If you interpret the red-shift data to mean velocities of galaxies, then the universe actually has begun accelerating outward after a period of initial gravitational deceleration, so by this interpretation it looks like the answer is that there are no cycles.
But this is an odd way of looking at it especially since quantum mechanics has discovered that space is a sea of energy in the form of planck particle pairs. So if space itself were expanding and the zero point energy were becoming less dense, the light would actually experience a blue shift en route.
But the doppler shift interpretation of red-shift data has run into more and more problems, so other interpretations should be sought.
Proponents of plasma cosmology are a funny group. They complain the big bang theory is bad science. They claim it requires too many ad hoc assumptions even though it has made numerous successful predictions about the universe, making it a good scientific theory. They seek to replace it with a model that a. makes many ad hoc assumptions of it's own and b. has not made successful testible predictions, leaving it as a mere model while the big bang is a theory. It's even hard to get proponents of plasma cosmology to reveal any prediction the model makes at all, bringing us to the question of whether or not the model is even scientific.