# Quarks, Gluons, and the Big Bang

### Maurice Barnhill

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## Class Notes XIII. Dark Matter

 Last revised 1999/05/05

## Class Notes on Dark Matter

Definition: "Dark matter" is any form of matter that cannot be detected by the light it emits.

### Predictions of Big-Bang Models

1. Meaning of "critical density"
If the cosmological constant vanishes, the fate of the universe is determined by the density of matter it contains. If the density is high enough, the universe is finite and will eventually collapse. If the density is low enough, the universe is infinite and will expand forever. The density where the behavior of the universe changes from one case to the other is called the critical density, denoted OMEGA0.

2. The simple versions of inflation predict that the matter density in the universe is equal to the critical density.

3. Almost any big-bang model predicts that the density of matter made up of baryons is now around 0.05 * OMEGA0 .
The prediction is made by examining how much deuterium (hydrogen with one neutron in its nucleus) and lithium are made by nuclear reactions in the early universe. The amounts are quite sensitive to the baryon density at the time when the temperature permits these reactions to occur. Comparing the amount of each that is observed to be present now to the amount that theory gives for each density tells us what the total baryon density has to be.

### Methods for determining the amount of matter actually present

Amount of matter in the "solar neighborhood"
Can be found by direct observation
Detecting mass by galactic rotation curves
The speed of a star or cloud of luminous gas in its orbit around the galaxy is determined by the total mass closer to the center of the galaxy than the object itself. We can determine the speed by using the Doppler frequency-shift of the light coming from the object and hence determine the amount of mass in the galaxy as a function of the distance from the center of the galaxy.
Detecting mass between the galaxies in a cluster
We also use the speeds of the galaxies to estimate the mass density in the cluster. However, the galaxies are moving in random direction rather than revolving around the center of the cluster, so the determination is less direct and less accurate.
Observational evidence for the total density of matter
The Supernova data described in the section on Expansion of the Universe gives direct evidence for the total matter density in the Universe, using the effect of the density of matter on the curvature of space.

### Mass-density numbers

Estimates from Joe Silk [accessed May 5, 1996], assuming zero cosmological constant. OMEGAbaryon is the big-bang estimate of the density of baryons in the Universe, 0.05 OMEGA0. One value inferred from verious recent supernova data is also included.

Object M/L solar unitsOMEGA/OMEGAbaryonOMEGA/OMEGA0
Sun 1

Solar neighborhoodca. 2 0.02 0.001
Typical galaxy 50 0.7 0.03
Baryon limit 75 1 (definition) 0.05 [0.02 to 0.1]
Supercluster 300 4 0.2
Supernova data 300 4 0.2 - 0.5
Closed universe 150020 1 (definition)

Given these numbers, it appears that both baryonic and nonbaryonic dark matter exists. Most of the Universe, in fact, is composed of unknown types of matter, and very likely most of the mass of the Universe is not baryonic.

### What could the dark matter be?

"Jupiters"
Large planet-like bodies not attached to visible stars. There is little evidence for their existance and little theoretical guidance for their expected numbers, but these objects are not generally expected to make a significant contribution to the overall mass density.
Brown Dwarfs
Gaseous objects large enough to shine using energy obtained by gravitational contraction but not large enough to generate energy by nuclear reactions. In general, the smallest stars are most abundant, so it is possible that there are large numbers of Brown Dwarfs. A few, but not many have been detected, but they are so faint that detection is difficult. These are perhaps the best candidates for large amounts of unseen baryonic matter.
Black Holes
Collections of matter so large in mass and small in volume that light itself cannot escape from the object. Many and perhaps most galaxies are believed to have a large black hole at their centers, but there are not enough known black holes to make much impact on the total amount of matter.
Intergalactic gas
There is known to be a significant amount of intergalactic gas but not enough to match the observed amount of matter.
Neutrinos
No experimental evidence is available for or against the possibility of neutrinos explaining the amount of dark matter. Calculations of the distribution of visible matter in the Universe tend to work well if neutrinos are responsible for the nonbaryonic dark matter in the Universe.
Really exotic particles
Speculative but not completely implausible possibility.

### Conclusion?

We don't know yet.

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