Light if energy density of photons were constant

[toughcanesrock]

Homework Statement

At what rate would stars have to be producing light (how many photons per second per solar mass start) in order for the energy density of photons in the universe be constant? Assume current values of cosmological parameters. Do it for current time.

Homework Equations

e = c^2/(8*pi*G)

The Attempt at a Solution

So I understand that the photon density decreases linearly as time goes on. I am able to calculate the photon energy density for current time and parameters. But now how do I calculate the amount of light that needs to be produced for that number to be constant throughout all of time.

 

[phinds]

I don't know the answer to your question but I'm pretty sure that the accelerating expansion of the universe means that it either already is, or at the very least will definitely become, impossible for the photon density to be constant. At some point, and whether or not it has already been reached or not I don't know, there just isn't any amount of photon production that can keep up with the accelerating expansion.