  An exact solution for the expansion of a flat universe with dark energy
evolving according to a simple model is explored. The equation for weak
primordial gravitational waves propagating in this universe is solved and
explored; gravitational waves in a flat cosmology possessing both a "big bang"
singularity and a "big rip" singularity can be described with confluent Heun
functions. We develop approximation methods for confluent Heun equations in
regimes of interest to gravitational wave astronomers and predict the
diminution in gravitational wave amplitude in a universe with both a Big Bang
and a Big Rip.
