Cosmology 566: Class 10 Nucleosynthesis: Constraints on Fundamental Physics

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Cosmology 566 Class 10Nucleosynthesis
Constraints on Fundamental Physics
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outline

• Review
• Light element abundance predictions
• Comparison with observations
• Constraint on WB
• Constraints on relativistic degrees of freedom
• Constraints on rate of change of fundamental
  constants
• Constraints on out of equilibrium decays

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Review
At T109-1010K nuclear reactions convert p,n to
4He via intermediate reactions that produce D and
3He. Reaction rates depend upon ?p and ?n
and thus ultimately on ?B. Production of 4He
cannot begin until sufficient D is produced so
that further reactions processing D to He can
take place.
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The details
Recall, once again
Evolution of species
But, once
Decoupling! Dist. Fn. Not TE value
massless
i.e. Not
massive
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The details
Slightly different for evolution of n, p
Weak interactions
As long as these reactions are in equilibrium ie
nsv gt H
Chemical equilibrium tells us that mn mn mp
me
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The details
Setting, in non-exponential terms, mnmp
Using fact that mn, m/Tn/T. Lepton number
conservation implies that the second term is
zero (note this must be verified) in any case,
charge neutrality implies me/T mp/T ltlt1.
Hence
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The details
More generally for nuclear reactions between
n,p, building A
In equilibrium
In chemical equilibrium
Thus
(prove)
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The details
Define Mass Fraction XAnAA/nN
Then
where
NOTE that we live in a hot universe (ie hltlt1)
is of vital importance, as it implies XAltlt1 when
T is large
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Weak Decoupling
Since
Boltzmann Eq is not quadratic in densities
Rather
where l are the weak rates for the reactions
above..
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Weak Decoupling
Calculate rates
All can be given in terms of 1st decay process
Fermis Golden Rule
Thus, in empty space
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Weak Decoupling
However, at finite T, one must take into acct
Fermi stats
Final States supppressed by factor equal to
fraction of states not filled
So that rate is given by
Similar relations exist for all other processes,
where, if scattering is occurring, Fermi factors
included for initial states
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Weak Decoupling
In this way, one can show (where Q(mn-mp)/me)
and integral is over all q, except for region
-Q-1,-Q1)
and
Note that for TgtgtQme l(n-gtp) l(p-gtn), since
TnT, so that
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Weak Decoupling
This should be compared to the age of the
Universe
Thus, for Tgt O(1 MeV), n/pequil.
valueexp(-Q/T), so
at T2 MeV
Let us estimate FREEZE-OUT ie. when l
Ht-1/2.21g1/2(T/Mev)2 sec-1
actual value 0.15
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Helium Abundance Estimate
1. When does helium form? The infamous D
bottleneck
Recall
So that
Because h 10-8, XA ltlt1 (for Agt1) until
TD.07 MeV T3He.11 MeV T4He.28 MeV
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Helium Abundance Estimate
1. When does helium form? The infamous D
bottleneck
Deuterium reaction rate
So that at T 1 Mev
This is TOO SMALL to allow subsequent dd
reactions to build 4He
until
TD.07 MeV
Recall that
tD100 sec!
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Helium Abundance Estimate
At this time XD1. Thus, following this, all
neutrons are quickly converted to 4He, since
!!!!
T4He.28 MeV
At this point
Eftsoons
!!!!
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Abundance as a function of h
In equilibrium XAhA-1
Hence XD increases earlier as h increases
4He forms earlier, when n/p is larger!
Thus, X4 is a monotonically increasing fn of h.
Since 4He forms earlier, it forms more
efficiently, and Less D and 3He are left frozen
out. Thus their abundance is a decreasing
(sensitively) function of h.
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Lithium Abundance
For h lt 3 x 10-10 Li is destroyed more
efficiently by reaction 7Li(p,a)4He as h
increases
For h gt 3 x 10-10 Li is formed more efficiently
by reaction 3He(a,g)8Be as h increases
Li has a minimum in its predicted abundance!
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Uncertainties (lmk pr,apj358,470)
For more recent values, see Copi, Davis, Krauss
etc..
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Traditionally Inferred upper limit on primordial
4He put strict upper limit on ?B .

• Problems
• Neutral helium not directly observed!
• No theory
• Weak dependence on ?B

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Direct Detection of Primordial Deuterium Abundance

• Advantages
• Deuterium destroyed in Stars, etc
• Sensitive dependence on ?B

Method Observe absorption of distant quasar
light by intervening Hydrogen clouds at high
redshift. Look for absorption at frequency (ie
equiv. Doppler) shift of 80 km/sec
Caveats multiple clouds, with different
relative velocities?
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Result
fD3.3.08 x 10-5
?Bh20.02.002
Significant Baryonic Dark Matter.
Is there enough?
NO!!!
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3He in the Milky Way (Bania et al 2002)
3He/H(1.10.2) x 10-5
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BBN Constraints A new philosophy!
CMB and BBN
(Thomson Scattering couples photons to electrons
and protons at last scattering surface results
in larger peak for larger WB
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BBN Constraints A new philosophy!
CMB Data
?Bh20.021
Great agreement With Deuterium!
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BBN Constraints A new philosophy!

• Hence instead of using BBN predictions in
  comparison to inferred light element abundances,
  USE measured agreement of ?Bh2 from CMB with
  inferred ?Bh2 from BBN to constrain particle
  physics changes that might destroy agreement!

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Constraints on Particle Physics
1. t1/2 (neutron) weak rates proportional to
this! Shorter half-life means stronger
interactions, hence freeze-out later, hence less
4He.
2. Number of relativistic species (ie
Nn) Recall
Hence
Thus, TF depends on g1/6. The higher g the
more 4He!
Note also expansion faster implies tD smaller
implies More 4He (but effect small cause
TDt1/2)
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Before
Nneff lt 4
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After Steigman 2003
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After Cyburt et al 2003
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After Cyburt et al 2003
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Primordial magnetic fields
rB B2/8p
assumeB T2
Kernan et al PRD 1996 rB lt 0.27 rn
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Changing Fundamental Constants
1. Fine structure constant, GF weak interaction
rates
2. Changing G
H G1/2
Hence, changing G, changes expansion rate
affects all abundances
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Changing Fundamental Constants
Before Accetta, Krauss
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Changing Fundamental Constants
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Changing Fundamental Constants
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After Copi, Davis, Krauss 2003
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Changing Fundamental Constants
Changing Alpha (Davis et al, to appear)
Changing nuclear, and weak rates!
Two effects S(E), and exponential factor..
Compete!
(Prelim)
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Unstable Particles

• h determined from BBN agrees to within O(2-5)
  with
• value determined from observation. Thus, this
  cannot
• change more than this amount since BBN

Limits on Entropy Production

• Energetic particles produced after D production
  ceases,
• will photo-dissociate D producing disagreement

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Unstable Particles
1. Gravitinos Td gt 2 MeV
Mg gt 5.5 x 104 GeV
2. Unstable neutrinos
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Unstable Particles
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Ellis et al 2002 SUSY, etc