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 @b4c50e1b how is it we know the universe is matter dominated, rather than having an equal amount of antimatter? Would we know if a star or galaxy we see is antimatter? Or if beyond our visible limit there is lots of antimatter? 
 @e64f5e94 - if our galaxy had significant amounts of antimatter in it, we would know that, because occasionally this antimatter would bump into matter and annihilate, releasing gamma rays with specific energies.  Physicists have spent a lot of time looking for these gamma rays, and other such evidence, and they haven't found it, so we feel very sure that our galaxy has almost no antimatter in it.  Similar studies have ruled out the possibility that clusters of galaxies or even superclusters contain significant amounts of both matter and antimatter.    So if the Universe contains more than a tiny bit of antimatter, we would need entire superclusters made of antimatter, besides those made of matter.  And it's very hard to come up with a workable theory where, starting from the dense hot gas in the early universe, we wind up with some large regions made of matter and others made of antimatter.

What we actually believe happened is very interesting: originally there was a lot of matter and antimatter all mixed up, but almost all of it annihilated, and there was a tiny excess of matter left.  The theories for how we got this tiny excess of matter are connected to the CP violation I discussed, which makes matter slightly different from antimatter.   For more:

https://en.wikipedia.org/wiki/Baryogenesis 
 @b4c50e1b thanks! I have to wonder where all the radiation (or energy from annihilation) went too - would this spontaneously turn back in to quarks of either type? 
 @e64f5e94 - Until about 47,000 years after the Big Bang, most of the energy was in the form of radiation - that is, particles moving at the speed of light or close to it, namely photons and neutrinos.  This is called the "radiation dominated era".  Eventually this radiation was either absorbed by matter or was set free as the cosmic background radiation we see today (stretched out by the expansion of universe, so mostly microwaves now).  

But the dominance of matter over antimatter must have started much earlier, because the radiation was only energetic enough to turn into quark-antiquark pairs (and be formed by them) for roughly the first 50 microseconds after the Big Bang.   After this, radiation would form (and be formed by) lighter things like electron-positron pairs, etc.