It's simple - there is no edge to the universe. It is thought that the universe is infinite in size. Data from WMAP seems to support this, because it shows that the universe is very close to "flat" - i.e. the overall curvature is zero. This does support the "infinite universe" models.
That said, there is an edge to our (or any other observer's) observable universe. This consists of all the objects we can see - or, rather, all the objects whose emitted light, gravity, or other effects we can detect. There isn't anything special going on at the edge of our observable universe, either, for those observers there. Nothing special happens for them, although any observer's observable universe is expanding.
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