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…
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