An Exception to the BVG Theorem

by Max Andrews

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.*

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

An example of this would be found in de Sitter cosmology. In mathematics and physics, a de Sitter space is similar to Minkoswkian spacetime.  It is maximally symmetric and has constant positive curvature. Assume that a spatially infinite universe contracted down to a singularity and then bounced into our present expansion.  In such a case, the universe cannot be said to be, on average, in a state of cosmic expansion through its history since the expansion phase, even if infinite, is canceled out by the contraction phase.  Though this is permissible under the BVG it is not a viable or popular option.

George Ellis, one of the world’s leading cosmologists, has two objections:

The problems are related: first, initial conditions have to be set in an extremely special way at the state of the collapse phase in order that it is a Robertson-Walker universe collapsing; and these conditions have to be set in an acausal way (in the infinite past).  It is possible, but a great deal of inexplicable fine-tuning to take place: how does the matter in widely separated causally disconnected places at the start of the universe know how to correlate its motions (and densities) so that they will come together correctly in a spatially homogenous way in the future? …. Secondly, if one gets that right, the collapse phase is unstable, with perturbations increasing rapidly, so only a very fine-tuned collapse phase remains close to the Robertson-Walker even if it started off so, and will be able to turn around as a whole (in general many black holes will form locally and collapse to a singularity)… So, yes, it is possible, but who focused the collapse so well that it turns around nicely? (Personal comments to William Lane Craig, Jan. 25, 2006).

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.


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


13 Responses to “An Exception to the BVG Theorem”

  1. Hey Max, I find that your comments on the multiverse, are seconded to none. But I must ask this question.

    Suppose that the contracting model is true, and that the universe or multiverse never had a beginning, even though, a God would be needed to fine-tune the singularity, does that mean God is no longer creator? Because if the contraction models are true that just makes God a designer and not a Creator. That doesn’t seem to match the God of the bible I believe in. Genesis 1:1, In the beginning, God CREATED the heavens and the earth. Can you please correct me if I’ve made a mistake, thank you, Harrison.

    • Thanks for your kind words, Harrison.

      If the universe is past-eternal then I don’t find that inconsistent with God’s creation of the universe/multiverse. This was Thomas Aquinas’ position. He didn’t think a finite-temporally past universe could be demonstrated philosophically or scientifically (at least with the science at the time). Hence, he rejects al Ghazali. His contingency argument allows for an eternal universe. It just requires God to be the first uncaused caused in the hierarchical sense and not a temporal sense. That’s why I use Thomas’ contingency argument instead of Kalam–I find it more persuasive and powerful. You can read more about my contingency argument and the permission of a non-finite temporally past universe.

      • But wait, how can God create a past eternal universe/multiverse, if it’s uncaused, and how can God be the first uncaused thing,. If the universe is uncaused, and has always existed. And if it’s always existed, how is he the creator?

      • But wait, how can God create a past eternal universe/multiverse, if it’s uncaused, and how can God be the first uncaused thing,. If the universe is uncaused, and has always existed. And if it’s always existed, how is he creator?

        • Doesn’t That mean the universe/multiverse doesn’t need him to exist? Or would have existed without him?
          (Sorry I posted the question twice technical difficulty :P).

        • It’s not uncaused. It is contingent and therefore requires a cause for it (non-contingent cause). There’s a difference in temporal causation and hierarchical causation. Think of a train. Boxcar A isn’t temporally prior to or temporally causing B, but it’s still causing A to move.

          • Wow thats a very good way to think of it :). I was just confused, thanks so even Contracting models need a cause and beginning? Can you explain to me how contracting models need a God (Sorry Im just learning about philosophy 🙂 ).

          • Sorry I mean a God to create it. (I already know god is needed for the a-causal fine-tuning.

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