@quirk @ZachWeinersmith No, light speed has nothing to do with space curvature.
Yes, a gradual expansion would *eventually* give you curvature so small it's indistinguishable from flat. But you need the expansion to be rapid for it to have flattened early enough in the history of the universe.
It would still not be absolutely flat, it could be open or closed, but on such a huge scale (vastly larger than the observable universe) you couldn't tell it isn't flat.
@doctroid @ZachWeinersmith then why does light have a measurable speed from our perspective?