June 15th, 2012

## A Third 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.*

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.

May 4th, 2012

## Antigravity and an Ekpyrotic Universe

I found an interesting paper on the big crunch that may help. It focuses on a non-singular model. In essence, after the big crunch the universe is still something, it doesn’t go out of existence. They’re, of course, setting up an ekpyrotic model. They have an isotropic and anisotropic model. The isotropic has a universe out of control, seemingly, and the anisotropic is very uniform in behavior. I thought it would have been the other way around. What seems to occur after the crunch is that the antigravity, cosmological constant, inverts the universe, ever so briefly, prior to re-expansion. Just like the energy of a rubber band increases when stretched out with the tendency to snap back in on itself so does the antigravity function this way. Why it’s so much shorter when crunched and inverted I don’t know.