Hi Nick

It's a common misconception that open and hyperbolic FRW Universes are finite, but in the usual conception they're not. Only closed Universes are finite in the strictly Friedman-Robertson-Walker equations. Such Universes form a hypersphere, with our 3+1 space being the 3-volume of the hypersphere. Open and "saddle-shaped" Universes don't have the same "finite but unbounded" geometry - they're only unbounded if infinite.

Of course you can have a finite and unbounded and forever expanding universe with a suitable geometry, but you've then gone from the standard Big Bang to something else.

Adam