One day, I might learn enough physics that my questions don’t sound like nonsense to physics graduates. Today is not that day — my working assumption is I sound like a freshman at best, and a homeopath at worst, and will remain so until I put numerical simulations of standard results in general relativity, quantum mechanics, and Navier-Stokes equations onto my GitHub page.
The baryon asymmetry problem is that matter and antimatter are always created and destroyed in equal quantity, yet the universe clearly has more of one than the other.
If you can make or destroy one without the other, in isolation, then you also get to violate charge conservation, which would mean that quantum field theory is wrong because something something Noether’s theorem. (Of course quantum field theory might be wrong; it’s known that general relativity and quantum physics can’t both be true because if they were both true the universe would’ve collapsed instantly at the very beginning).
The only way you can conserve charge but take antiparticles out of the system is if the process requires an equal number of antiprotons and positrons.
Both of these options — either violate charge conservation or take out multiple particles at once — have interesting consequences which can probably be tested, although not by me, given my degree is in a totally unrelated field.
If charge conservation is violated, then the universe should have a net electric charge. This charge should change over time, as there are still natural processes creating positron-electron pairs but not (at least to the same degree) proton-antiproton pairs. I don’t understand what this would do to the Einstein field equations (only that it would do something; given the effect on black holes I have to ask if it could be dark energy?), but I’m fairly sure lots of free electrons in the interstellar or intergalactic medium should be noticeable.
On the other hand, if antiprotons combine with positrons and that composite — possibly but not necessarily, given how conjectural this already is, an antineutron — either that composite is stable or it has a way of decaying into something other than an antiproton and a positron. The obvious question this raises is: could this be dark matter?
The obvious counter-point to the question “what if antineutrons are stable” is “surely someone would have noticed”, which is a fair question that I cannot answer — I genuinely do not know if anyone would have noticed yet, given how hard it is to make antimatter, how hard it is to trap antimatter, how hard it is to trap even normal neutrons, and the free-neutron half-life.
I can say other people have thought about neutron-antineutron oscillations, which might well solve the baryon asymmetry problem all by itself without any consequences for dark energy/dark matter: https://arxiv.org/abs/0902.0834
(Another thing I definitely don’t know, and which my physics MOOC won’t teach me, is how to separate legit ArXiv papers from the bogus ones; that reflects badly on me, not on the authors of that paper).