Today the visible mass Omega is at least greater than 0.01,
whereas the mass Omega right after annihilation had to be much less than 0.01.
In my opinion the Omega problem is the outstanding difficulty facing cosmologists today, as it takes away from the credibility of a self-consistent Big Bang cosmology. That makes this problem most appropriate for discussion on an astronomical forum as all the evidence for the big bang cosmology comes from astronomy. The Creationists on this forum should pay special attention as the Big Bang cosmology is the alternative science to creationism.
Omega is defined to be the ratio the mass in the universe to the critical mass of the universe. The critical mass is the amount that makes the universe have a flat space-time curvature. If the mass were less than critical during the big bang, the universe would have disappeared from over-expansion by now. If it were greater than critical, the universe would have re-contracted by now. In fact, according to calculations based on the General Theory of Relativity, the universe had to be extremely close to one at the time of the big bang, within one part in ten to the minus 27th power they say, in order for us to be here today.
So it seems that General Relativity is incorrect. GUT particle theory came to the rescue. Gut stands for Grand Unification Theory, a misnomer since it does not unify gravity with the other forces. An MIT professor named Guth, which should stand for Grand Unification Theoretical Hypothesis, developed a solution to the GUT equations called “Inflation” that provides for a sufficiently accurate Omega. He showed that the initial curvature of the universe right after inflation was absolutely flat. So Omega = 1 is the initial condition of the big bang.
Astronomical measurements of very distant supernovae today indicate that the universe is still flat. It’s interesting that flat earth thinking was blamed on religion, and now flat universe thinking can be blamed on science. Omega still equals one. However, the definition of omega has had to be generalized. It turns out that space-time curvature depends on more than just mass. It also depends on energy. Only the Omega for energy produces an acceleration in the expansion of the universe, whereas the mass Omega produces and acceleration in the contraction of the universe. The mass Omega, mainly due to dark matter, is measured to be about 1/3, whereas the dark energy Omega is measured to be about 2/3, and they add to one so the universe in flat. The Omega we get from the mass that we can see, as in starlight, is about 1/50. So it is a small percentage of the total force in the universe.
That’s all background information. The “Omega Problem” is this. Guth’s inflation theory starts in a vacuum- no mass whatsoever. At the end of inflation, a critical density of mass has precipitated out. This mass includes both matter and anti-matter, most likely in the form of quarks and anti-quarks. The problem is that very shortly thereafter, the universe has expanded and cooled sufficiently for the matter and anti-matter to annihilate each almost entirely producing energy in the of light. But there was slightly more matter than anti-matter, so what was left over became us.
I have seen widely divergent estimates of the fraction of matter left over from 1/327 to 1/10,000 and even less. The problem is that this fraction then becomes the Omega for ordinary matter, which might or might not include dark matter. So GUT theory gave us inflation, but it also gives us a mass omega of 0.001 or less. Now the energy produced from annihilation could have maintained an omega of one early in the big bang. But as the universe expands, the total energy drops as the wavelength of light increases so that today it is insignificant. So one Omega problem is “How was an Omega=1 maintained during the expansion of the universe?”
A second Omega problem, that is much closer to measurement, is that today the visible mass Omega is at least greater than 0.01, whereas the matter Omega right after annihilation had to be much less than 0.01.
So you students of physics and astronomy out, please pose this problem to your professors, and report back. And you creationists out there can submit it for publication and make some money.