## A Fourth Exception to the BVG Theorem

The Borde-Vilenkin-Guth Theorem states that any universe, which has, on average, a rate of expansion greater 1 that system had to have a finite beginning. This would apply in any multiverse scenario as well.  There are four exceptions to the theorem.*

Time reversal at singularity

Example: Aguirre-Gratton

(Regarding BVG): The Intuitive reason why de Sitter inflation cannot be past eternal is that in the full de Sitter space, exponential expansion is preceded by exponential contraction.  Such a contracting phase is not part of standard inflationary models, and does not appear to be consistent with the physics of inflation.  If thermalized regions were able to form all the way to past infinity in the contracting spacetime, the whole universe would have been thermalized before inflationary expansion could begin.  In our analysis we will exclude the possibility of such a contracting phase by considering spacetimes for which the past region obeys an averaged expansion condition, by which we mean that the average expansion rate in the past is greater than zero: Havg > 0. (Borde, Guth, and Vilenkin 2003, p1)

Aguirre and Gratton have proposed models to evade the BVG in which the arrow of time reverses at the t =-infinity hypersurface, so the universe ‘expands’ in both halves and the full de Sitter space.  Thus, the BVG is avoided by a deconstruction of time.  Time then flows in both directions away from the singularity.

This does not seem reasonable.  The Aguirre-Gratton scenario denies the evolutionary continuity of the universe, which is topologically prior to t, and our universe.  The other side of the de Sitter space is not our past.  For the moments of that time are not earlier than t or any of the moments later than t in our universe.  There is no connection or temporal relation whatsoever of our universe to that other reality.  Efforts to deconstruct time thus fundamentally reject the evolutionary paradigm.

Main Problem:  Rejects an evolutionary universe

*This information is primarily from and available in William Lane Craig and James Sinclair’s “The Kalam Cosmological Argument,”
inThe Blackwell Companion to Natural Theology Eds. William Lane Craig and J.P. Moreland (Oxford, UK: Blackwell, 2009), 143-147. Diagram on 146.