My equation to model the expansion of the universe

[Oss Spy]

This equation only models the expansion, I'm not including the theory of contraction, only deccelaration.

Greek characters: (so you have an easier way to remember my equations)

α- The "super atom" (Super Atom is just what I use to describe the singularity.)
β- The point where the universe had volume.
γ- Time
δ- Growth of the universe
ε- Energy present in the universe
Σ- Volume of the universe
σ- Factors slowing the growth of the universe

∞- infinity

The formation of my thoughts
The Super Atom is represented by α. α is a singularity, and so the volume is 0. The density of a singularity is represented by ∞=M/0. (Density=Mass/Volume.) Mass is the amount of matter in any object. Since any singularity has no volume but has a density then it must have a mass which is all of the matter in our universe. From this Super Atom comes our universe. At one point, it expanded into our universe we have today...

Σ=(α+β)^δ

However, since α is a singularity, it is negligable. But what does δ mean? δ is the expansion of the universe. Normally I would leave that as it is, but many factors play into the rate of expansion (will be referred to as δ), so that means δ=ε-σ, where ε is the amount of energy released at the time of the Big Bang and σ are the variables which are slowing the growth. Now the equation becomes Σ=(α+β)^(ε-σ). We all know what comes next. Since σ contains more variables, I can simplify (when I say simplify I mean give it more value) it up even further into σ=Σ/ε, where Σ is the current size of the universe divided by ε, the energy still present in our universe.

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)).

But there is one thing missing from that equation. We have three dimensions of the universe but are missing one, and the most important factor of the equation: time, represented as γ (not Y.)

It took me a few hours of thinking, trial and error, and talking with my friends about where γ comes into play. I was thinking back to my Algebra I course and thought about interest (money gained over time) and realized γ had to be an exponent- and exponent on top of another exponent! We now reach my current equation, Σ=β^(ε-(Σ/ε)^γ). If you were to plug in numbers for the variables you would come up with some...interesting results. I did a few of these in my head (as in I figured out which results make no logical sense, I didn't really do all of that math) and came up with these limits and if/then statements:

γ>0
ε>0
β>1 Planck Length
Σ≤ε^2 (if Σ>ε^2, then Σ will contract)
If δ=1, then Σ has reached maximum value.

γ>0
Since time can't be negative (since the Big Bang), γ must be greater than zero. But by how much? It is unclear what unit must be used to measure time with at this point. A Planck Time is the smallest unit of time. One Planck Time is 1^-43 of a second (1 followed by 43 zeroes.) In one Planck Time after the Big Bang the universe doubled in size and slowly decreased in the rate since then. This is where the problems begin.

ε>0
The energy in the universe can never be less than zero. If there were no energy there would be no universe.

β>1 Planck Length
β MUST be greater than one Planck Length, the smallest division of length. One Planck Length is 10^-35 of a millimeter, or 100,000,000,000,000,000,000,000,000,000,000 of a millimeter. This is THE unit of measure. Nothing can be smaller except zero, and it cannot be divided into less, which really should be represented as β≥2.

Σ≤ε^2
This limit is so that the universe will reach maximum point at some time. If it ever comes to Σ>ε^2, then the universe will begin to contract which is NOT a part of this theory.

δ=1 or (Σ/ε^2)=1
This is where the exponent which increases the volume of the universe equals one. Any number raised to the first power will be that number, which is to say X^1=X. The universe will reach moot point and will not increase any further. However, thanks to γ, this would seem to cause a problem. Another rule to exponents is that the number one raised to ANY exponent will equal one, or 1^X=1.



Holes in the theory
The hole in the theory is γ. We can't give a unit to γ without causing the equation further complications. I need your help to help me figure out what to do with γ. Give me all of your ideas as how to fix this problem. If you see any other holes, let me know where they are and what is wrong (telling me why would also be nice as well.)

Edit: There is a hole that I forgot to mention. It is when matter is converted into energy, thus would accelerate the expansion...but the creation of energy would affect the mass of the universe. I also don't know if the mass can be created through energy. If anyone can answer these questions I would like to have them answered soon.


Current equation and limits (as of 9/29):

Σ=β^(ε-(Σ/ε^2)^γ)
γ>0
ε>0
β≥2 planck length
Σ≤ε (if Σ>ε^2, then Σ will contract)
If δ=1 (also known as ε-(Σ/ε^2)=1), then Σ has reached maximum value.

If you can't contribue to my idea, feel free to tell me what you think of it