There
must have been initial asymmetry because the universe as we know it is what remained from that. That means also that there is very few (as in none at all) natural antimatter left in the universe, because if there was some it would by now have collided with matter and produced photons.
What I was trying to say above was, that our universe might as well only have antimatter, since it really only depends on what side you are as an observer. We baptized matter matter because it is what we know. Had there been more of what we call antimatter at the beginning, we would be made of that and we would call that matter. If someone could replace all the matter in the universe with antimatter, we would be unable to detect it, like we were unable to tell whether we are on the "right" or "wrong" side of a mirror's glass pane if we switched places with our reflection.
If the matter-antimatter process is going on between photons and antiphotons it has absolutely no effect on anything. Since photons and antiphotons are exactly the same, the process makes (anti-)photons out of (anti-)photons. The reagents are the same as the product, hence there is no reaction at all.
The matter-antimatter process went on until all antimatter had found their matter and the both annihilated into (anti-)photons. The matter that didn't find any antimatter because none was left, is what the universe is made of. The (anti-)photons the universe is filled with are as old as that.
BTW: Potatoes and Tomatoes are actually related botanically
Anyway, if exotic matter has anti-gravity properties, the electromagnetic force as well as the weak and the strong force must still have some effect on its particles. assuming all (or even one more) of the forces are reversed for exotic matter, it simply can't exist in lumps or structures bigger than single particles, because it can't build nuclei or even atoms.
Let's assume all forces but gravity work the same on exotic matter as they do on "common" matter. It can't be built from the same particles as "common" matter, since those don't have any anti-gravity properties. You need atoms that are made of exotic particles then, particles that can't be predicted by the standard model of particle physics. Anti-gravity requires those particles to have anti-mass. This implies an anti-higgs-field which the universe simply has no room for as it would neutralize the higgs-field, which would make matter behave very different from what it does now. Gravity wouldn't work and hence anti-gravity would be a moot concept.
Exotic matter is an idea similar to opening the fridge door to have a look whether the light is out when the door is closed.