Matter/Anti-Matter Asymmetry

In the early Universe, matter is created via pair production and destroyed by annihilation. Since an equal amount of matter and anti-matter is produced in pair production (at least based on simple theories), there could be a problem.

Pair Production -- To make pairs, the temperature must be high so that photons (or whatever) can make virtual particles real ===> since the Universe cools as it expands, at some point a threshold is reached beyond which pairs can no longer be created.
Annihilations -- Annihilations don't require high temperatures. All that is needed is a density that is sufficiently high so that the probability that a matter particle and its anti-matter twin will re-unite is high.
In the early Universe, this allows the annihilation reactions to persist long after pair production halts.

Because of the symmetry of pair production and annihilation, calculations suggest that annihilations would remove all of the matter/anti-matter from the Universe leading to a Universe which is filled entirely with photons. Is this true? Well, obviously not since we are here.

The problem is more than a little vexing because the asymmetry is small.

Number of photons in the Universe. Statement: The energy contained per cubic centimeter in the CMBR (based on blackbody radiation laws) is

U = constant T4, where constant = 7.6 x 10(-15) in c.g.s. units
The average energy of a photon in the CMBR is roughly kT and so, the number of photons per cubic centimeter in the Universe is

N(photons) ~ constant T4 / kT = 1,100 photons per cubic centimeter

Number of matter particles in the Universe (are there anti-matter galaxies?) is roughly

N(m) ~ rho(now)/(m[hydrogen atom]) = 6 x 10(-7) particles per cubic centimeter

The ratio of photons to matter particles is then

N(photons)/N(m) ~ 1,900,000,000 !
This is a huge number. For example, note that

1,000,000,001 electrons + 1,000,000,000 positrons ---> 2,000,000,000 photons + 1 electron
There must have been 1,000,000,000 and 1 electrons for every 1,000,000,000 positrons in the early Universe. If an asymmetry at this level did not exist, then we would not be here.

The small matter/anti-matter asymmetry is another mystery of the Universe which we can either simply accept or try to explain

Let's think about a point that we skirted around before.

Q + anti-Q <----> photon + photon is a statistical process, that is, the probability is that on average both events occur. However, just as when one flips a coin, on average one expects to get equal numbers of heads and tails, there still will be stretches of time when the balance gets thrown off. These stretches always eventually smooth-out, unless the coin isn't balanced. However, we note that these excursions always happen and can't be gotten rid of. A measure of the size of these excursions is known as the standard deviation (or variance). This is what allows the drunken sailor to wander off from the lamppost.

For random processes, if we have N trials (coin flips, reactions, for example), then we will get sqrt[N] out-of-balance events. What does this say about the Universe?

N(protons) ~ (4 pi R(Universe)**3 / 3) rho(Universe) / mass(hydrogen) ---> N(protons) ~ 3 x 10**80
If we interpreted this to mean that we had 3 x 10**80 out of balance reactions then we must have had (3 x 10**80)**2 ~ 9 x 10**160 protons in the early Universe. If this were true, then the Universe would be swamped with photons; the ratio of photons to matter would be
some probability that the sailor will wind up very far from the origin.