Project Heaven

This is an extra homework that some students of the General Relativity class did to make up for one that did not count earlier in the semester. While writing it, I realized that this universe is in fact, Heaven! You know, we become beings of light, and live forever, etc…

I thought it would be fun to share its final form:

“You work in the design section of the company that manufactures universes. (This is where most of the Gods order the universes that they preside over.) An special order comes in from a God who wants a very particular design. It must be an unchanging universe filled only with light. Derive expressions for the size and temperature of this universe in terms of the cosmological constant [tex]\Lambda[/tex]. Show all your work and your reasoning (using diagrams and equations as needed) that leads to your answers for full credit. (Work in units where [tex]G=c=\hbar=k_B=1[/tex].)”

It was due on Friday afternoon and everything is handed in now, so feel free to talk about it.

Fun.

-cvj

[Update: Answers discussed in a later post here.]