Cosmological Principle

The Cosmological Principle states that when we observe the universe at a very great distance, the distribution is thesame as any other part of the universe. This does not work for small scale things like a classroom or planet, but at a much larger scale it has been observed to be accurate. While it has not been and may never be proved by mathematics it has been clearly observed. 

Fig: cosmic microwave background.

This theory is supported by the fact that the CMB is isotropic, meaning the same in all directions. They then applied this theory to the fact that the laws of physics are universal. The laws we use to explain observations on Earth can be applied all over the universe. Constants like the speed of light are the same across the universe as well. This led scientists to the assumption that everything came from one place and one time. Using all of these assumptions scientists can describe what happened in the earlier universe and model it as well.

I feel that this theory supports the Big Bang Theory because they both state that all matter came from the same place at one time. Without such a key observation of the universe it would have been a lot harder to model past events, if it were even possible at all. It is a marvelous thing to see such uniformity in a place that is so chaotic. Inflation can also be supported by this theory because if everything is the same and came from the same place, then the only way the universe got to be how it is now is if it expanded. The fact that the universe is isotropic and homogenous has led to a great amount of correct assumptions that could not have been made without this first one. 

Sources:

http://abyss.uoregon.edu/~js/cosmo/lectures/lec05.html 

http://csep10.phys.utk.edu/astr162/lect/cosmology/solutions.html