Well terminology seems to be one problem here.

Universe conventionally means 'everything there is'

But, that doesn't preclude there being many BIG BANGS within that everything.

Every time that man has tried to define the Universe his answer has always come up WAY TOO SMALL.

So I would say that Gulliver is absolutely correct in surmising that many big bangs have ocurred. Whether you call them parts of the one universe or the creation of separate universes is just a question of semantics.