Exponential Growth in Flat Spacetime II

I've been wanting to put this up for a while, since apparently the conclusions of my last post weren't justified; I missed an important case! The bacteria *can* survive if, instead of filling space, they restrict themselves to a spherical shell!

The bacteria are able to sustain their growth while staying under the speed of light and using reasonable amounts of energy. They can even experience an unlimited amount of proper time. The downside to this is that any two bacteria in different locations will eventually lose contact with each other. This may remind you of galaxies drifting out of sight under the influence of dark energy, and that turns out to be a very similar situation.

More details below the fold. PDF forthcoming, since math in HTML is awkward.

( Lots of symbol-shuffling ensues... )