The Universe after the Big Bang was presumably finite and bounded, in that after the Dark Ages, a beam of light would in principle keep going around in a spiral of ever increasing circles in curved space-time but never ‘escape’, due to the very high mass density. The Universe (or more correctly space-time) has been expanding at an ever increasing rate due to the influence of its Dark Energy. Also, recent measurement of space-time curvature on an incredibly large Galactic scale have revealed that it is flat. This implies that at some stage a transition has occurred with the Universe suddenly becoming infinite and unbounded.