Imagine a spherical oven with radius R. The inside of the spherical wall is at temperature T (everywhere) and is assumed emit perfect black body radiation (everywhere).
(1) What is the energy density in the interior of the oven?
(2) Is the energy density homogeneous or does it depend on the radius?
I wonder whether the radiation density of the universe can be described in this way, i.e., as result of a "hot" horizon. Of course, in this case there is the additional issue that the horizon ("oven wall") is growing with time.