The question of first-cause has troubled philosophers and cosmologists alike. Now that it is apparent that our universe began in a Big Bang explosion, the question of what happened before the Big Bang arises. Inflation seems like a very promising answer, but as Borde and Vilenkin have shown, the inflationary state preceding the Big Bang must have had a beginning also. Ultimately, the difficult question seems to be how to make something out of nothing.
However, the possible existence of closed timelike curves under certain extreme conditions may offer a solution to the problem of what came before the Big Bang, which most cosmologists believe started our universe.
In a paper submitted for publication, Li and Gott explore the question of whether anything in the laws of physics would prevent the universe from creating itself. "The universe wasn't made out of nothing," Gott suggests. "It arose out of something, and that something was itself. To do that, the trick you need is time travel."
Li and Gott speculate that a universe undergoing the rapid early expansion known as inflation could give rise to baby universes, one of which (by means of a closed timelike curve) would turn out to be the original universe.
The two physicists found a self-consistent vacuum state demonstrating that closed time loops can occur under inflationary conditions in certain space-times. Hence, the researchers say, "the laws of physics may allow the universe to be its own mother."
However this doesn't mean we could build a machine to travel back in time. The amount of space-time warping required for such a feat would lead to all sorts of practical problems.
Original paper here: Can the Universe Create Itself?