A Third 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.*

For a greater context please see the first exception to the BVG theorem, which is Initial Contraction (Havg<0).

The third exception: Infinite Cyclicity (Havg=0)

Example: Baum-Frampton “phantom bounce”

These models suggest that the universe goes through a cycle in which it grows from zero (or non-zero) size to a maximum and then contracts back to its starting condition.  The average expansion rate would be a pure zero.

Cyclic models face a thermodynamic problem: “A truly cyclic universe has a problem with entropy increase: it should have reached thermodynamic equilibrium by now. (Alexander Vilenkin personal commentary to William Lane Craig, Jan. 19, 2007).  Our observation of the present universe indicates that we are not at a condition of thermodynamic equilibrium, which is good because life requires non-equilibrium to exist.  As one looks into the past, the size of each cycle is also thought to decrease (due to radiation effect on entropy).  Eventually the cycles are so small that one ends up with a different physics—which would preclude the cycling and imply a beginning of the universe.

Baum-Frampton bounce:  They assume that a type of dark energy pervades the universe where its equation of state (the ratio between pressure and energy density) is less than -1.  This type of expansion is thought to lead to an event called the Big Rip.  Dark energy (phantom energy in this context) causes the acceleration in the expansion of the universe to become so great that our visible horizon shrinks over time.  Eventually, this causal horizon shrinks so much that cosmological objects of smaller and smaller size become causally unbound.  Galaxies, planets, even atoms get ripped apart as the expansion rate of the universe tends towards infinity.

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.


*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.

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