A curved universe doesn't "have an edge," I'm referring to Euclidean and non-Euclidean geometry [1]. As in, if the curvature is truly and perfectly zero, then the space-time we live in goes on forever. If it has even the tiniest curvature, then it curves back onto itself and is non-Euclidean.
If it is truly and perfectly zero, then all I'm trying to say is that it goes on forever like an "ideal" 2D plane or 3D space.