Bubbles created from vacuum fluctuation

We show that bubbles of S-2 X S-2 can be created from vacuum fluctuation in the background de Sitter universes of k = 0,1, so the space-time foam-like structure might really be constructed from bubbles of S-2 X S-2 in the ver y early inflating phase of our universe. Still, whether such a foam-like st ructure persisted during the later evolution of the universe is a problem u nsolved at present.