COSMOLOGY: 2001 2' Dark Matter and Dark Stuff

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COSMOLOGY 20012. Dark Matter and Dark Stuff

• Lawrence M. Krauss
• Scottish Universities Summer School
• Aug 21, 2001

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Isothermal Spheres A Cultural Aside
Assume v isotropic, independent of radius, ie
ltv2gt T
Collisionless No interactions
Hydrostatic Equilibrium
Solve as r-gtinfinity
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How Much Dark Matter is out there?
(1) How much can be Baryonic? Big Bang
Nucleosynthesis
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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t(T) Dependent on N?
Thus f(4He) ????B f(D) ???1/?B f(4He)
???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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Weighing Clusters of Galaxies
X-Ray Clusters Top of the Cosmic Food Chain
Large Clusters of Galaxies, containing 100s of
galaxies. -The largest bound clumps in the
Universe. Tens of millions of light years across.
- anything that can fall into them, will -good
probes of total matter density?
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Largest clusters galaxies a small contamination,
most of the mass of these systems is in HOT GAS!
T107K
X-Rays!
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Assume in Hydrostatic Equilibrium (uniform,
spherical)
Pressure lt-gtGrav
(T,R) -gt (Mgas,Mtot)
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(SZE indep estimate of Mgas
)
If Mgas MB (a reasonable assumption) then
DARK MATTER IS NON-BARYONIC!
Note ?m lt 1 !!!!!!!!!!!
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Gravitational Lensing
Invert!
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Mtot comparable with X-Ray data
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Large Scale Structure Formation A Primer

• Primordial Fluctuations

Scale independent
Scale invariant n1 (isotropy and BHs)
But observed fluctuations Gravity Plus equation
of state
Large k -gt small wavelength
rad
Comes inside causal horizon sooner i.e. during
radiation domination..
matter
?
aeq
Damped
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keq
k
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.25lt?mhlt.35
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Late time Evolution of Large Scale Structure
In a flat, matter dominated universe, ?? a(t)
for all scales inside the horizon.
Hence, large scale structure does not stop
forming.
Hence there should be many more large scale
galaxy clusters today than there were at higher
redshift
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?mlt. 5 ?
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Results

• Dark Matter dominates all large scale structure
• It is probably non-baryonic
• THERE IS NOT ENOUGH DARK MATTER TO MAKE THE
  UNIVERSE FLAT

QUESTIONS?

• What IS the Dark Matter?
• What about a flat universe?

Stay tuned
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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
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
!!!
Massive
Before D
After D
Our existence! Neutrons..
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Weak interactions ?W E2T2
Hence, for T -gt inf. lt ?W vgt gtgt H and n? n?
W.I. decouple at T 2 MeV (recall neutrons)
gtgt m?
Hence, following that, n? n? (up to factor of
4/11 -e ann.)
Now, if neutrinos have small mass
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2. Topological Defects
i.e. Magnetic Monopoles Recall, when any
semi-simple group breaks to a subgroup (i.e.
SU(5) ) containing an explicit U(1) factor -gt
magnetic monopoles with charge g1/e. Dirac
explain quantization of charge!
Existence of an HORIZON! ct
Symmetry breaking phase transition, say order
parameter a scalar field ??that gets a VEV..
If vacuum manifold non-trivial field can get
different VEVs in different causally disconnected
regions
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1 Defect/horizon volume?
Overclose the Universe if mdefect is too big, or
horizon volume too smalli.e. T too large
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Dark Matter Achievers WIMPS
Prototype VERY HEAVY NEUTRINOS (Mgtgt 2 MeV)
??vgt GFM2constant (TltM)
Distribution function goes like exp(-M/T) for TltM
until decoupling, at which point annihilations
stop and distribution remains fixed at exp(-M/TD)
For above cross section TD M/20
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Hence
Massive Weakly Interacting Particle a Natural
Candidate for Dark Matter!
Unfortunately, Massive Neutrinos (lt1/2 Mz are
Ruled out by LEP!
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SUSY to the RESCUE!
SUSY Solve hierarchy problem Contribution to
the Higgs Mass from loops.. Cancel all bosonic
loops with fermionic loops!. Add new particle
spectrum. Since cancellation must not produce M
gt O(MW), new particles cannot have masses much
larger than O(MW). Also, Lightest SUSY particle
is stable in most models (R-parity). This
implies 2 SUSY particles at ever vertex..
Consider annihilation of neutral SUSY particles
e
e-
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Since intermediate particles all have masses
O(MW), cross sections are all of order weak
interaction!
LSP (Neutralino) a NATURAL WIMP!!!!
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Reluctant Dark Matter Axions
A truly beautiful solution of the STRONG CP
problem
Recall QCD
Instantons..
? term is CP violating. EDM of neutron -gt
??lt10-10
Solution (PQ) Add an extra U(1)axial
spontaneously broken symmetry to the theory. The
goldstone boson of this symmetry (called an
axion) gets a mass, since symmetry is anomalous.
Miraculously, one finds a potential for axions of
the form V(a/F) -cos???which is minimized when
?0!
(Since a is PGB, it can be represented by angular
variable a/F)
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In the early universe, Tgtgtma V(a) ltlt T, so
axion can have a VEV
V(a/F)
ma2
Curvature ma2
Axion field starts to relax when t ma-1
Until then ?aconstant, while ?other stuffRn
Hence as ma -gt 0, ?a/ ?other stuff goes to
infinity.
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Dark Matter Detection
(1) Monopoles Mass gt O(1016 GeV). They move
slowly in galaxy. Flux is very small. But cross
section is electromagnetic. Look for in magnetic
detectors or in large detectors sensitive to
slowly moving ionizing particles..
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Predicted signal in superconducting loop of
material when monopole traverses
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Cabrera Valentines Day event
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WIMPS
Flux 106 (M/GeV) /cm2sec
v10-3c
Cross section for scattering on matter is much
larger than light neutrinos ie O( GFM2)
Max energy Deposit mv2keV
How to detect small energy deposits rarely in
large targets?
Bolometry ie Cv(T/TD)3 .silicon, etc
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An Axion Radio
Detect Gravity
Coherence!
Detect Axions
E
X
B
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Why isnt the Universe flat?
1929-1999
Expansion Rate Density Curvature
?
R
8
G
2
p
r ( ?)

2
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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THE UNIVERSE IS FLAT!!!!
BUT!!!!!
1995-2000 THERE IS NOT ENOUGH MATTER IN THE
UNIVERSE TO MAKE IT FLAT!
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WHAT GIVES??????