Ingen diastitel

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Thermodynamics in the early universe
In equilibrium, distribution functions have the
form
When m T particles disappear because of
Boltzmann supression
Decoupled particles If particles are decoupled
from other species their comoving number
density is conserved. The momentum redshifts
as p 1/a
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The entropy density of a species with MB
statistics is given by
In equilibrium,
(true if processes like occur
rapidly)
This means that entropy is maximised when
In equilibrium neutrinos and anti-neutrinos are
equal in number! However, the neutrino lepton
number is not nearly as well constrained
observationally as the baryon number
It is possible that
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Leptogenesis (more to come in the last lecture)
Conditions for lepto (baryo) genesis (Sakharov
conditions)
L-violation Processes that can break lepton
number (e.g. )
CP-violation Asymmetry between particles and
antiparticles e.g. has other
rate than
Non-equilibrium thermodynamics In equilibrium
always applies.
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Non-equilibrium
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Different possibilities
Electroweak baryogenesis does not require new
physics, does not work!
SUSY electroweak baryogenesis requires new
physics, does not work in the MSSM
GUT baryogenesis requires plausible new physics,
it works possible problems with reheating
Baryogenesis via leptogenesis requires
plausible new physics, it works
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Thermal evolution after the end of inflation
Total energy density
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Temperature evolution of N(T)
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In a radiation dominated universe the
time-temperature relation is then of the form
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The number and energy density for a given
species, X, is given by the Boltzmann equation
Cef Elastic collisions, conserves particle
number but energy exchange possible (e.g.
) scattering
equilibrium Cif Inelastic collisions, changes
particle number (e.g. )
chemical equilibrium
Usually, Cef gtgt Cif so that one can assume
that elastic scattering equilibrium always
holds. If this is true, then the form of f is
always Fermi-Dirac or Bose-Einstein, but with a
possible chemical potential.
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Particle decoupling
The inelastic reaction rate per particle for
species X is
In general, a species decouples from
chemical equlibrium when
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The prime example is the decoupling of light
neutrinos (m lt TD)
After neutrino decoupling electron-positron
annihilation takes place (at Tme/3)
Entropy is conserved because of equilibrium in
the e- e-- g plasma and therefore
The neutrino temperature is unchanged by this
because they are decoupled and therefore
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BIG BANG NUCLEOSYNTHESIS
The baryon number left after baryogenesis is
usually expressed in terms of the parameter h
According to observations h 10-10 and therefore
the parameter
is often used
From h the present baryon density can be found as
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Immediately after the quark-hadron transition
almost all baryons are in pions. However, when
the temperature has dropped to a few MeV (T ltlt
mp) only neutrons and protons are left
In thermal equilibrium
However, this ratio is dependent on weak
interaction equilibrium
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n-p changing reactions
Interaction rate (the generic weak interaction
rate)
After that, neutrons decay freely with a lifetime
of
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However, before complete decay neutrons are bound
in nuclei.
Nucleosynthesis should intuitively start when T
Eb (D) 2.2 MeV via the reaction
However, because of the high entropy it does
not. Instead the nucleosynthesis starting point
can be found from the condition
Since t(TBBN) 50 s ltlt tn only few neutrons have
time to decay
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At this temperature nucleosynthesis proceeds via
the reaction network
The mass gaps at A 5 and 8 lead to small
production of mass numbers 6 and 7, and almost
no production of mass numbers above 8
The gap at A 5 can be spanned by the reactions
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ABUNDANCES HAVE BEEN CALCULATED USING THE
WELL-DOCUMENTED AND PUBLICLY AVAILABLE FORTRAN
CODE NUC.F, WRITTEN BY LAWRENCE KAWANO
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The amounts of various elements produced depend
on the physical conditions during
nucleosynthesis, primarily the values of N(T)
and h
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Helium-4 Essentially all available neutrons are
processed into He-4, giving a mass fraction of
Yp depends on h because TBBN changes with h
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D, He-3 These elements are processed
to produce He-4. For higher h, TBBN is higher
and they are processed more efficiently
Li-7 Non-monotonic dependence because of
two different production processes Much lower
abundance because of mass gap
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Higher mass elements. Extremely low abundances
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Confronting theory with observations
He-4
He-4 is extremely stable and is in general always
produced, not destroyed, in astrophysical
environments
The Solar abundance is Y 0.28, but this is
processed material
The primordial value can in principle be found by
measuring He abundance in unprocessed (low
metallicity) material.
