We see that Graham's idea is basically correct, but not strictly about antineutrino annihilation, as follows. Taking one single (electron) antineutrino of mass $0.001169$ eV and turning it into a photon, Wien's law for a black body spectrum (which keeps $hc$ constant) gives us the temperature of $2.732$ K.

On the other hand, the observed CMB temperature of $2.725$ K does not require a great scale change in the Koide triplet. The accuracy of this scale is currently limited by the neutrino experiments. So there is potentially a play off between neutrino mass observations and the precisely observed CMB temperature, assuming that $\overline{m}_{1}$ is a good generator for it. However, it seems more likely that the discrepancy is due to competing effects from other species.

7 years ago

In fact, we could take the $2.725$ K as a predictor for the neutrino mass scale, and it comes out just under the $\mu = 0.01$ in current use (ie. $0.009975$). This agrees better with the measured delta square for the neutrino sector than the value in older posts.

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