neutrinos in the very early universe
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Sakharov conditions
Problems of GUTS for baryogenesis
Leptogenesis can generate B-asymmetry
Decays of heavy Majoranas of see-saw.
Relation to nu mass and mixing phases
Neutrinos in the very late universe
Scale of Dark Energy might be nu mass
- Mass Varying Neutrinos
- nu condensate
Conclusion
plays an active role in cosmology
properties constrained by cosmology
(complementary to other type of constraints)