Is there any cosmological evidence that neutrinos travel at a speed other than c? I've been looking into neutrinos. One thing I'm puzzled about is how fast they travel. 

See the Wikipedia SN1987A article where you can read this: “approximately two to three hours before the visible light from SN1987A reached Earth, a burst of neutrinos was observed at three separate neutrino observatories”. Some reports describe an initial burst of neutrinos which arrived 7.7 hours before the light. It's thought that the neutrinos were emitted before the light because of the way stars collapse, wherein photons take longer to get out. I don't have much of an issue with that. But what's interesting is that in 168,000 years travelling through space, the photons didn’t overtake the neutrinos. That suggests to me that neutrinos are massless, which ties in with what Fermi said in section VII of his 1934 paper. He plotted three curves and noted that the μ=0 curve matched the empirical curves. He concluded that “the rest mass of the neutrino is either zero, or, in any case, very small in comparison to the mass of the electron”.

The thing is that if neutrinos travel at exactly c they have no mass at all. And I can't find any evidence that they don't. I can find plenty of evidence for electrons travelling at speeds less than c. The neutrino is said to be a fermion like an electron. But I can't find any evidence of neutrinos travelling at speeds less than c. 

Can anybody give me a reference to any cosmological evidence that neutrinos travel at less than c? Or any other hard scientific evidence? By evidence I don't mean an inference such as "neutrinos go missing so they must oscillate therefore they must have mass therefore they must travel at less than c". I mean evidence.
A paper by Wie et al. (2016) uses the coincidence between gamma rays from Gamma ray bursts and individual 3-30 TeV neutrinos to estimate the difference in propagation speed between neutrinos and photons.

They find
$$ \frac{|v-c|}{c} &lt; 2.5 \times 10^{-18} $$  

They say this is about 7 orders of magnitude more precise than any previously published limit. However, it does rely on the genuine coincidencce between the GRBs and these individual neutrino events, which does seem to be in question or even doubtful in some cases.

The mass limit this places on the neutrinos appears to be a rather uninteresting $&lt;6.8$ keV, but it is a direct measurement of speed rather than an extrapolation of the speed from a mass limit and special relativity.