Cosmology 566: Class 6 Flatness and Dark Matter

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Cosmology 566 Class 6Flatness and Dark Matter
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Why isnt the Universe flat?
1929-1999
Expansion Rate Density Curvature
?
R
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G
2
p
r ( ?)

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R
3
2000 A NEW WAY! MEASURE THE GEOMETRY
DIRECTLY!
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Q How could you measure curvature of the Earth
if (a) no recourse to outside space? (b) not
able to go around it?
GEOMETRY
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Last Scattering Surface
dct J 10
t105 yrs T 3000 K
t109 yrs T 10 K
t1010 yrs T 2.735 K
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First Scale to Collapse after Recombination
(sound speeddistance spanned by light ray
horizon size)
OPEN CLOSED FLAT
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COBE FIRST ANISOTROPY!
COBE FIRST ANISOTROPY!
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CMB Power Spectrum
(Prove)
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THE UNIVERSE IS FLAT!!!!
BUT!!!!!
1995-2000 THERE IS NOT ENOUGH MATTER IN THE
UNIVERSE TO MAKE IT FLAT!
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• Questions
• Why is Wm 0.3?
• Why is Wm WX ?
• Why is WNB WB ?

What is the Dark Matter?
See below
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• How much Dark Matter can be Baryonic?
• Big Bang Nucleosynthesis. An Intro..

At T1010K 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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Note t(T) Dependent on N? (later this term)
Thus f(4He) ????B f(D) ???1/?B f(3He)
???1/?B
Hence, observational limits on primordial
elemental abundances put limits on ?B .
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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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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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CMB Data
?Bh20.021
Great agreement With BBN!
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Dark Matter Particle Physics to the Rescue

• Note There is 1 baryon for every 109 photons in
  the Universe
• The Standard Model has natural dark matter
  candidates
• Every extension to the Standard Model has dark
  matter candidates

Candidates NOT invented for cosmological
purposes
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Some Elementary Particles are Either
Neutrinos, Monopoles

• Born Dark!

2. Achieve Dark Matter-dom!
WIMPS
or
3. Have Dark Matter-dom thrust upon them!
Axions
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1. Born Dark, and Proud of it Neutrinos
Review of Equilibrium Thermodynamics for
Relativistic Particles (refs, Pathria, Landau
and Lifshitz, Kolb and Turner.)
Recall (assuming chemical potentials0, g
internal degrees of freedom)
Now for isotropc dist. and relativistic particles
(ie m0)
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1. Born Dark, and Proud of it Neutrinos
Hence
(Prove)
Note (!)
(Prove)
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1. Born Dark, and Proud of it Neutrinos
Note for NON-relativistic particles (mgtgtT)
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1. Born Dark, and Proud of it Neutrinos
Now we can calculate CMB photon density today
Note since nBrc/3mp3.75 x 10-6/cm3,
then ng/nB108 !!!!
Photons dominate by number! But invisible
till 1965!
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1. Born Dark, and Proud of it Neutrinos
Since for MgtgtT, only relativistic particles
contribute to energy density and pressure in
equilibrium, one has, for the total energy of a
gas of particles with species i at temperature Ti
Thus, Einsteins equations yield, for such a
radiation dominated Universe.
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1. Born Dark, and Proud of it Neutrinos
Finally Entropy Density
where
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1. Born Dark, and Proud of it Neutrinos
When are species in Equilibrium?
The Most important equation in cosmology (BBN,
DM,CMB) Boltzmann equation for expanding
Universe
Evolution of species
In T.E. nneq -gt n1/R3
But, once
Decoupling! Dist. Fn. Not TE value
massless
i.e. Not
massive
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Instead
Massless
Before D
After D
!!!
Prove
Massive
Before D
After D
Our existence! Neutrons..