Is 3k Background of Cosmological Origin or It Is a Mixture of Radiations of Small Sources?

It has been recently suggested that a background radiation can be explained as a combination of weak background sources. We provide a mathematical argument in favor of a cosmological origin of the background. Namely, the background radiation is well described by Planck’s law. As for possible sources (stars, etc), for their spectra the black-body formula is a very crude approximation, because the individual differences between the stars with the same temperature T are very big. However, these differences are truly individual, they go in different directions for different stars. So, it makes sense to assume that for the total spectra of many sources, these differences more or less cancel each other, and the resulting total spectrum is close to the sum of the approximate blackbody expressions. We prove that Planck’s spectrum cannot be represented as a sum of black-body spectra. Of course, we can always explain the Planck spectrum as a result of some process that “thermalizes” the initially non-Planck one. But if we exclude this rather ad hoc explanation, then, in the abovedescribed approximation, cosmological interpretation is the only one possible. Since we are dealing with approximations to real spectra, our result is not an ultimate proof of cosmological nature of background radiation, but we believe that it is a strong argument in favor of this hypothesis.