## The Exceptions to the BVG Theorem

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

1. First Exception: Initial Contraction (Havg<0) … (The average rate of the Hubble expansion is less than zero)

• Main Problem: Another problem this raises is that this requires acausal fine-tuning.  Any attempt to explain the fine-tuning apart from a fine-tuner is left bereft of any explanation.

2. Second Exception: Asymptotically static (Havg=O)

• Main Problem: The exception is that it does not allow for an expanding or evolutionary universe.  This model cannot be true.  The best evidence and empirical observations indicate that the universe is not static; rather, it is expanding and evolving.  This might have been a great model under Newton but not since Einstein’s field equation concerning the energy-momentum of the universe.

3. Third Exception: Infinite cyclicity (Havg=0)

• Main Problem: The universe splits into non-interacting patches.  The universe has expanded so much at this point that nearly all of these patches are empty of matter and radiation and only contain phantom energy.

4. Fourth Exception: Time reversal at singularity

• Main Problem:  Rejects an evolutionary universe

Also, be sure to read Alexander Vilenkin and Audrey Mithani’s paper, “Did the Universe Have a Beginning?”

Here’s their abstract:

We discuss three candidate scenarios which seem to allow the possibility that the universe could have existed forever with no initial singularity: eternal infation, cyclic evolution, and the emergent universe. The first two of these scenarios are geodesically incomplete to the past, and thus cannot describe a universe without a beginning. The third, although it is stable with respect to classical perturbations, can collapse quantum mechanically, and therefore cannot have an eternal past.

*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.

### 4 Comments to “The Exceptions to the BVG Theorem”

1. Vilenkin writes:

“Whatever it’s worth, my view is that the BGV theorem does not say anything about the existence of God one way or the other. In particular, the beginning of the universe could be a natural event, described by quantum cosmology.”

What is your take on this comment?

• Hi Les,

Concerning the first sentence: The BGV (BVG was incorrect on my part) is a scientific theorem and makes no metaphysical claims as to what the cause or identity of the cause is. So, a cumulative case would be needed to get to God. So, I agree with this first sentence.

Concerning the second sentence: A scientific theorem could describe whatever that initial event was (i.e. describing the event post-initial cause described by quantum cosmology) but I don’t think a natural event could be the absolute beginning predicted by BGV. It seems that Vilenkin would opt for a self-caused universe, judging from the two possibilia listed, but I don’t think that’s a viable option.

• Max, this statement by Vilenkin is not very logical by my hobbyist understanding of philosophy 🙂

“In particular, the beginning of the universe could be a natural event, described by quantum cosmology.”

If the beginning of of the universe were be a natural event, then he would be obliged to explain the cause of that natural event… I think he is trapped in an infinite loop or he believes that some natural events need no explanation. What do you think?

2. If entropy resets at each bounce then an infinite cyclic model cannot be not ruled out by default.