There's also the possibility of a much larger universe filled with "cells" of matter and antimatter. While there would be annihilation at the boundaries, it would be very tenuous, as the radiation would push both regions apart (in the same way a drop of water survives on a hot pan by floating on a cushion of vapor).
Putting aside this theory (which I believe is bogus): It's absolutely possible that huge cells exist, but the radiation pressure would have to be very high to actually push those regions apart and we'd probably still still see lot of stuff colliding. Even if the boundaries are huge and uniform, the effects should be visible. Apart from the radiation we would also observe boundary galaxies that are stripped of their gas and dust clouds. As you suggested, it might very well happen somewhere out there beyond our horizon, as we really have no idea how big the universe actually is.
There wouldn't be any real interaction between such cells, would there? From the perspective of ourselves, in our observable Universe, perhaps the detail of such other cells can't ever be measured in the same way scales smaller than the Planck distance and time can't be measured. That is, quantum effects occur at the largest scale as well as the smallest.
> There wouldn't be any real interaction between such cells, would there?
That's a difficult question to answer without a simulation. All we know is how the visible portion of the universe is structured. The matter seeding works a bit like a procedural terrain generator (where quantum fluctuations introduce a chaotic and self-similar structure) and then gravity and expansion do their thing, so we end up with a universe that is filled with a uniform web of filaments made up of galaxies. Both simulation and observation agree with this model. The primary interaction mechanism at this scale is gravity.
Now if there are pockets of antimatter in there, they'd either be separated from normal matter early on in the process (leading to huge gaps between the cells) or they would visibly communicate with their nearest neighbors when they annihilate stray matter. I don't know which would be more likely. But either scenario is observable if it happens within our field of view, and so far that doesn't seem to be the case. There might be something like this hidden in the ultra-deep field close to the edge of time, but it currently doesn't look like it.
> if there are pockets of antimatter in there, they'd [...] be separated from normal matter early on in the process (leading to huge gaps between the cells)
Thanks to inflation, I suspect that something like this might indeed be possible. Any cosmologist around who knows enough about ΛCDM to give an educated guess?
http://en.wikipedia.org/wiki/Plasma_cosmology#Alfv.C3.A9n_an...
Not endorsing this theory, just illustrating some possibilities.