The Background Radiation in Homogeneous Isotropic World-Models, I

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Abstract
The problem of background radiation in homogeneous isotropic world-models is considered in more detail and greater generality than has been attempted previously. The present paper is based on the assumptions that the galaxies can be represented as point-sources and that intergalactic space is effectively transparent. (These assumptions will be relaxed in a subsequent paper.) General formulae and theorems are derived for the background spectrum and bolometric radiation for various classes of world-model, including models for which the number-density of sources is constant in co-moving coordinates, the steady-state model with continual creation, and static world-models in which the frequency of a travelling photon decays with time. Numerical calculations for specific world-models have also been made on the further assumption that, on the average, the sources radiate steadily as approximately black-body radiators.

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