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.
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