Whoa, that is really weird/interesting. Are you suggesting that space from another, higher dimension is somehow leaking through into our Universe, causing the expansion?
Since I dont have a good understanding of higher dimensions, I dont know if that is even plausible, but its a fascinating idea. (I assume I understood you right). It sort of reminds me of the theory that gravitons are leaking up into higher dimensions. Your theory would also explain the 'rich get richer' and the 'poor get poorer' scenario we have for galaxies. This is where galaxies get more and more unevenly distributed. This can be explained by normal theories, but by your theory it should mean that this effect would happen at an accelerated rate.
Anyway, Im trying to think of a serious fault with the theory, but Im not knowledgeable enough to give you one atm. Nice thinking!