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Extragalactic H-II regions
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I Zw 18 is the lowest metallicity H-II region
known
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Olive, Skillman Steigman
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Izotov Thuan
Most recent values
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Deuterium Deuterium is weakly bound and
therefore can be assumed to be only destroyed
in astrophysical environments
Primordial deuterium can be found either by
measuring solar system or ISM value and doing
complex chemical evolution calculations
OR Measuring D at high redshift
The ISM value of can be regarded as a firm
lower bound on primordial D
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1994 First measurements of D in high-redshift
absorption systems
A very high D/H value was found
Carswell et al. 1994 Songaila et al. 1994
However, other measurements found much lower
values
Burles Tytler 1996
Burles Tytler
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The discrepancy has been resolved in favour of
a low deuterium value of roughly
Burles, Nollett Turner 2001
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Li-7 Lithium can be both produced and
destroyed in astrophysical environments Product
ion is mainly by cosmic ray interactions Destruc
tion is in stellar interiors
Old, hot halo stars seem to be good probes of the
primordial Li abundance because there has been
only limited Li destruction
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Li-abundance in old halo stars in units of
Spite plateau
Molaro et al. 1995
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Li-7 abundances are easy to measure, but the
derivation of primordial abundances is completely
dominated by systematics
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There is consistency between theory and
observations
All observed abundances fit well with a single
value of eta
This value is mainly determined by the High-z
deuterium measurements
The overall best fit is
Burles, Nollett Turner 2001
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This value of h translates into
And from the HST value for h
One finds
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BOUND ON THE RELATIVISTIC ENERGY DENSITY (NUMBER
OF NEUTRINO SPECIES) FROM BBN
The weak decoupling temperature depends on the
expansion rate
And decoupling occurs when
N(T) is can be written as
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Since
The helium production is very sensitive to Nn
Nn 4
Nn 3
Nn 2
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The bound using most recent deuterium
measurements (Abazajian 2002)
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Sterile neutrinos
If there are nA-ns oscillations in the early
universe at T gt Tdec,n then DNngt0
However, DNnlt1 always (corresponding to 1
extra neutrino flavour)
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FLAVOUR DEPENDENCE OF THE BOUNDS
Muon and tau neutrinos influence only the
expansion rate. However, electron neutrinos
directly influence the weak interaction rates,
i.e. they shift the neutron-proton ratio
n-p changing reactions
More electron neutrinos shifts the balance
towards more neutrons, and a higher relativistic
energy density can be accomodated
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Ways of producing more electron neutrinos 1) A
neutrino chemical potential 2) Decay of massive
particle into electron neutrinos
Increasing xne decreases n/p so that Nn can be
much higher than 4
Yahil 76, Langacker 82, KangSteigman 92,
LesgourguesPastor 99, LesgourguesPeloso 00,
Hannestad 00, Orito et al. 00, Esposito et al.
00, LesgourguesLiddle 01, Zentner Walker
01
BBN alone
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Allowed region
xne 0.2
xne 0.1
Allowed for xne 0
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If oscillations are taken into account these
bounds become much tighter
Oscillations between different flavours become
important once the vacuum oscillation term
dominates the matter potential at a temperature of
For nm-nt this occurs at T 10 MeV gtgt TBBN,
leading to complete equilibration before
decoupling.
For ne-nm,t the amount of equilibration depends
completely on the Solar neutrino mixing
parameters.
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SH 02
Dolgov et al., hep-ph/0201287
If all flavours equilibrate before BBN the bound
on the flavour asymmetry becomes much stronger
because a large asymmetry in the muon or tau
sector cannot be masked by a small electron
neutrino asymmetry
Lunardini Smirnov, hep-ph/0012056 (PRD), Dolgov
et al., hep-ph/0201287 Abazajian, Beacom Bell,
astro-ph/0203442, Wong hep-ph/0203180
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For the LMA solution the bound becomes
equivalent to the electron neutrino bound for all
species
Dolgov et al. 02
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Using BBN to probe physics beyond the standard
model Non-standard physics can in general
affect either Expansion rate during BBN
extra relativistic species massive decaying
particles quintessence . The interaction
rates themselves neutrino degeneracy changing
fine structure constant .
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Example A changing fine-structure constant a
Many theories with extra dimensions predict
4D-coupling constants which are functions of the
extra-dimensional space volume.
Webb et al. Report evidence for a change in a at
the Da/a 10-5 level in quasars at z 3
BBN constraint BBN is useful because a
changing a would change all EM interaction rates
and change nuclear abundance
Bergström et al Da/a lt 0.05 at z 1012