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According to NASA, "the source of this cosmic radio background remains a mystery". It's not primordial stars, it's not any known radio source, and in fact, the problem here is that there is "not enough radio galaxies to account for the signal". In other words, nothing in the known cosmos is capable of producing this deafening sound. University of Maryland at College Park's Dale Fixsen—part of NASA's ARCADE team— says, that to get this kind of signal, "you'd have to pack [radio galaxies] into the universe like sardines. There wouldn't be any space left between one galaxy and the next". So in more scientific terms: They don't have a flying frak about what the hell this may be.
By process of elimination, that leaves some unknown source — possibly the first generation of supermassive black holes or the first stars — from the early universe. The radio spectrum seen by ARCADE “is telling us that we’re actually seeing a signature from a period of time that we know very little about and are very interested in,” says Spergel. A more exotic, less likely possibility, he adds, is radio emission from some new type of elementary particle.