(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known dataFor my project for the intel competition, I'm trying to prove that the expansion of the universe defies conservation of energy. In order to do this i want to simulate the universe as a expanding sphere which has a acceleration that constantly increases. Also in the sphere i want there to be a set amount of particles in it initially, but as the sphere expands the amount of particles in it increases as well. Then using noether's theorem i want to show that this expansion defies conservation of energy. My problem right now is that i don't know how to make a single equation that represent the sphere expanding and the amount of particles in it increasing.

2. Relevant equations

X^2+Y^2+Z^2=r*t times cosmological constant

amount of particles=n*t*cosmological constant

n= arbitrary number of initial particles

I still don't know what the modern constant of expansion of the universe is, but I know it's causing a non constant acceleration and I'm sure incorporating it into my equation would be that easy. The problem is I want one equation that describes it all not two separate equations. I know my sphere equation is no where near complete because I'll need to convert it to a Lagrange form so I can compute it in noether's theorem, but I plan on doing that soon.

3. The attempt at a solution

All I can think of is setting them up at two equations but then I don't think I'll be able to use noether's theorem to show any conservation laws. Can anyone help me please

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# Homework Help: Help in a equation I'm going to use for the intel competition

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