Relativistically speaking, I think you forgot to factor in the speed of light. Now, I'm a Renaissance man, I focus on learning a little bit of everything rather then a lot in any specific subject, so I am in no way an expert.

The reason that part is VITAL is because the larger something grows the more energy it takes to grow at a fixed rate, and since ε is a constant (which means once we find the unit of energy ε will become a number and not a variable) ε will not grow with the universe (which will now be referred to as Σ), ε is dispersed throughout Σ. This is because there is more or less the same amount of energy at the edges of our universe, and the larger the edges get, the thinner the energy gets and thus δ (the rate of expansion) decreases (which is exactly where ε-(Σ/ε) comes into importance.) Now we have the equation Σ=β^(ε-(Σ/ε)).
This post right here, now it was my understanding that it only takes more energy to expand at a constant rate the more expanded you get relative to the speed of light, but in this case we are speaking purely relative of one part of the universe to another. In which case, remembering gravity, the energy needed to expand at a constant rate actually decreases the further apart it gets. Which is why the rate of slowing is itself slowing down.