[The mirror universe idea is suddenly popular. I notice that others had it before me. Maybe I saw something about it and I later thought I'd invented it?? I don't remember doing so.]
There is matter and antimatter, but luckily for us there is more matter, otherwise the matter and antimatter would annihilate each other leaving nothing but photons. Why is there more matter? I have an answer! Since I'm not an expert in the field, and haven't done due diligence on it, it is, by definition, a crackpot theory. But I like it.
The great Richard Feynman said that antimatter behaves, for computational purposes like ordinary matter travelling backwards in time. Let's take that literally.
Our Universe is expanding from the big bang in accordance with Einstein's equations. Another solution of those equations would be a universe contracting to a reverse big crunch. It doesn't take too much imagination to imagine that immediately before the big bang another universe was coming in to a big crunch. You can regard that as being an earlier part of our Universe, but I want to imagine it as separate. I'll call it the negative universe since it is in negative time if the big bang is at zero.
Particles don't have well defined positions in our quantum universe, which lets them tunnel through apparently insurmountable barriers. So it is possible for some particles moving forward in time from the negative universe to tunnel through to our Universe. And similarly some of our particles moving backward in time (i.e. antimatter) can tunnel through to the negative universe.
So naturally we end up with an excess of matter, and the negative universe ends up with an excess of antimatter. I suggest that in the negative universe, the arrow of time defined by increasing entropy would point backwards. So folk living there would perceive that antimatter as moving forward in time, and perceive the universe as expanding.
It's such a beautiful symmetric picture, it just has to be.
It makes a prediction. In the very early universe particles don't survive long before being annihilated by antiparticles. In the current model where matter is assumed to be slightly different from antimatter, the preponderance of matter happens later. In my model it would appear earlier, so that there is net matter even when the energy level is very high and particles don't last long.