Well, I don't know of a way to completely rule out the concept of some sort of boundary, especially if we are rather vague as to what we mean by the boundary. It is certainly true that we don't observe any boundary. And it is also true that it isn't something that we can describe in our equations just yet (so far as I am aware). But just because we can't describe it mathematically just yet doesn't necessarily
mean it can't exist. How likely it is, then, just depends upon what you think, "have a hard time describing it in the mathematics," means.
Finally, as to Cosmo Novice's statement about homogeneity and isotropy, the fact of the matter is that these assumptions are known to be not completely accurate. They are approximations
to the true behavior, and we know that these assumptions break down on small scales. It is entirely conceivable that they also break down on scales much larger than the cosmological horizon.