I don't understand. Are you saying that there's something about the physical universe that is not describable mathematically?
I'd prefer to stick with expansion, so as not to cause conceptual distractions. I haven't taught this subject, so I may be wrong, but at least to me it's easier to focus on the question of whether the expanding universe is expanding "into" something.
But that in itself is a conceptual distraction. Again: the universe is not an object that exists in space, and which needs to take up more space as it grows. The universe is the space itself. It requires no medium in which it can float.
[Geek alert: there are several popular models that postulate the existence of additional physical dimensions, but these don't solve your conceptual problem. In some models these additional dimensions are themselves expanding, and in others, they are radically contracting! These models are denoted "AdS5" models, which means that the 5th dimension is "anti-deSitter". In such models, the universe as we see it is a 4-dimensional slice of a 5-dimensional space. The 5th dimension extends outwards from our slice, but it's constantly contracting back towards the slice. Any particle that makes an excursion into the 5th dimension is inexorably drawn by geometry back to this orbifold plane. So you see that although in such a model, our universe does exist in an external medium, there is no sense in which our universe "expands into" that medium. But expand it nevertheless does.]
No. But I'm saying that although I can accept that a cosmic contraction would mathematically be the same as cosmic expansion, I suspected that if everything really were shrinking we'd encounter difficulties. (Buffoon alert: I'm very deep into your area of expertise here, so I'm treading lightly.) I was specifically thinking of the fact that particles would be getting smaller, atomic nuclei would be smaller, reactions would occur over smaller distances, thus they'd occur faster (the speed of light wouldn't change). With no deep analysis of this, I was gussing (always a risk) that the observable consequences of a shrinking and speeded-up universe would be different than for an expanding universe.