Bubbles Created from Vacuum Fluctuation

The authors show that the bubbles S² x S² 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 S² x S² in the very early inflating phase of our universe. Still, whether such foam-like structure persisted during the later evolution of the universe is a problem unsolved at present.