I think you can start with the GR equations, and explicitly plug in 'only photons' ... it gets a little hairy to also include the Standard Model (of particle physics) in such a way that no matter (or anti-matter) gets created, but as long as the universe remains radiation dominated, I guess you could remove the matter and watch what happens ... (you'd also, probably, have to turn off the weak and strong force; while photon-photon collision cross-sections are small, they are not zero, and so, by the ergodic principle ...)