Cross Posted from Wintery Knight
First, Dr. Craig posted the e-mail from Vilenkin to Krauss, which Krauss used in his debate with Craig, with the parts Krauss omitted in bold:
Any theorem is only as good as its assumptions. The BGV theorem says that if the universe is on average expanding along a given worldline, this worldline cannot be infinite to the past.
A possible loophole is that there might be an epoch of contraction prior to the expansion. Models of this sort have been discussed by Aguirre & Gratton and by Carroll & Chen. They had to assume though that the minimum of entropy was reached at the bounce and offered no mechanism to enforce this condition. It seems to me that it is essentially equivalent to a beginning.
On the other hand, Jaume Garriga and I are now exploring a picture of the multiverse where the BGV theorem may not apply. In bubbles of negative vacuum energy, expansion is followed by cocntraction, and it is usually assumed that this ends in a big crunch singularity. However, it is conceivable (and many people think likely) that singularities will be resolved in the theory of quantum gravity, so the internal collapse of the bubbles will be followed by an expansion. In this scenario, a typical worldline will go through a succession of expanding and contracting regions, and it is not at all clear that the BGV assumption (expansion on average) will be satisfied.
I suspect that the theorem can be extended to this case, maybe with some additional assumptions. But of course there is no such thing as absolute certainty in science, especially in matters like the creation of the universe. Note for example that the BGV theorem uses a classical picture of spacetime. In the regime where gravity becomes essentially quantum, we may not even know the right questions to ask.